arXiv subjects

L. K. Dash

Publications and source records attributed to L. K. Dash.

15 recordsLinked to original sources

arXiv2014

Nonequilibrium fluctuation-dissipation relations for one- and two-particle correlation functions in steady-state quantum transport

We study the non-equilibrium (NE) fluctuation-dissipation (FD) relations in the context of quantum thermoelectric transport through a two-terminal nanodevice in the steady-state. The FD relations for the one- and two-particle correlation functions are derived for a model of the central region consisting of a single electron level. Explicit expressions for the FD relations of the Green's functions (one-particle correlations) are provided. The FD relations for the current-current and charge-charge (two-particle) correlations are calculated numerically. We use self-consistent NE Green's functions calculations to treat the system in the absence and in the presence of interaction (electron-phonon) in the central region. We show that, for this model, there is no single universal FD theorem for the NE steady state. There are different FD relations for each different class of problems. We find that the FD relations for the one-particle correlation function are strongly dependent on both the NE conditions and the interactions, while the FD relations of the current-current correlation function are much less dependent on the interaction. The latter property suggests interesting applications for single-molecule and other nanoscale transport experiments.

cond-mat.stat-mech↗

arXiv2013

Nonequilibrium Fluctuation-Dissipation Theorems for Interacting Quantum Transport

We study non-equilibrium (NE) fluctuation-dissipation (FD) relations in the context of quantum thermoelectric transport through a two-terminal nanodevice, in the steady-state and with interaction. The FD relations for the one- and two-particle correlation functions are derived. Numerical applications, using self-consistent NE Green's functions calculations, are given for electron-phonon interaction in the central region. We find that the FD relations for the one-particle correlation function are strongly dependent on both the NE conditions and the interactions, while they are much less dependent on the interactions for the two-particle correlation. This suggests interesting applications for single-molecule and other nanoscale transport experiments: the two-particle correlation functions, obtained from noise and transport measurement, provide information about the gradients of chemical potential and temperature, and other properties of the system.

cond-mat.mes-hall↗

arXiv2012

Dynamical equations for time-ordered Green's functions: from the Keldysh time-loop contour to equilibrium at finite and zero temperature

We study the dynamical equation of the time-ordered Green's function at finite temperature. We show that the time-ordered Green's function obeys a conventional Dyson equation only at equilibrium and in the limit of zero-temperature. In all other cases, i.e. finite-temperature at equilibrium or non-equilibrium, the time-ordered Green's function obeys instead a modified Dyson equation. The derivation of this result is obtained from the general formalism of the non-equilibrium Green's functions on the Keldysh time-loop contour. At equilibrium, our result is fully consistent with the Matsubara temperature Green's function formalism and also justifies rigorously the correction terms introduced in an ad hoc way with Hedin and Lundqvist. Our results show that one should use the appropriate dynamical equation for the time-ordered Green's function when working beyond the equilibrium zero-temperature limit.

cond-mat.other↗

arXiv2012

Non-equilibrium renormalised contacts for transport in nanodevices with interaction: a quasi-particle approach

We present an application of a new formalism to treat the quantum transport properties of fully interacting nanoscale junctions. We consider a model single-molecule nanojunction in the presence of two kinds of electron-vibron interactions. In terms of the electron density matrix, one interaction is diagonal in the central region and the second off-diagonal between the central region and the left electrode. We use a non-equilibrium Green's function technique to calculate the system's properties in a self-consistent manner. The interaction self-energies are calculated at the Hartree-Fock level in the central region and within a dynamical mean-field-like approach for the crossing interaction. Our calculations are performed for different transport regimes ranging from the far off-resonance to the quasi-resonant regime, and for a wide range of parameters. They show that a non-equilibrium (i.e. bias dependent) dynamical (i.e. energy dependent) renormalisation is obtained for the contact between the left electrode and the central region in the form of a non-equilibrium renormalisation of the lead embedding potential. The conductance is affected by the renormalisation of the contact: the amplitude of the main resonance peak is modified as well as `the lineshape of the first vibron side-band.

cond-mat.mes-hall↗

arXiv2012

Non-equilibrium transport with self-consistent renormalised contacts for a single-molecule nanodevice with electron-vibron interaction

We present an application of a new formalism to treat the quantum transport properties of fully interacting nanoscale junctions [Phys. Rev. B {\bf 84}, 235428 (2011)]. We consider a model single-molecule nanojunction in the presence of two kinds of electron-vibron interactions. In terms of electron density matrix, one interaction is diagonal in the central region and the second is off-diagonal in between the central region and the left electrode. We use a non-equilibrium Green's function technique to calculate the system's properties in a self-consistent manner. The interaction self-energies are calculated at the Hartree-Fock level in the central region and at the Hartree level for the crossing interaction. Our calculations are performed for different transport regimes ranging from the far off-resonance to the quasi-resonant regime, and for a wide range of parameters. They show that a non-equilibrium (i.e. bias dependent) static (i.e. energy independent) renormalisation is obtained for the nominal hopping matrix element between the left electrode and the central region. Such a renormalisation is highly non-linear and non-monotonic with the applied bias, however it always lead to a reduction of the current, and also affects the resonances in the conductance. Furthermore, we show that the relationship between the non-equilibrium charge susceptibility and dynamical conductance still holds even in the presence of crossing interaction.

