H. Okuyama, H. So, S. Hatta, T. Frederiksen, and T. Aruga

**Effect of adsorbates on single-molecule junction conductance**

Surface Science **xxx**, xxx (2018), accepted
[DOI]

Electronic conduction through molecular junctions depends critically on the electronic state at the anchor site,
suggesting that local reactions on the electrodes may play an important role in determining the transport
properties. However, single-molecule junctions have never been studied with the chemical states of the electrodes
controlled down to the atomic scale. Here, we study the effect of surface adsorbates on the molecular junction
conductance by using a scanning tunneling microscope (STM) combined with density functional theory (DFT)
and nonequilibrium Green's function (NEGF) calculations. By vertical control of a STM tip over a phenoxy (PhO)
molecule on Cu(110), we can lift and release the molecule against the tip, and thus reproducibly control a
molecular junction. Using this model system, we investigate how the conductance changes as the molecule is brought
to the vicinity of oxygen atoms or a hydroxyl group chemisorbed on the surface. This proximity effect of surface
adsorbates on the molecular conductance is simulated by DFT-NEGF calculations.

B. de la Torre, M. Svec, G. Foti, O. Krejci, P. Hapala, A. Garcia-Lekue, T. Frederiksen, R. Zboril, A. Arnau, H. Vazquez, and P. Jelinek

**Submolecular resolution by variation of inelastic electron tunneling spectroscopy amplitude and its relation to the AFM/STM signal**

Phys. Rev. Lett. **119**, 166001 (2017)
[DOI]
[ PDF ]
[arXiv:1710.06180].

Here we show scanning tunnelling microscopy (STM), non-contact atomic force microscopy (AFM) and inelastic electron tunnelling spectroscopy (IETS) measurements on organic molecule with a CO-terminated tip at 5K. The high-resolution contrast observed simultaneously in all channels unambiguously demonstrates the common imaging mechanism in STM/AFM/IETS, related to the lateral bending of the CO-functionalized tip. The IETS spectroscopy reveals that the submolecular contrast at 5K consists of both renormalization of vibrational frequency and variation of the amplitude of IETS signal. This finding is also corroborated by first principles simulations. We extend accordingly the probe-particle AFM/STM/IETS model to include these two main ingredients necessary to reproduce the high-resolution IETS contrast. We also employ the first principles simulations to get more insight into different response of frustrated translation and rotational modes of CO-tip during imaging.

E. Minamitani, R. Arafune, T. Frederiksen, T. Suzuki, S. M. F. Shahed, T. Kobayashi, N. Endo, H. Fukidome, S. Watanabe, and T. Komeda

**Atomic-scale characterization of the interfacial phonon in graphene/SiC**

Phys. Rev. B **96**, 155431 (2017)
[DOI]
[ PDF ]

Epitaxial graphene on SiC that provides wafer-scale and high-quality graphene sheets on an insulating substrate is a promising material to realize graphene-based nanodevices. The presence of the insulating substrate changes the physical properties of free-standing graphene through the interfacial phonon, e.g., limiting the mobility. Despite such known impacts on the material properties, a complete and microscopic picture is missing. Here we report on atomically resolved inelastic electron tunneling spectroscopy (IETS) with a scanning tunneling microscope for epitaxial graphene grown on 4H-SiC(0001). Our data reveals a strong spatial dependence in the IETS spectrum which cannot be explained by intrinsic graphene properties. We show that this variation in the IETS spectrum originates from a localized low-energy vibration of the interfacial Si atom with a dangling bond via ab-initio electronic and phononic state calculations. This insight may help advancing graphene device performance through interfacial control.

T. Jasper-Tönnies, A. Garcia-Lekue, T. Frederiksen, S. Ulrich, R. Herges, and R. Berndt

**Conductance of a freestanding conjugated molecular wire** (*Editors' suggestion* )

Phys. Rev. Lett. **119**, 066801 (2017)
[DOI]
[ PDF ]

A freestanding molecular wire is placed vertically on Au(111) using a platform molecule and contacted by a scanning tunneling microscope. Despite the simplicity of the single-molecule junction its conductance G reproducibly varies in a complex manner with the electrode separation. Transport calculations show that G is controlled by a deformation of the molecule, a symmetry mismatch between the tip and molecule orbitals, and the breaking of a C\equivC triple in favor of a Au--C--C bond. This tip-controlled reversible bond formation/rupture alters the electronic spectrum of the junction and the states accessible for transport, resulting in an order of magnitude variation of the conductance.

F. Mazzola, T. Frederiksen, T. Balasubramanian, P. Hofmann, B. Hellsing, and J. W. Wells

**Strong electron-phonon coupling in the σ band in graphene**

Phys. Rev. B **95**, 075430 (2017)
[DOI]
[ PDF ]
[arXiv:1607.00939].

First-principles studies of the electron-phonon coupling in graphene predict a high coupling strength for the σ band with λ values of up to 0.9. Near the top of the σ band, λ is found to be ≈ 0.7. This value is consistent with the recently observed kinks in the σ band dispersion by angle-resolved photoemission. While the photoemission intensity from the σ band is strongly influenced by matrix elements due to sub-lattice interference, these effects differ significantly for data taken in the first and neighboring Brillouin zones. This can be exploited to disentangle the influence of matrix elements and electron-phonon coupling. A rigorous analysis of the experimentally determined complex self-energy using Kramers-Kronig transformations further supports the assignment of the observed kinks to strong electron-phonon coupling and yields a coupling constant of 0.6(1), in excellent agreement with the calculations.

P. Brandimarte, M. Engelund, N. Papior, A. Garcia-Lekue, T. Frederiksen, D. Sánchez-Portal

**A tunable electronic beam splitter realized with crossed graphene nanoribbons**

J. Chem. Phys. **146**, 092318 (2017)
[DOI]
[ PDF ]
[arXiv:1611.03337].

Graphene nanoribbons (GNRs) are promising components in future nanoelectronics due to the large mobility of graphene electrons and their tunable electronic band gap in combination with recent experimental developments of on-surface chemistry strategies for their growth. Here we explore a prototype 4-terminal semiconducting device formed by two crossed armchair GNRs (AGNRs) using state-of-the-art first-principles transport methods. We analyze in detail the roles of intersection angle, stacking order, inter-GNR separation, and finite voltages on the transport characteristics. Interestingly, when the AGNRs intersect at θ=60˚, electrons injected from one terminal can be split into two outgoing waves with a tunable ratio around 50% and with almost negligible back-reflection. The splitted electron wave is found to propagate partly straight across the intersection region in one ribbon and partly in one direction of the other ribbon, i.e., in analogy of an optical beam splitter. Our simulations further identify realistic conditions for which this semiconducting device can act as a mechanically controllable electronic beam splitter with possible applications in carbon-based quantum electronic circuits and electron optics. We rationalize our findings with a simple model that suggests that electronic beam splitters can generally be realized with crossed GNRs.

N. Papior, N. Lorente, T. Frederiksen, A. García, and M. Brandbyge

**Improvements on non-equilibrium and transport Green function techniques: the next-generation TRANSIESTA**

Comput. Phys. Commun. **212**, 8–24 (2017)
[DOI]
[ PDF ]
[arXiv:1607.04464].

