Generalization and applicability of the Landauer formula for nonequilibrium current in the presence of interactions

2017

Entropy

Abstract:We consider the generic model of a finite-size quantum electron system connected to two (temperature and particle) reservoirs. The quantum open system is driven out of equilibrium by the presence of both potential temperature and chemical differences between the two reservoirs. The nonequilibrium (NE) thermodynamical properties of such a quantum open system are studied for the steady state regime. In such a regime, the corresponding NE density matrix is built on the so-called generalised Gibbs ensembles. From different expressions of the NE density matrix, we can identify the terms related to the entropy production in the system. We show, for a simple model, that the entropy production rate is always a positive quantity. Alternative expressions for the entropy production are also obtained from the Gibbs-von Neumann conventional formula and discussed in detail. Our results corroborate and expand earlier works found in the literature.

Section: An Examplementioning

confidence: 99%

Section: An Example For the Entropy Of The Central Regionmentioning

confidence: 99%

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

2017

Entropy

“…A full description of our methodology, for the interaction inside the region C, is provided in Refs. [78][79][80]. Furthermore, we consider that the electron-vibron interaction exist also at one contact (the left L electrode for instance).…”

Section: A Hamiltoniansmentioning

confidence: 99%

Nonequilibrium transport with self-consistent renormalized contacts for a single-molecule nanodevice with electron-vibron interaction

Dash

2012

Phys. Rev. B

Self Cite

We present an application of a new formalism to treat the quantum transport properties of fully interacting nanoscale junctions [Phys. Rev. B 84, 235428 (2011)]. We consider a model singlemolecule 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 offdiagonal 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. I. INTROThe theory of quantum transport in nano-scale devices has evolved rapidly over the past decade, as advances in experimental techniques have made it possible to probe transport properties (at different temperatures) down to the single-molecule scale. Furthermore simultaneous measurement of charge and heat transport through single molecules is now also possible 1 . The development of accurate theoretical methods for the description of quantum transport at the single-molecule level is essential for continued progress in a number of areas including molecular electronics, spintronics, and thermoelectrics.One of the longstanding problems of quantum charge transport is the establishment of a theoretical framework which allows for quantitatively accurate predictions of conductance from first principles. The need for methods going beyond the standard approach based on density functional theory combined with Landauer-like elastic scattering 2-12 has been clear for a number of years. It is only recently that more advanced methods to treat electronic interaction have appeared, for example those based on the many-body GW approximation 13-15 . Alternative frameworks to deal with the steady-state or timedependent transport are given by many-body perturbation theory based on the non-equilibrium (NE) Green's function (GF) formalism: in these approaches, the interactions and (initial) correlations are taken into account by using conserving approximations for the many-body self-energy [16][17][18][19][20][21][22][23][24][25] . Other kinds of interactions, e.g. electron-vibron coupling, also play an impo...

“…The current is calculated as in Ref. [4] using different approximations for the NE distribution function.…”

Section: Approximated Ne Distributionsmentioning

confidence: 99%

“…This was done in a critical analysis of the applicability of Landauer formalism for NE current in the presence of interactions 4 , and in the study of the NE charge susceptibility and its relation with the nonlinear dynamical conductance 5 .…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium distribution functions for quantum transport: Universality and approximation for the steady state regime

2014

Phys. Rev. B

Self Cite

We derive a general expression for the electron nonequilibrium (NE) distribution function in the context of steady state quantum transport through a two-terminal nanodevice with interaction. The central idea for the use of NE distributions for open quantum systems is that both the NE and many-body (MB) effects are taken into account in the statistics of the finite size system connected to reservoirs. We develop an alternative scheme to calculate the NE steady state properties of such systems. The method, using NE distribution and spectral functions, presents several advantages, and is equivalent to conventional steady-state NE Green's functions (NEGF) calculations when the same level of approximation for the MB interaction is used. The advantages of our method resides in the fact that the NE distribution and spectral functions have better analytic behaviour for numerical calculations. Furthermore our approach offer the possibility of introducing further approximations, not only at the level of the MB interaction as in NEGF, but also at the level of the functional form used for the NE distributions. For the single level model with electron-phonon coupling we have considered, such approximations provide a good representation of the exact results, for either the NE distributions themselves or the transport properties. We also derive the formal extensions of our method for systems consisting of several electronic levels and several vibration modes.