cond-mat.mes-hall↗

arXiv2012

Many-body current formula and current conservation for non-equilibrium fully interacting nanojunctions

We consider the electron transport properties through fully interacting nanoscale junctions beyond the linear-response regime. We calculate the current flowing through an interacting region connected to two interacting leads, with interaction crossing at the left and right contacts, by using a non-equilibrium Green's functions (NEGF) technique. The total current at one interface (the left one for example) is made of several terms which can be regrouped into two sets. The first set corresponds to a very generalised Landauer-like current formula with physical quantities defined only in the interacting central region and with renormalised lead self-energies. The second set characterises inelastic scattering events occurring in the left lead. We show how this term can be negligible or even vanish due to the pseudo-equilibrium statistical properties of the lead in the thermodynamic limit. The expressions for the different Green's functions needed for practical calculations of the current are also provided. We determine the constraints imposed by the physical condition of current conservation. The corresponding equation imposed on the different self-energy quantities arising from the current conservation is derived. We discuss in detail its physical interpretation and its relation with previously derived expressions. Finally several important key features are discussed in relation to the implementation of our formalism for calculations of quantum transport in realistic systems.

cond-mat.mes-hall↗

arXiv2012

Non-equilibrium charge susceptibility and dynamical conductance: Identification of scattering processes in quantum transport

We calculate the non-equilibrium charge transport properties of nanoscale junctions in the steady state and extend the concept of charge susceptibility to the non-equilibrium conditions. We show that the non-equilibrium charge susceptibility is related to the non-linear dynamical conductance. In spectroscopic terms, both contain the same features versus applied bias when charge fluctuation occurs in the corresponding electronic resonances. However, we show that while the conductance exhibits features at biases corresponding to inelastic scattering with no charge fluctuations, the non-equilibrium charge susceptibility does not. We suggest that measuring both the non-equilibrium conductance and charge susceptibility in the same experiment will permit us to differentiate between different scattering processes in quantum transport.

cond-mat.mes-hall↗

arXiv2012

Functionality in single-molecule devices: Model calculations and applications of the inelastic electron tunneling signal in molecular junctions

We analyze how functionality could be obtained within single-molecule devices by using a combination of non-equilibrium Green's functions and ab-initio calculations to study the inelastic transport properties of single-molecule junctions. First we apply a full non-equilibrium Green's function technique to a model system with electron-vibration coupling. We show that the features in the inelastic electron tunneling spectra (IETS) of the molecular junctions are virtually independent of the nature of the molecule-lead contacts. Since the contacts are not easily reproducible from one device to another, this is a very useful property. The IETS signal is much more robust versus modifications at the contacts and hence can be used to build functional nanodevices. Second, we consider a realistic model of a organic conjugated molecule. We use ab-initio calculations to study how the vibronic properties of the molecule can be controlled by an external electric field which acts as a gate voltage. The control, through the gate voltage, of the vibron frequencies and (more importantly) of the electron-vibron coupling enables the construction of functionality: non-linear amplification and/or switching is obtained from the IETS signal within a single-molecule device.

cond-mat.mes-hall↗

arXiv2011

Non-equilibrium quantum transport in fully interacting single-molecule nanojunctions

Using non-equilibrium Green's functions, we derive a formula for the electron current through a lead-molecule-lead nanojunction where the interactions are not restricted to the central region, but are spread throughout the system, including the leads and the lead-molecule interfaces. The current expression consists of two sets of terms. The first set corresponds to a generalised Meir and Wingreen expression where the leads' self-energies are renormalised by the interactions crossing at the molecule-lead contacts. The second set corresponds to inelastic scattering events in the leads arising from any arbitrary interaction, including electron-electron and electron-phonon coupling, treated beyond mean-field approximations. Using different levels of approximation, we are able to recover well-known expressions for the current. We also analyse how practical calculations can be performed with our formalism by using the new concept of generalised embedding potentials.

cond-mat.mes-hall↗

arXiv2011

GW approximations and vertex corrections on the Keldysh time-loop contour: application for model systems at equilibrium

We provide the formal extension of Hedin's GW equations for single-particle Green's functions with electron-electron interaction onto the Keldysh time-loop contour. We show an application of our formalism to the plasmon model of a core electron within the plasmon-pole approximation. We study in detail the diagrammatic perturbation expansion of the core-electron/plasmon coupling on the spectral functions of the so-called S-model which provides an exact solution, concentrating especially on the effects of self-consistency and vertex corrections on the GW self-energy. For the S-model, self-consistency is essential for GW-like calculations to obtain the full spectral information. The second- order exchange diagram (i.e. a vertex correction) is crucial to obtain a better spectral description of the plasmon peak and side-band peaks in comparison to GW-like calculations. However, the vertex corrections are well reproduced within a non-self-consistent calculation. We also consider conventional equilibrium GW calculations for the pure jellium model. We find that with no second-order vertex correction, we cannot obtain the full set of plasmon side-band peaks. Finally, we address the issues of formal connection for the Dyson equations of the time-ordered Green's function and the Keldysh Green's functions at equilibrium in the cases of zero and finite temperature.