We present novel methods implemented within the non-equilibrium Green function code (NEGF) transiesta based on density functional theory (DFT). Our flexible, next-generation DFT-NEGF code handles devices with one or multiple electrodes (*N*≥1) with individual chemical potentials and electronic temperatures. We describe its novel methods for electrostatic gating, contour opti- mizations, and assertion of charge conservation, as well as the newly implemented algorithms for optimized and scalable matrix inversion, performance-critical pivoting, and hybrid parallellization. Additionally, a generic NEGF post-processing code (tbtrans/phtrans) for electron and phonon transport is presented with several novelties such as Hamiltonian interpolations, *N*≥1 electrode capability, bond-currents, generalized interface for user-defned tight-binding transport, transmission projection using eigenstates of a projected Hamiltonian, and fast inversion algorithms for large-scale simulations easily exceeding 10^{6} atoms on workstation computers. The new features of both codes are demonstrated and bench-marked for relevant test systems.

A. Shiotari, H. Okuyama, S. Hatta, T. Aruga, M. Alducin, and T. Frederiksen

**Role of valence states of adsorbates in inelastic electron tunneling spectroscopy: A study of nitric oxide on Cu(110) and Cu(001)**

Phys. Rev. B **94**, 075442 (2016).

We studied nitric oxide (NO) molecules on Cu(110) and Cu(001) surfaces with low-temperature scanning tunneling microscopy (STM) and density functional theory (DFT). NO monomers on the surfaces are characterized by STM images reflecting 2π^{*} resonance states located at the Fermi level. NO is bonded vertically to the twofold short-bridge site on Cu(110) and to the fourfold hollow site on Cu(001). When NO molecules form dimers on the surfaces the valence orbitals are modified due to the covalent bonding. We measured inelastic electron tunneling spectroscopy (IETS) for both NO monomers and dimers on the two surfaces, and detected characteristic structures assigned to frustrated rotation and translation modes by density functional theory simulations. Considering symmetries of valence orbitals and vibrational modes, we explain the intensity of the observed IETS signals in a qualitative manner.

M. Engelund, N. Papior, P. Brandimarte, T. Frederiksen, A. Garcia-Lekue, and D. Sánchez-Portal

**Search for a Metallic Dangling-Bond Wire on H-Passivated Semiconductor Surface**

J. Phys. Chem. C **120**, 20303–20309 (2016)
[arXiv:1609.03842].

We have theoretically investigated the electronic properties of neutral and n-doped dangling bond (DB) quasi-one-dimensional structures (lines) in the Si(001):H and Ge(001):H substrates with the aim of identifying atomic-scale interconnects exhibiting metallic conduction for use in on-surface circuitry. Whether neutral or doped, DB lines are prone to suffer geometrical distortions or have magnetic ground-states that render them semiconducting. However, from our study we have identified one exception – a dimer row fully stripped of hydrogen passivation. Such a DB-dimer line shows an electronic band structure which is remarkably insensitive to the doping level and, thus, it is possible to manipulate the position of the Fermi level, moving it away from the gap. Transport calculations demonstrate that the metallic conduction in the DB-dimer line can survive thermally induced disorder, but is more sensitive to imperfect patterning. In conclusion, the DB-dimer line shows remarkable stability to doping and could serve as a one-dimensional metallic conductor on n-doped samples.

J. N. Ladenthin, T. Frederiksen, M. Persson, J. C. Sharp, S. Gawinkowski, J. Waluk, and T. Kumagai

**Force-induced tautomerization in a single molecule**

Nature Chemistry **8**, 935–940 (2016)

Heat transfer, electrical potential and light energy are common ways to activate chemical reactions. Applied force is another way, but dedicated studies for such a mechanical activation are limited, and this activation is poorly understood at the single-molecule level. Here, we report force-induced tautomerization in a single porphycene molecule on a Cu(110) surface at 5 K, which is studied by scanning probe microscopy and density functional theory calculations. Force spectroscopy quantifies the force needed to trigger tautomerization with submolecular spatial resolution. The calculations show how the reaction pathway and barrier of tautomerization are modified in the presence of a copper tip and reveal the atomistic origin of the process. Moreover, we demonstrate that a chemically inert tip whose apex is terminated by a xenon atom cannot induce the reaction because of a weak interaction with porphycene and a strong relaxation of xenon on the tip as contact to the molecule is formed.

M. Engelund, S. Godlewski, M. Kolmer, R. Zuzak, B. Such, T. Frederiksen, M. Szymonski, and D. Sánchez-Portal

**The Butterfly – A Well-Defined Constant-Current Topography Pattern On Si(001):H and Ge(001):H Resulting From Current-Induced Defect Fluctuations
**

Phys. Chem. Chem. Phys. **18**, 19309 (2016)
[ PDF ]

Dangling bond (DB) arrays on Si(001):H and Ge(001):H surfaces can be patterned with atomic precision and they exhibit complex and rich physics making them interesting from both technological and fundamental perspectives. But their complex behavior often makes scanning tunneling microscopy (STM) images difficult to interpret and simulate. Recently it was shown that low-temperature imaging of unoccupied states of an unpassivated dimer on Ge(001):H results in a symmetric butterfly-like STM pattern, despite that the equilibrium dimer configuration is expected to be a bistable, buckled geometry. Here, based on a thorough characterization of the low-bias switching events, we propose a new imaging model featuring a dynamical two-state rate equation. This model allows us to reproduce the features of the observed symmetric empty-state images which strongly corroborates the idea that the patterns arise due to fast switching events and provides insight into the relation between the tunneling current and switching rates. Our new imaging model is general and can be applied to other systems that exhibit rapid fluctuations during STM experiments.

Y. Kitaguchi, S. Habuka, H. Okuyama, S. Hatta, T. Aruga,
T. Frederiksen, M. Paulsson, and H. Ueba

**Controlled switching of single-molecule junctions by mechanical motion of a phenyl ring**

Beilstein J. Nanotechnol. **6**, 2088-2095 (2015)
[ PDF ]

Mechanical methods for single-molecule control have potential for wide application in nanodevices and machines. Here we demonstrate the operation of a single-molecule switch made functional by the motion of a phenyl ring, analogous to the lever in a conventional toggle switch. The switch can be actuated by dual triggers, either by a voltage pulse or by displacement of the electrode, and electronic manipulation of the ring by chemical substitution enables rational control of the on-state conductance. Owing to its simple mechanics, structural robustness, and chemical accessibility, we propose that phenyl rings are promising components in mechanical molecular devices.

M. Engelund, R. Zuzak, S. Godlewski, M. Kolmer, T. Frederiksen, A. García-Lekue, D. Sánchez-Portal, and M. Szymonski

**Tunneling spectroscopy of close-spaced dangling-bond pairs in Si(001):H**

Scientific Reports **5**, 14496 (2015)
[ PDF ]

We present a combined experimental and theoretical study of the electronic properties of close-
spaced dangling-bond (DB) pairs in a hydrogen-passivated Si(001):H p-doped surface. Two types of
DB pairs are considered, called "cross" and "line" structures. Our scanning tunneling spectroscopy
(STS) data show that, although the spectra taken over different DBs in each pair exhibit a remarkable
resemblance, they appear shifted by a constant energy that depends on the DB-pair type. This
spontaneous asymmetry persists after repeated STS measurements. By comparison with density
functional theory (DFT) calculations, we demonstrate that the magnitude of this shift and the
relative position of the STS peaks can be explained by distinct charge states for each DB in the
pair. We also explain how the charge state is modified by the presence of the scanning tunneling
microscopy (STM) tip and the applied bias. Our results indicate that, using the STM tip, it is
possible to control the charge state of individual DBs in complex structures, even if they are in close
proximity. This observation might have important consequences for the design of electronic circuits
and logic gates based on DBs in passivated silicon surfaces.

T. Frederiksen

**First-Principles Simulations of Electron Transport in Atomic-Scale Systems**

Book chapter for Handbook of Single-Molecule Electronics
edited by K. Moth-Poulsen, Pan Stanford (2015).

