Nonequilibrium electronic structure of interacting single-molecule nanojunctions: Vertex corrections and polarization effects for the electron-vibron coupling

Finite Temperature Green's Function Approach for Excited State and Thermodynamic Properties of Cool to Warm Dense Matter

We present a finite-temperature extension of the retarded cumulant Green's function for calculations of exited-state, correlation, and thermodynamic properties of electronic systems. The method incorporates a cumulant to leading order in the screened Coulomb interaction W, and improves on the GW approximation of many-body perturbation theory. Results for the homogeneous electron gas are presented for a wide range of densities and temperatures, from cool to warm dense matter regimes, which reveal several hitherto unexpected properties. For example, correlation effects remain strong at high T while the exchange-correlation energy becomes small; also the spectral function broadens and damping increases with temperature, blurring the usual quasiparticle picture. These effects are evident, e.g., in Compton scattering which exhibits many-body corrections that persist at normal densities and intermediate T. The approach also yields exchange-correlation energies and potentials in good agreement with existing methods.

Padé resummation of many-body perturbation theories

In a typical scenario the diagrammatic many-body perturbation theory generates asymptotic series. Despite non-convergence, the asymptotic expansions are useful when truncated to a finite number of terms. This is the reason for the popularity of leading-order methods such as the GW approximation in condensed matter, molecular and atomic physics. Appropriate truncation order required for the accurate description of strongly correlated materials is, however, not known a priori. Here an efficient method based on the Padé approximation is introduced for the regularization of perturbative series allowing to perform higher-order self-consistent calculations and to make quantitative predictions on the convergence of many-body perturbation theories. The theory is extended towards excited states where the Wick theorem is not directly applicable. Focusing on the plasmon-assisted photoemission from graphene, we treat diagrammatically electrons coupled to the excited state plasmons and predict new spectral features that can be observed in the time-resolved measurements.

Nonequilibrium density matrix in quantum open systems: generalization for simultaneous heat and charge steady-state transport

We suggest a generalization of the expression of the nonequilibrium (NE) density matrix obtained by Hershfield's method for the cases where both heat and charge steady-state currents are present in a quantum open system. The finite-size quantum system, connected to two temperature and particle reservoirs, is driven out of equilibrium by the presence of both a temperature gradient and a chemical potential gradient between the two reservoirs. We show that the NE density matrix is given by a generalized Gibbs-like ensemble and is in full agreement with the general results of the McLennan-Zubarev nonequilibrium ensembles. The extra nonequilibrium terms are related to the entropy production in the system and characterize the fluxes of heat and particle. An explicit example, for the lowest-order expansion, is provide for a model system of noninteracting fermions.

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.

Nonequilibrium density matrix for quantum transport: Hershfield approach as a McLennan-Zubarev form of the statistical operator

In this paper, we formally demonstrate that the nonequilibrium density matrix developed by Hershfield for the steady state has the form of a McLennan-Zubarev nonequilibrium ensemble. The correction term in this pseudoequilibrium Gibbs-like ensemble is directly related to the entropy production in the quantum open system. The fact that both methods state that a nonequilibrium steady state can be mapped onto a pseudoequilibrium, permits us to develop nonequilibrium quantities from formal expressions equivalent to the equilibrium case. We provide an example: the derivation of a nonequilibrium distribution function for the electron population in a scattering region in the context of quantum transport.

Nonequilibrium perturbation theory in Liouville-Fock space for inelastic electron transport

We use a superoperator representation of the quantum kinetic equation to develop nonequilibrium perturbation theory for an inelastic electron current through a quantum dot. We derive a Lindblad-type kinetic equation for an embedded quantum dot (i.e. a quantum dot connected to Lindblad dissipators through a buffer zone). The kinetic equation is converted to non-Hermitian field theory in Liouville-Fock space. The general nonequilibrium many-body perturbation theory is developed and applied to the quantum dot with electron-vibronic and electron-electron interactions. Our perturbation theory becomes equivalent to a Keldysh nonequilibrium Green's function perturbative treatment provided that the buffer zone is large enough to alleviate the problems associated with approximations of the Lindblad kinetic equation.

Nonequilibrium charge susceptibility and dynamical conductance: identification of scattering processes in quantum transport

We calculate the nonequilibrium charge transport properties of nanoscale junctions in the steady state and extend the concept of charge susceptibility to the nonequilibrium conditions. We show that the nonequilibrium charge susceptibility is related to the nonlinear 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 nonequilibrium charge susceptibility does not. We suggest that measuring both the nonequilibrium conductance and charge susceptibility in the same experiment will permit us to differentiate between different scattering processes in quantum transport.