cond-mat.other↗

arXiv2011

Non-equilibrium inelastic electronic transport: Polarization effects and vertex corrections to the self-consistent Born approximation

We study the effect of electron-vibron interactions on the inelastic transport properties of single-molecule nanojunctions. We use the non-equilibrium Green's functions technique and a model Hamiltonian to calculate the effects of second-order diagrams (double-exchange DX and dressed-phonon DPH diagrams) on the electron-vibration interaction and consider their effects across the full range of parameter space. The DX diagram, corresponding to a vertex correction, introduces an effective dynamical renormalization of the electron-vibron coupling in both the purely inelastic and the inelastic-resonant features of the IETS. The purely inelastic features correspond to an applied bias around the energy of a vibron, while the inelastic-resonant features correspond to peaks (resonance) in the conductance. The DPH diagram affects only the inelastic resonant features. We also discuss the circumstances in which the second-order diagrams may be approximated in the study of more complex model systems.

cond-mat.mes-hall↗

arXiv2010

Generalization and applicability of the Landauer formula for non-equilibrium current in the presence of interactions

Using non-equilibrium Green's functions (NEGF), we calculate the current through an interacting region connected to non-interacting leads. The problem is reformulated in such a way that a Landauer-like term appears in the current as well as extra terms corresponding to non-equilibrium many-body effects. The interaction in the central region renormalizes not only the Green's functions but also the coupling at the contacts between the central region and the leads, allowing the total current to be further expressed as a generalized Landauer-like current formula. The general expression for the dynamical functional that renormalizes the contacts is provided. We analyze in detail under what circumstances Landauer-like approaches to the current, i.e. without contact renormalization, are valid for interacting electron-electron and/or electron-phonon systems. Numerical NEGF calculations are then performed for a model electron-phonon coupled system in order to validate our analytical approach. We show that the conductance for the off-resonant transport regime is adequately described by Landauer-like approach in the small-bias limit, while for the resonant regime the Landauer-like approach results depart from the exact results even at small finite bias. The validity of applying a Landauer-like approach to inelastic electron tunneling spectroscopy is also studied in detail.

cond-mat.mes-hall↗

arXiv2010

Non-equilibrium electronic structure of interacting single-molecule nanojunctions: vertex corrections and polarization effects for the electron-vibron coupling

We consider the interaction between electrons and molecular vibrations in the context of electronic transport in nanoscale devices. We present a method based on non-equilibrium Green's functions to calculate both equilibrium and non-equilibrium electronic properties of a single-molecule junction in the presence of electron-vibron interactions. We apply our method to a model system consisting of a single electronic level coupled to a single vibration mode in the molecule, which is in contact with two electron reservoirs. Higher-order diagrams beyond the usual self-consistent Born approximation (SCBA) are included in the calculations. In this paper we consider the effects of the double-exchange diagram and the diagram in which the vibron propagator is renormalized by one electron-hole bubble. We study in detail the effects of the first- and second-order diagrams on the spectral functions for a large set of parameters and for different transport regimes (resonant and off-resonant cases), both at equilibrium and in the presence of a finite applied bias. We also study the linear response (linear conductance) of the nanojunction for all the different regimes. We find that it is indeed necessary to go beyond the SCBA in order to obtain correct results for a wide range of parameters.

cond-mat.mes-hall↗

arXiv2002

Hybrid Luttinger liquid/Fermi liquid behaviour in an atomic wire on a surface

Recent advances in single atom manipulation have made it possible to create "wires" in the form of atomic scale linear structures on a semiconductor surface. If such structures are to be used in future electronic devices, it will be necessary to know to what extent they behave as one-dimensional conductors, in which the presence of electron-electron interactions in the wire lead to properties quite different from those found in higher-dimensional systems. In particular, it would be useful to know if these structures retain any of the Luttinger liquid properties that are predicted for a pure one-dimensional metal. However, experimental studies of such structures have so far yielded unclear and contradictory results. We investigate this problem theoretically by creating a highly simplified model of a wire on a surface--a chain of atoms that includes electron-electron interactions to represent the wire, coupled to a similar chain that excludes electron-electron interactions to represent, albeit crudely, the surface. We present results for the eigenstates and spectral functions for such systems that suggest that many Luttinger liquid indicators are present. However the system as a whole retains some residual Fermi liquid characteristics, and therefore merges properties of both one and higher dimensions.

cond-mat.str-el↗

arXiv2001

Does Luttinger liquid behaviour survive in an atomic wire on a surface?

We form a highly simplified model of an atomic wire on a surface by the coupling of two one-dimensional chains, one with electron-electron interactions to represent the wire and and one with no electron-electron interactions to represent the surface. We use exact diagonalization techniques to calculate the eigenstates and response functions of our model, in order to determine both the nature of the coupling and to what extent the coupling affects the Luttinger liquid properties we would expect in a purely one-dimensional system. We find that while there are indeed Luttinger liquid indicators present, some residual Fermi liquid characteristics remain.

cond-mat.str-el↗