An important theoretical challenge in the field of single-molecule electronics is to develop general methods
for quantitative simulations of real devices taking into account the atomistic details. This chapter
describes an approach toward this goal based on density-functional theory (DFT) for the electronic
structure in combination with nonequilibrium Green's functions (NEGF) for the transport.
We also address recent developments based on the DFT+NEGF
approach to describe electron--vibration interactions in molecular
junctions, local heating effects, and inelastic signatures in device
current--voltage and shot noise characteristics.

Y. Kitaguchi, S. Habuka, H. Okuyama, S. Hatta, T. Aruga, T. Frederiksen, M. Paulsson, and H. Ueba

**Controlling single-molecule junction conductance by molecular interactions**

Scientific Reports **5**, 11796 (2015)
[ PDF ]

For the rational design of single-molecular electronic devices, it is essential to understand
environmental effects on the electronic properties of a working molecule. Here we investigate the
impact of molecular interactions on the single-molecule conductance by accurately positioning
individual molecules on the electrode. To achieve reproducible and precise conductivity
measurements, we utilize relatively weak π-bonding between a phenoxy molecule and a
STM-tip to form and cleave one contact to the molecule. The anchoring to the other electrode is kept
stable using a chalcogen atom with strong bonding to a Cu(110) substrate. These non-destructive
measurements permit us to investigate the variation in single-molecule conductance under different
but controlled environmental conditions. Combined with density functional theory calculations, we
clarify the role of the electrostatic field in the environmental effect that influences the molecular
level alignment.

R. B. Christensen, T. Frederiksen, and M. Brandbyge

**Identification of pristine and defective graphene nanoribbons by phonon signatures in the electron transport characteristics**

Phys. Rev. B **91**, 075434 (2015) [arXiv:1501.02266]

Inspired by recent experiments where electron transport was measured across graphene nanoribbons (GNRs) suspended between a metal surface and the tip of a scanning tunneling microscope [Koch et al., Nat. Nanotechnol. **7**, 713 (2012)], we present detailed first-principles simulations of inelastic electron tunneling spectroscopy (IETS) of long pristine and defective armchair and zigzag nanoribbons under a range of charge carrier conditions. For the armchair ribbons we find two robust IETS signals around 169 and 196 mV corresponding to the D and G modes of Raman spectroscopy as well as additional fingerprints due to various types of defects in the edge passivation. For the zigzag ribbons we show that the spin state strongly influences the spectrum and thus propose IETS as an indirect proof of spin polarization.

G. Foti, D. Sánchez-Portal, A. Arnau, and T. Frederiksen

**Role of k-point sampling in the supercell approach to inelastic electron tunneling spectroscopy simulations of molecular monolayers**

Phys. Rev. B **91**, 035434 (2015)

While the role of sampling of the electron momentum k in supercell calculations of the elastic electron transmission is well understood, its influence in the case of inelastic electron tunneling (IET) has not yet been systematically explored. Here we compare ab initio IET spectra of molecular monolayers in the commonly used Γ-point approximation to rigorously k-converged results. We study four idealized molecular junctions with either alkanedithiolates or benzenedithiolates, and explore variations due to varying molecular tilt angle, density, as well as chemical identity of the monolayer. We show that the Γ-point approximation is reasonable for a range of systems, but that a rigorous convergence is needed for accurate signal amplitudes. We also describe an approximative scheme which reduces the computational cost of the k-averaged calculation in our implementation.

Y. Kim, K. Motobayashi, T. Frederiksen, H. Ueba, and M. Kawai

**
Action Spectroscopy for Single-Molecules reactions - Experiment and Theory**

Prog. Surf. Sci. **90**, 85-143 (2015) [DOI]

We review several representative experimental results of action spectroscopy (AS) of single molecules on metal surfaces using a scanning tunneling microscope (STM) by M. Kawai's group over last decade. The experimental procedures to observe STM-AS are described. A brief description of a low-temperature STM and experimental setup are followed by key experimental techniques of how to determine an onset bias voltage of a reaction and how to measure a current change associated with reactions and finally how to observe AS for single molecule reactions. The experimental results are presented for vibrationally mediated chemical transformation of trans-2-butene to 1.3-butadiene molecule and rotational motion of a single cis-2-butene molecule among four equivalent orientations on Pd(110). The AS obtained from the motion clearly detects more vibrational modes than inelastic electron tunneling spectroscopy with an STM. AS is demonstrated as a useful and novel single molecule vibrational spectroscopy. The AS for a lateral hopping of water dimer on Pt(111) is presented as an example of novelty. Several distinct vibrational modes are detected as the thresholds in the AS. The assignment of the vibrational modes determined from the analysis of the AS is made from a view of the adsorption geometry of hydrogen-bond donor or acceptor molecules in water dimer.

A generic theory of STM-AS, i.e., a reaction rate or yield as a function of bias voltage, is presented using a single adsorbate resonance model for single molecule reactions induced by the inelastic tunneling current. Formulas for the reaction rate R(V) and Y(V), i.e., reaction yield per electron Y(V) = e R(V)/I are derived. It provides a versatile framework to analyze any vibrationally mediated reactions of single adsorbates on metal surfaces. Numerical examples are presented to demonstrate generic features of the vibrational generation rate and Y(V) at different levels of approximations and to show how the effective broadening of the vibrational density of states (as described by Gaussian or Lorentzian functions) manifest themselves in Y(V) near the threshold bias voltage corresponding to a vibrational excitation responsible for reactions. A prefactor of Y(V) is explicitly derived for various types of elementary processes. Our generic formula of Y(V) also underlines the need to observe Y(V) at both bias voltage polarities, which can provide additional insight into the adsorbate projected density of states near the Fermi level within a span of the vibrational energy.

The theory is applied to analysis of some highlights of the experimental results: Xe transfer, hopping of a single CO molecule on Pd(110), a dissociation of a single dimethyl disulfide (CH_{3}S)_{2} and a hopping of a dissociated product, i.e., single methyl thiolate CH_{3}S on Cu(111). It underlines that an observation of Y(V) at both bias polarities permits us to certain insight into the molecular alignment with respect to the Fermi level.

K. Smaali, S. Desbief, G. Foti, T. Frederiksen, D. Sánchez-Portal, A. Arnau, J.-P. Nys, P. Leclere, D. Vuillaume, and N. Clement

**
On the Mechanical and Electronic Properties of Thiolated Gold Nanocrystals**

Nanoscale **7**, 1809-1819 (2015) [arXiv:1412.7698]

*Selected as "Hot article"*

We present a quantitative exploration, combining experiment and simulation, of the mechanical and electronic properties, as well as the modifications induced by an alkylthiolated coating, at the single nanoparticle (NP) level. We determined the response of the NPs to external pressure in a controlled manner using an atomic force microscope tip. We found a strong reduction in their Young's modulus, as compared to bulk gold, and a significant influence of strain on the electronic properties of the alkylthiolated NPs. Electron transport measurements of tiny molecular junctions (NP/alkylthiol/CAFM tip) show that the effective tunnelling barrier through the adsorbed monolayer strongly decreases by increasing the applied load, which translates in a remarkable and unprecedented increase in the tunnel current. These observations are successfully explained using simulations based on the finite element analysis (FEA) and first-principles calculations that permit one to consider the coupling between the mechanical response of the system and the electric dipole variations at the interface.

