Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime

Abstract

We propose a time-dependent many-body approach to study the short-time dynamics of correlated electrons in quantum transport through nanoscale systems contacted to metallic leads. This approach is based on the time-propagation of the Kadanoff-Baym equations for the nonequilibrium many-body Green's function of open and interacting systems out of equilibrium. An important feature of the method is that it takes full account of electronic correlations and embedding effects in the presence of time-dependent external fields, while at the same time satisfying the charge conservation law. The method further extends the Meir-Wingreen formula to the time domain for initially correlated states. We study the electron dynamics of a correlated quantum wire attached to two-dimensional leads exposed to a sudden switch-on of a bias voltage using conserving many-body approximations at Hartree-Fock, second Born and GW level. We obtain detailed results for the transient currents, dipole moments, spectral functions, charging times, and the many-body screening of the quantum wire as well as for the time-dependent density pattern in the leads, and we show how the time-dependence of these observables provides a wealth of information on the level structure of the quantum wire out of equilibrium. For moderate interaction strenghts the 2B and GW results are in excellent agreement at all times. We find that many-body effects beyond the Hartree-Fock approximation have a large effect on the qualitative behavior of the system and lead to a bias dependent gap closing and quasiparticle broadening, shortening of the transient times and washing out of the step features in the current-voltage curves.

Correlation effects in bistability at the nanoscale: Steady state and beyond

“…(17) requires a transformation into equations for real times, known as KB equations, which are then solved by time propagation. 16,20,21,52 From the knowledge of the Green's function any one-particle property of the system can be extracted. In particular, the time-dependent density can be obtained from the lesser Green's function as…”

“…Therefore the many-body self-energy has nonvanishing elements only for the central region, because the diagrammatic expansion starts and ends with an interaction line. 20,21 Equation (17) is an exact equation for G CC , provided an exact expression for MB is inserted. Of course, for practical calculations the many-body self-energy must be approximated.…”

“…An alternative approach to TDDFT for transport is the time-dependent MBPT formulation of transport 20,21 based on the time evolution of the Green's function via the KB equations. [15][16][17][18][19] In the MBPT, the many-body self-energy MB can be approximated by a selection of suitable Feynman diagrams, relevant for the description of the main scattering processes.…”

“…To overcome the problem we implement a time-dependent strategy. [20][21][22][23][24][25][26][27][28][29][31][32][33][34] We first solve the steady-state equations of DFT and mean-field theory to determine the parameter range for bistability. Then we go beyond the current state-of-the-art and provide a TD description of the bistability phenomenon in adiabatic TDDFT [23][24][25][26][27][28][29] and TD mean-field theory.…”

“…13,14 In the context of time-dependent (TD) DFT, the inclusion of memory effects beyond the adiabatic approximation is not straightforward and the development of accurate functionals to be used in numerical calculations is still under way. A promising and timely, even though computationally demanding, alternative is the solution of the Kadanoff-Baym (KB) equations [15][16][17][18][19][20][21] using self-energies from many-body perturbation theory (MBPT). The advantage of MBPT over TDDFT is the inclusion of dynamical exchangecorrelation (XC) effects, i.e., effects arising from a frequencydependent self-energy, in a more systematic way through the selection of suitable Feynman diagrams.…”