G. Foti, H. Vázquez, D. Sánchez-Portal, A. Arnau, and T. Frederiksen

**Identifying Highly-Conducting Au-C Links through Inelastic Electron Tunneling Spectroscopy**

J. Phys. Chem. C **118**, 27106-27112 (2014)

We use inelastic electron tunneling spectroscopy first-principles simulations to identify the different chemical bonds present at metal-molecule junctions. We unambiguously identify the nature of these bonds from two distinctive features in the calculated spectra: (i) the presence (or absence) of active vibrational modes and (ii) the dependence of vibrational frequencies on electrode separation. We use this method to present a study of the vibrational properties of alkanes bound to the electrodes via highly conducting Au-C links. In the experiment, these links were formed from molecules synthesized with trimethyl-tin (SnMe_{3}) terminations, where the SnMe_{3} groups were removed in situ at the junction, in a process involving both breaking and formation of bonds [Cheng, Z.-L.; Skouta, R.; Vázquez, H.; Widawsky, J. R.; Schneebeli, S.; Chen, W.; Hybertsen, M. S.; Breslow, R.; Venkataraman, L. Nat. Nanotechnol. 2011, **6**, 353-357]. We obtain the vibrational fingerprint of these direct Au-alkane links and extend this study to the other scenario considered in that paper (bonding via SnMe_{2} groups), which may be relevant under other experimental conditions. We also explore the effect of deuteration on inelastic electron tunneling spectroscopy (IETS). Complete deuteration of the molecules diminishes the differences of the spectra corresponding to the two bonding geometries, making identification more difficult. IETS of an isolated SnMe_{3} fragment provides an additional basis for comparison in the characterization of the molecular junction.

T. Frederiksen, G. Foti, F. Scheurer, V. Speisser, and G. Schull

**Chemical control of electrical contacts to sp ^{2} carbon atoms**

Nat. Commun.

Carbon-based nanostructures are attracting tremendous interest as components in ultrafast electronics and optoelectronics. The electrical interfaces to these structures play a crucial role for the electron transport, but the lack of control at the atomic scale can hamper device functionality and integration into operating circuitry. Here we study a prototype carbon-based molecular junction consisting of a single C_{60} molecule and probe how the electric current through the junction depends on the chemical nature of the foremost electrode atom in contact with the molecule. We find that the efficiency of charge injection to a C_{60} molecule varies substantially for the considered metallic species, and demonstrate that the relative strength of the metal-C bond can be extracted from our transport measurements. Our study further suggests that a single-C_{60} junction is a basic model to explore the properties of electrical contacts to meso- and macroscopic sp^{2} carbon structures.

J.-T. Lü, R. B. Christensen, G. Foti, T. Frederiksen, T. Gunst, and M. Brandbyge

**Efficient calculation of inelastic vibration signals in electron transport: Beyond the wide-band approximation**

Phys. Rev. B **89**, 081405(R) (2014)
[arXiv:1312.7625].

We extend the simple and efficient lowest order expansion (LOE) for inelastic electron tunneling spectroscopy (IETS) to include variations in the electronic structure on the scale of the vibration energies. This enables first-principles calculations of IETS line shapes for molecular junctions close to resonances and band edges. We demonstrate how this is relevant for the interpretation of experimental IETS using both a simple model and first-principles simulations.

T. Frederiksen, M. Paulsson, and H. Ueba

**Theory of action spectroscopy for single-molecule reactions induced by vibrational excitations with STM**

Phys. Rev. B **89**, 035427 (2014)

A theory of action spectroscopy, i.e., a reaction rate or yield as a function of bias voltage, is presented for single-molecule reactions induced by the inelastic tunneling current with a scanning tunneling microscope. A formula for the reaction yield is derived using the adsorbate resonance model, which provides a versatile tool to analyze vibrationally mediated reactions of single adsorbates on conductive surfaces. This allows us to determine the energy quantum of the excited vibrational mode, the effective broadening of the vibrational density of states (as described by Gaussian or Lorentzian functions), and a prefactor characterizing the elementary process behind the reaction. The underlying approximations are critically discussed. We point out that observation of reaction yields at both bias voltage polarities can provide additional insight into the adsorbate density of states near the Fermi level. As an example, we apply the theory to the case of flip motion of a hydroxyl dimer (OD)_{2} on Cu(110) which was experimentally observed by Kumagai *et al.* [Phys. Rev. B **79**, 035423 (2009)]. In combination with density functional theory calculations for the vibrational modes, the vibrational damping due to electron-hole pair generation, and the potential energy landscape for the flip motion, a detailed microscopic picture for the switching process is established. This picture reveals that the predominant mechanism is excitation of the OD stretch modes which couple anharmonically to the low-energy frustrated rotation mode.

G. Foti, D. Sánchez-Portal, A. Arnau, and T. Frederiksen

**Interface Dipole Effects as a Function of Molecular Tilt: Mechanical Gating of Electron Tunneling through Self-Assembled Monolayers?**

J. Phys. Chem. C **117**, 14272-14280 (2013)

Control of electron transport through molecular devices is a fundamental step toward design of functional molecular electronics. In this respect, the application of the field-effect transistor principle to molecular junctions appears to be a desirable strategy. Here we study the possibility of mechanically controlling the molecular orbital alignment in self-assembled monolayers via the electrostatic fields originating from dipoles at the metal-molecule interfaces. More specifically, we analyze first-principles simulations of prototype alkanedithiolate and alkanediamine monolayer junctions between Au(111) electrodes as a function of inclination of the molecules in the film. We find that the molecular orbital alignment and hence the low-bias conductance of the junctions, sensitively depends on the interface dipole. The dipole change with molecular tilt is rationalized in terms of two electrostatic effects: (i) the reorientation of a dipole associated with the anchoring group and (ii) a dipole modification arising from charge redistribution due to the metal-molecule bond. The first effect, dominating for the thiolates, is the desired way to gate the junctions by tuning of the molecular tilt. However, the second effect, equally important for the amines, may hamper the mechanical control of the level alignment because it depends on other geometric details than the tilt angle. Our results thus suggest that mechanical gating by tilt is achievable with molecules and anchoring groups with strong intrinsic dipole moments and well-defined binding geometry rather than with interface dipoles associated with weak and flexible metal-molecule bonds.

S. Ulstrup, T. Frederiksen, and M. Brandbyge,

**
Nonequilibrium electron-vibration coupling and conductance fluctuations in a C _{60}-junction**

Phys. Rev. B

We investigate chemical bond formation and conductance in a molecular C_{60} junction under finite bias voltage using first-principles calculations based on density functional theory and nonequilibrium Green's functions (DFT-NEGF). At the point of contact formation we identify a remarkably strong coupling between the C_{60} motion and the molecular electronic structure. This is only seen for positive sample bias, although the conductance itself is not strongly polarity dependent. The nonequilibrium effect is traced back to a sudden shift in the position of the voltage drop with a small C_{60} displacement. Combined with a vibrational heating mechanism we construct a model from our results that explain the polarity-dependent two-level conductance fluctuations observed in recent scanning tunneling microscopy (STM) experiments [N. Néel et al., Nano Lett. **11**, 3593 (2011)]. These findings highlight the significance of nonequilibrium effects in chemical bond formation/breaking and in electron-vibration coupling in molecular electronics.

Y. Kim, A. Garcia-Lekue, D. Sysoiev, T. Frederiksen, U. Groth, and E. Scheer,

**Charge transport in azobenzene-based single-molecule junctions**

Phys. Rev. Lett. **109**, 226801 (2012)

Azobenzene-derivative molecules change their conformation as a result of a cis-trans transition when exposed to ultraviolet or visible light irradiation and this is expected to induce a significant variation in the conductance of molecular devices. Despite extensive investigations carried out on this type of molecule, a detailed understanding of the charge transport for the two isomers is still lacking. We report a combined experimental and theoretical analysis of electron transport through azobenzene-derivative single-molecule break junctions with Au electrodes. Current-voltage and inelastic electron tunneling spectroscopy (IETS) measurements performed at 4.2 K are interpreted based on first-principles calculations of electron transmission and IETS spectra. This qualitative study unravels the origin of a slightly higher conductance of junctions with the cis isomer and demonstrates that IETS spectra of cis and trans forms show distinct vibrational fingerprints that can be used for identifying the isomer.

R. Avriller, and T. Frederiksen,

**Inelastic shot noise characteristics of nanoscale junctions from first principles**

Phys. Rev. B **86**, 155411 (2012) [arXiv:1209.3599]

We describe an implementation of ab initio methodology to compute inelastic shot noise signals due to electron-vibration scattering in nanoscale junctions. The method is based on the framework of nonequilibrium Keldysh Green's functions with a description of electronic structure and nuclear vibrations from density functional theory. Our implementation is illustrated with simulations of electron transport in Au and Pt atomic point contacts. We show that the computed shot noise characteristics of the Au contacts can be understood in terms of a simple two-site tight-binding model representing the two apex atoms of the vibrating nanojunction. We also show that the shot noise characteristics of Pt contacts exhibit more complex features associated with inelastic interchannel scattering. These inelastic noise features are shown to provide additional information about the electron-phonon coupling and the multichannel structure of Pt contacts than what is readily derived from the corresponding conductance characteristics. We finally analyze a set of Au atomic chains of different lengths and strain conditions and provide a quantitative comparison with the recent shot noise experiments reported by Kumar et al. [Phys. Rev. Lett. **108**, 146602 (2012)].

N. Hauptmann, F. Mohn, L. Gross, G. Meyer, T. Frederiksen, and R. Berndt,

**Force and Conductance during Contact Formation to a C _{60} Molecule**

New J. Phys.

Force and conductance were simultaneously measured during the formation of Cu-C_{60} and C_{60}-C_{60} contacts using a combined cryogenic scanning tunneling and atomic force microscope. The contact geometry was controlled with submolecular resolution. The maximal attractive forces measured for the two types of junctions were found to differ significantly. We show that the previously reported values of the contact conductance correspond to the junction being under maximal tensile stress.

T. Kumagai, A. Shiotari, H. Okuyama, S. Hatta, T. Aruga, I. Hamada, T. Frederiksen, and H. Ueba,

**H-atom relay reactions in real space**

Nature Materials **11**, 167-172 (2012)

Hydrogen bonds are the path through which protons and hydrogen atoms can be transferred between molecules. The relay mechanism, in which H-atom transfer occurs in a sequential fashion along hydrogen bonds, plays an essential role in many functional compounds. Here we use the scanning tunnelling microscope to construct and operate a test-bed for real-space observation of H-atom relay reactions at a single-molecule level. We demonstrate that the transfer of H-atoms along hydrogen-bonded chains assembled on a Cu(110) surface is controllable and reversible, and is triggered by excitation of molecular vibrations induced by inelastic tunnelling electrons. The experimental findings are rationalized by ab initio calculations for adsorption geometry, active vibrational modes and reaction pathway, to reach a detailed microscopic picture of the elementary processes.

B. W. Heinrich, M. V. Rastei, D.- J. Choi, T. Frederiksen, and L. Limot,

**Engineering negative differential conductance with the Cu(111) surface state**

Phys. Rev. Lett. **107**, 246801 (2011) [arXiv:1112:1801v1].

Low-temperature scanning tunneling microscopy and spectroscopy are employed to investigate electron tunneling from a C_{60}-terminated tip into a Cu(111) surface. Tunneling between a C_{60} orbital and the Shockley surface states of copper is shown to produce negative differential conductance (NDC) contrary to conventional expectations. NDC can be tuned through barrier thickness or C_{60} orientation up to complete extinction. The orientation dependence of NDC is a result of a symmetry matching between the molecular tip and the surface states.

Y. Ootsuka, T. Frederiksen, H. Ueba, and M. Paulsson,

**Vibrationally induced flip motion of a hydroxyl dimer on Cu(110)**

Phys. Rev. B **84**, 193403 (2011) [arXiv:1111.2252v1]

Recent low-temperature scanning-tunneling microscopy experiments [T. Kumagai et al., Phys. Rev. B **79**, 035423 (2009)] observed the vibrationally induced flip motion of a hydroxyl dimer (OD)_{2} on Cu(110). We propose a model to describe two-level fluctuations and current-voltage characteristics of nanoscale systems that undergo vibrationally induced switching. The parameters of the model are based on comprehensive density functional calculations of the system's vibrational properties. For the dimer (OD)_{2}, the calculated population of the high- and low-conductance states, the I-V, dI/dV, and d^{2}I/dV^{2} curves are in good agreement with the experimental results and underline the different roles played by the free and shared OD stretch modes of the dimer.

A. Garcia-Lekue, D. Sánchez-Portal, A. Arnau, and T. Frederiksen,

**Simulation of inelastic electron tunneling spectroscopy of single molecules with functionalized tips**

Phys. Rev. B **83**, 155417 (2011) [arXiv:1103.4302v1]

The role of the tip in inelastic electron tunneling spectroscopy (IETS) performed with scanning tunneling microscopes (STM) is theoretically addressed via first-principles simulations of vibrational spectra of single carbon monoxide (CO) molecules adsorbed on Cu(111). We show how chemically functionalized STM tips modify the IETS intensity corresponding to adsorbate modes on the sample side. The underlying propensity rules are explained using symmetry considerations for both the vibrational modes and the molecular orbitals of the tip and sample. This suggests that single-molecule IETS can be optimized by selecting the appropriate tip orbital symmetry.

G. Schull, T. Frederiksen, A. Arnau, D. Sánchez-Portal, and R. Berndt,

**Atomic-scale engineering of electrodes for single-molecule contacts**

Nature Nanotechnology **6**, 23-27 (2011)

The transport of charge through a conducting material depends on the intrinsic ability of the material to conduct current and on the charge injection efficiency at the contacts between the conductor and the electrodes carrying current to and from the material. According to theoretical considerations, this concept remains valid down to the limit of single-molecule junctions. Exploring this limit in experiments requires atomic-scale control of the junction geometry. Here we present a method for probing the current through a single C_{60} molecule while changing, one by one, the number of atoms in the electrode that are in contact with the molecule. We show quantitatively that the contact geometry has a strong influence on the conductance. We also find a crossover from a regime in which the conductance is limited by charge injection at the contact to a regime in which the conductance is limited by scattering at the molecule. Thus, the concepts of 'good' and 'bad' contacts, commonly used in macro- and mesoscopic physics, can also be applied at the molecular scale.

M. Paulsson, T. Frederiksen, and M. Brandbyge

**Molecular Electronics: Insight from First-Principles Transport Simulations**

CHIMIA **64**, 350-355 (2010)

Conduction properties of nanoscale contacts can be studied using first-principles simulations. Such calculations give insight into details behind the conductance that is not readily available in experiments. For example, we may learn how the bonding conditions of a molecule to the electrodes affect the electronic transport. Here we describe key computational ingredients and discuss these in relation to simulations for scanning tunneling microscopy (STM) experiments with C_{60} molecules where the experimental geometry is well characterized. We then show how molecular dynamics simulations may be combined with transport calculations to study more irregular situations, such as the evolution of a nanoscale contact with the mechanically controllable break-junction technique. Finally we discuss calculations of inelastic electron tunnelling spectroscopy as a characterization technique that reveals information about the atomic arrangement and transport channels.

M. Brandbyge, T. Frederiksen, and M. Paulsson

**DFT-NEGF approach to current-induced forces, vibrational signals, and heating in nanoconductors**

Book chapter in T. Seideman Ed.
Current-Driven Phenomena in Nanoelectronics.

In this chapter we first introduce the DFT-NEGF method, which combines density
functional theory (DFT) with the nonequilibrium Green's function (NEGF) method in order
to treat atomic-scale conductors in the presence of current. We introduce the concept of
conductance eigenchannels within DFT-NEGF as a means of analysis of the elastic
conduction process. We then describe how the inelastic processes involving interaction
with vibrations can be calculated efficiently using DFT-NEGF and further approximations.
We show how these methods can be used to investigate how the electronic current can heat
the vibrations in the atomic-scale conductors and conclude with a discussion of some
current experiments in which this is observed.

L. Vitali, R. Ohmann, K. Kern, A. Garcia-Lekue, T. Frederiksen, D. Sánchez-Portal, and A. Arnau

**Surveying molecular vibrations during the formation of metal-molecule nanocontacts**

Nano Lett. **10**, 657-660 (2010)

Molecular junctions have been characterized to determine the influence of the metal contact formation in the electron transport process through a single molecule. With inelastic electron tunneling spectroscopy and first-principles calculations, the vibration modes of a carbon monoxide molecule have been surveyed as a function of the distance from a copper electrode with unprecedented accuracy. We observe a continuous but nonlinear blue shift of the frustrated rotation mode in tunneling with decreasing distance followed by an abrupt softening upon contact formation. This indicates that the presence of the metal electrode sensibly alters the structural and conductive properties of the junction even without the formation of a strong chemical bond.

C. R. Arroyo, T. Frederiksen, G. Rubio-Bollinger, M. Vélez, A. Arnau, D. Sánchez-Portal, and N. Agraït

**Characterization of single-molecule pentanedithiol junctions by inelastic electron
tunneling spectroscopy and first-principles calculations**

Phys. Rev. B **81**, 075405 (2010) [arXiv:1001.2392v1]

We study pentanedithiol molecular junctions formed by means of the break-junction technique with a scanning tunneling microscope at low temperatures. Using inelastic electron tunneling spectroscopy and first-principles calculations, the response of the junction to elastic deformation is examined. We show that this procedure makes a detailed characterization of the molecular junction possible. In particular, our results indicate that tunneling takes place through just a single molecule.

G. Schull, T. Frederiksen, M. Brandbyge, and R. Berndt

**Passing Current through Touching Molecules** (*Editors' suggestion* )

Phys. Rev. Lett. **103**, 206803 (2009) [arXiv:0910:1281]

*Featured in Physics Focus story:* Molecular currents

The charge flow from a single C_{60} molecule to another one has been probed. The conformation and electronic states of both molecules on the contacting electrodes have been characterized using a cryogenic scanning tunneling microscope. While the contact conductance of a single molecule between two Cu electrodes can vary up to a factor of 3 depending on electrode geometry, the conductance of the C_{60}-C_{60} contact is consistently lower by 2 orders of magnitude. First-principles transport calculations reproduce the experimental results, allow a determination of the actual C_{60}-C_{60} distances, and identify the essential role of the intermolecular link in bi- and trimolecular chains.

T. Frederiksen, C. Munuera, C. Ocal, M. Brandbyge, M. Paulsson, D. Sánchez-Portal, and A. Arnau

**Exploring the Tilt-Angle Dependence of Electron Tunneling across Molecular Junctions of Self-Assembled Alkanethiols**

ACS Nano **3**, 2073-2080 (2009)

Electronic transport mechanisms in molecular junctions are investigated by a combination of first-principles calculations and current-voltage measurements of several well-characterized structures. We study self-assembled layers of alkanethiols grown on Au(111) and form tunnel junctions by contacting the molecular layers with the tip of a conductive force microscope. Measurements done under low-load conditions permit us to obtain reliable tilt-angle and molecular length dependencies of the low-bias conductance through the alkanethiol layers. The observed dependence on tilt-angle is stronger for the longer molecular chains. Our calculations confirm the observed trends and explain them as a result of two mechanisms, namely, a previously proposed intermolecular tunneling enhancement as well as a hitherto overlooked tilt-dependent molecular gate effect.

M. Paulsson, C. Krag, T. Frederiksen, and M. Brandbyge

**Conductance of alkanedithiol single-molecule junctions: a molecular dynamics study**

Nano Lett. **9**, 117-121 (2009)

We study formation and conductance of alkanedithiol junctions using density functional based molecular dynamics. The formation involves straightening of the molecule, migration of thiol end-groups, and pulling out Au atoms. Plateaus are found in the low-bias conductance traces which decrease by 1 order of magnitude when gauche defects are present. We further show that the inelastic electron tunneling spectra depend on the junction geometry. In particular, our simulations suggest ways to identify gauche defects.

T. Frederiksen, K. Franke, A. Arnau, G. Schulze, J. I. Pascual, and N. Lorente

**Dynamic Jahn-Teller effect in electron transport through single C _{60} molecules**

Phys. Rev. B

Low-temperature scanning tunneling spectroscopy and first-principles calculations are used to characterize electron transport through vibronic states of C_{60} molecules. This is achieved by positioning a C_{60} molecule on top of a molecular self-assembled template on Au(111). In these conditions, conductance spectra are shown to reveal the dynamic Jahn-Teller effect of the C_{60} molecule. This vibronic transport study helps in solving a long-standing debate [Phys. Rev. Lett. **74**, 1875 (1995); Phys. Rev. Lett. **91**, 196402 (2003)] on density-functional calculations of the C_{60} electron-phonon coupling strength.

E. J. McEniry, T. Frederiksen, T. N. Todorov, D. Dundas, and A. P. Horsfield

**Inelastic quantum transport in nanostructures: The self-consistent Born approximation and correlated electron-ion dynamics**

Phys. Rev. B **78**, 035446 (2008) [arXiv:0802.4174]

A dynamical method for inelastic transport simulations in nanostructures is compared to a steady-state method based on nonequilibrium Green's functions. A simplified form of the dynamical method produces, in the steady state in the weak-coupling limit, effective self-energies analogous to those in the Born approximation due to electron-phonon coupling. The two methods are then compared numerically on a resonant system consisting of a linear trimer weakly embedded between metal electrodes. This system exhibits an enhanced heating at high biases and long phonon equilibration times. Despite the differences in their formulation, the static and dynamical methods capture local current-induced heating and inelastic corrections to the current with good agreement over a wide range of conditions, except in the limit of very high vibrational excitations where differences begin to emerge.

M. Paulsson, T. Frederiksen, H. Ueba, N. Lorente, and M. Brandbyge

**Unified description of inelastic propensity rules for electron transport through nanoscale junctions**

Phys. Rev. Lett. **100**, 226604 (2008) [arXiv:0711.3392]

We present a method to analyze the results of first-principles based calculations of electronic currents including inelastic electron-phonon effects. This method allows us to determine the electronic and vibrational symmetries in play, and hence to obtain the so-called propensity rules for the studied systems. We show that only a few scattering states - namely those belonging to the most transmitting eigenchannels - need to be considered for a complete description of the electron transport. We apply the method on first-principles calculations of four different systems and obtain the propensity rules in each case.

T. Frederiksen, N. Lorente, M. Paulsson, and M. Brandbyge

**From tunneling to contact: Inelastic signals in an atomic gold junction from first principles**

Phys. Rev. B **75**, 235441 (2007) [cond-mat/0702176]

The evolution of electron conductance in the presence of inelastic effects is studied as an atomic gold contact is formed evolving from a low-conductance regime (tunneling) to a high-conductance regime (contact). In order to characterize each regime, we perform density-functional theory (DFT) calculations to study the geometric and electronic structures, together with the strength of the atomic bonds and the associated vibrational frequencies. The conductance is calculated by, first, evaluating the transmission of electrons through the system and, second, by calculating the conductance change due to the excitation of vibrations. As found in previous studies [Paulsson et al., Phys. Rev. B **72**, 201101(R) (2005)], the change in conductance due to inelastic effects permits us to characterize the crossover from tunneling to contact. The most notorious effect is the crossover from an increase in conductance in the tunneling regime to a decrease in conductance in the contact regime when the bias voltage matches a vibrational threshold. Our DFT-based calculations actually show that the effect of vibrational modes in electron conductance is rather complex, in particular, when modes localized in the contact region are permitted to extend into the electrodes. As an example, we find that certain modes can give rise to decreases in conductance when in the tunneling regime, opposite to the above-mentioned result. Whereas details in the inelastic spectrum depend on the size of the vibrational region, we show that the overall change in conductance is quantitatively well approximated by the simplest calculation where only the apex atoms are allowed to vibrate. Our study is completed by the application of a simplified model where the relevant parameters are obtained from the above DFT-based calculations.

T. Frederiksen, M. Paulsson, M. Brandbyge, and A.-P. Jauho

**Inelastic transport theory from first principles: methodology and application to nanoscale devices**

Phys. Rev. B **75**, 205413 (2007) [cond-mat/0611562]

We describe a first-principles method for calculating electronic structure, vibrational modes and frequencies, electron-phonon couplings, and inelastic electron transport properties of an atomic-scale device bridging two metallic contacts under nonequilibrium conditions. The method extends the density-functional codes SIESTA and TRANSIESTA that use atomic basis sets. The inelastic conductance characteristics are calculated using the nonequilibrium Green's function formalism, and the electron-phonon interaction is addressed with perturbation theory up to the level of the self-consistent Born approximation. While these calculations often are computationally demanding, we show how they can be approximated by a simple and efficient lowest order expansion. Our method also addresses effects of energy dissipation and local heating of the junction via detailed calculations of the power flow. We demonstrate the developed procedures by considering inelastic transport through atomic gold wires of various lengths, thereby extending the results presented in Frederiksen et al. [Phys. Rev. Lett. **93**, 256601 (2004)]. To illustrate that the method applies more generally to molecular devices, we also calculate the inelastic current through different hydrocarbon molecules between gold electrodes. Both for the wires and the molecules our theory is in quantitative agreement with experiments, and characterizes the system-specific mode selectivity and local heating.

T. Frederiksen, M. Paulsson, M. Brandbyge, and A.-P. Jauho

**
First-principles theory of inelastic transport and local heating in atomic gold wires**

AIP Conf. Proc. **893**, 727-728 (2007)

We present theoretical calculations of the inelastic transport properties in atomic gold wires. Our method is based on a combination of density functional theory and nonequilibrium Green's functions. The vibrational spectra for extensive series of wire geometries have been calculated using SIESTA, and the corresponding effects in the conductance are analyzed. In particular, we focus on the heating of the active vibrational modes. By a detailed comparison with experiments we are able to estimate an order of magnitude for the external damping of the active vibrations.

T. Frederiksen, M. Paulsson, and M. Brandbyge

**Inelastic Fingerprints of Hydrogen Contamination in Atomic Gold Wire Systems**

J. Phys.: Conf. Ser. **61**, 312-316 (2007) [cond-mat/0608510]

We present series of first-principles calculations for both pure and hydrogen contaminated gold wire systems in order to investigate how such impurities can be detected. We show how a single H atom or a single H_{2} molecule in an atomic gold wire will affect forces and Au-Au atom distances under elongation. We further determine the corresponding evolution of the low-bias conductance as well as the inelastic contributions from vibrations. Our results indicate that the conductance of gold wires is only slightly reduced from the conductance quantum G_{0} = 2e^{2}/h by the presence of a single hydrogen impurity, hence making it difficult to use the conductance itself to distinguish between various configurations. On the other hand, our calculations of the inelastic signals predict significant differences between pure and hydrogen contaminated wires, and, importantly, between atomic and molecular forms of the impurity. A detailed characterization of gold wires with a hydrogen impurity should therefore be possible from the strain dependence of the inelastic signals in the conductance.

N. Néel, J. Kröger, L. Limot, T. Frederiksen, M. Brandbyge, and R. Berndt

**Controlled Contact to a C _{60} Molecule**

Phys. Rev. Lett.

The tip of a low-temperature scanning tunneling microscope is approached towards a C_{60} molecule adsorbed at a pentagon-hexagon bond on Cu(100) to form a tip-molecule contact. The conductance rapidly increases to ~0.25 conductance quanta in the transition region from tunneling to contact. Ab-initio calculations within density functional theory and nonequilibrium Green's function techniques explain the experimental data in terms of the conductance of an essentially undeformed C_{60}. The conductance in the transition region is affected by structural fluctuations which modulate the tip-molecule distance.

T. Frederiksen,

**
Inelastic transport theory for nanoscale systems**

PhD thesis, MIC, DTU, February 2007.
[ PDF ]

This thesis describes theoretical and numerical investigations of inelastic scattering and energy dissipation in electron transport through nanoscale systems. A computational scheme, based on a combination of density functional theory (DFT) and nonequilibrium Green's functions (NEGF), has been developed to describe the electrical conduction properties taking into account the full atomistic details of the systems. The scheme involves quantitative calculations of electronic structure, vibrational modes and frequencies, electron-vibration couplings, and inelastic current-voltage characteristics in the weak coupling limit.

When a current is passed through a nanoscale device, such as a single molecule or an atomic-size contact, it will heat up due to excitations of the nuclear vibrations. The developed scheme is able to quantify this local heating effect and to predict how it affects the conductance.

The methods have been applied to a number of specific systems, including monatomic gold chains, atomic point contacts, and metal-molecule-metal configurations. These studies have clarified the inelastic effects in the electron transport and characterized the vibrational modes that couple to the current. For instance, the dominant scattering for gold chains could be traced back to the longitudinal "alternating bond-length" mode. Furthermore, the results have been compared critically with experimental measurements for the different systems, and provided a microscopic understanding for the important physics. An example is the current-induced fluctuations that have been shown to influence the transport though individual C 60 molecules on copper surfaces.

M. Paulsson, T. Frederiksen, and M. Brandbyge

**Inelastic Transport through Molecules: Comparing First-Principles Calculations to Experiments**

Nano Lett. **6**, 258-262 (2006)

We present calculations of the elastic and inelastic conductance through three different hydrocarbon molecules connected to gold electrodes. Our method is based on a combination of the nonequilibrium Green's function method with density functional theory. Vibrational effects in these molecular junctions were previously investigated experimentally by Kushmerick et al. (Nano Lett. 2004, **4**, 639). Our results are in good agreement with the measurements and provide insights into (i) which vibrational modes are responsible for inelastic scattering, (ii) the width of the inelastic electron tunneling signals, and (iii) the mechanisms of heating and cooling of the vibrational modes induced by the coupling to the charge carriers.

M. Paulsson, T. Frederiksen, and M. Brandbyge

**Phonon Scattering in Nanoscale Systems: Lowest Order Expansion of the Current and Power Expressions**

J. Phys.: Conf. Ser. **35**, 247-254 (2006)

We use the non-equilibrium Green's function method to describe the effects of phonon scattering on the conductance of nano-scale devices. Useful and accurate approximations are developed that both provide (i) computationally simple formulas for large systems and (ii) simple analytical models. In addition, the simple models can be used to fit experimental data and provide physical parameters.

M. Paulsson, T. Frederiksen, and M. Brandbyge

**Modeling Inelastic Phonon Scattering in Atomic- and Molecular-wire Junctions**

Phys. Rev. B **72**, 201101(R) (2005); **75**, 129901(E) (2007) [cond-mat/0505473]

Computationally inexpensive approximations describing electron-phonon scattering in molecular-scale conductors are derived from the nonequilibrium Green's function method. The accuracy is demonstrated with a first-principles calculation on an atomic gold wire. Quantitative agreement between the full nonequilibrium Green's function calculation and the newly derived expressions is obtained while simplifying the computational burden by several orders of magnitude. In addition, analytical models provide intuitive understanding of the conductance including nonequilibrium heating and provide a convenient way of parameterizing the physics. This is exemplified by fitting the expressions to the experimentally observed conductances through both an atomic gold wire and a hydrogen molecule.

M. C. Sullivan, D. R. Strachan, T. Frederiksen, R. A. Ott, and C. J. Lobb

**Effects of Self-field and Low Magnetic Fields on the Normal-Superconducting Phase Transition**

Phys. Rev. B **72**, 092507 (2005) [cond-mat/0505334].

Researchers have studied the normal-superconducting phase transition in the high-Tc cuprates in a magnetic field (the vortex-glass or Bose-glass transition) and in zero field. Often, transport measurements in "zero field" are taken in the Earth's ambient field or in the remnant field of a magnet. We show that fields as small as the Earth's field will alter the shape of the current vs voltage curves and will result in inaccurate values for the critical temperature T_{c} and the critical exponents ν and z, and can even destroy the phase transition. This indicates that without proper screening of the magnetic field it is impossible to determine the true zero-field critical parameters, making correct scaling and other data analysis impossible. We also show, theoretically and experimentally, that the self field generated by the current flowing in the sample has no effect on the current vs voltage isotherms.

T. Frederiksen, M. Brandbyge, N. Lorente, and A. P. Jauho

**
Modeling of Inelastic Transport in One-dimensional Metallic Atomic Wires**

J. Comp. Electronics **3**, 423-427 (2004) [cond-mat/0411108]

Inelastic effects in electron transport through nano-sized devices are addressed with a method based on nonequilibrium Green's functions (NEGF) and perturbation theory to infinite order in the electron-vibration coupling. We discuss the numerical implementation which involves an iterative scheme to solve a set of coupled non-linear equations for the electronic Green's functions and the self-energies due to vibrations. To illustrate our method, we apply it to a one-dimensional single-orbital tight-binding description of the conducting electrons in atomic gold wires, and show that this simple model is able to capture most of the essential physics.

T. Frederiksen, M. Brandbyge, N. Lorente, and A. P. Jauho

**
Inelastic Scattering and Local Heating in Atomic Gold Wires**

Phys. Rev. Lett. **93**, 256601 (2004) [cond-mat/0410700]

We present a method for including inelastic scattering in a first-principles density-functional computational scheme for molecular electronics. As an application, we study two geometries of four-atom gold wires corresponding to two different values of strain and present results for nonlinear differential conductance vs device bias. Our theory is in quantitative agreement with experimental results and explains the experimentally observed mode selectivity. We also identify the signatures of phonon heating.

M. C. Sullivan, T. Frederiksen, J. M. Repaci, D. R. Strachan, R. A. Ott, and C. J. Lobb

**Normal-Superconducting Phase Transition Mimicked by Current Noise**

Phys. Rev. B **70**, 140503(R) (2004) [cond-mat/0407144]

As a superconductor goes from the normal state into the superconducting state, the voltage versus current characteristics at low currents change from linear to nonlinear. We show theoretically and experimentally that the addition of current noise to nonlinear voltage versus current curves will create ohmic behavior. Ohmic response at low currents for temperatures below the critical temperature T_{c} mimics the phase transition and leads to incorrect values for T_{c} and the critical exponents ν and z. The ohmic response occurs at low currents, and will occur in both the zero-field transition and the vortex-glass transition. Our results indicate that the transition temperature and critical exponents extracted from the conventional scaling analysis are inaccurate if current noise is not filtered out. This is a possible explanation for the wide range of critical exponents found in the literature.

D. R. Strachan, M. C. Sullivan, T. Frederiksen, R. A. Ott, and C. J. Lobb

**What a superconducting transition should look like: extrapolating data from scaling plots**

Physica C **408-410**, 562-563 (2004)

We compare measured current-voltage measurements of a YBa_{2}Cu_{3}O_{7-δ} film with data extrapolated from various scaling collapses. We find that in general the extrapolated data show opposite concavity about the transition temperature at all currents; whereas the experimental data do not. This indicates that the experiments do not demonstrate unambiguous evidence for a superconducting transition.

M. C. Sullivan, D. R. Strachan, T. Frederiksen, R. A. Ott, M. Lilly, and C. J. Lobb

**Zero-Field Superconducting Phase Transition Obscured by Finite-Size Effects in Thick YBa _{2}Cu_{3}O_{7-δ} Films**

Phys. Rev. B

We report on the normal-superconducting phase transition in thick YBa_{2}Cu_{3}O_{7-δ} films in zero magnetic field. We find significant finite-size effects at low currents even in our thickest films (d=3200 Å). Using data at higher currents, we can unambiguously find T_{c} and z, and show z=2.1±0.15, as expected for the three-dimensional XY model with diffusive dynamics. The crossover to two-dimensional behavior, seen by other researchers in thinner films (d ≤ 500 Å), obscures the three-dimensional transition in both zero field and the vortex-glass transition in field, leading to incorrect values of T_{c} (or T_{g}), ν, and z. The finite-size effects, usually ignored in thick films, are an explanation for the wide range of critical exponents found in the literature.

T. Frederiksen,

**
Inelastic Electron Transport in Nanosystems**

MSc thesis, MIC, DTU, February 2004.
[ PDF ]

The emerging field of molecular electronics, in which individual molecules play the role of active devices, is receiving much attention due to its possible technological impact. Recent advances in nanoscale fabrication and engineering techniques have made it possible to study the transport properties of devices on the atomic scale. At this level one inherently probes the quantum mechanical nature of matter which manifests a number of effects not well understood yet. One such effect is the mutual interaction between electrical current and atomic vibrations.

In this thesis we describe a method for calculating dc current-voltage characteristics of nanostructures connected between metallic leads taking into account electron-vibration scattering inside the device. The method is based on nonequilibrium Green's functions (NEGF) and a Meir-Wingreen type formula for the current through an interacting region of space. Within the Born-Oppenheimer approximation we calculate the electronic Green's functions for this region treating the electron-phonon interaction perturbatively in the self-consistent Born approximation. The numerical implementation of the present method is discussed in detail, and we compare it with results in the literature as well as with our own calculations based on an exact diagonalization technique.

In particular we look at transport through metallic wires of single atoms. With a simple single-orbital tight-binding model and parameters fitted for Au chains we show how to determine the normal modes of vibration, the electron-vibration couplings, and the influence of the different modes on the conductance. Finally, we discuss the potential of combining our method with ab initio calculations of electronic structure, vibrational modes, and couplings, and present some preliminary results in this direction.