Truncation method for Green's functions in time-dependent fields

Abstract

We investigate the influence of a time dependent, homogeneous electric field on scattering properties of non-interacting electrons in an arbitrary static potential. We develop a method to calculate the (Keldysh) Green's function in two complementary approaches. Starting from a plane wave basis, a formally exact solution is given in terms of the inverse of a matrix containing infinitely many 'photoblocks' which can be evaluated approximately by truncation. In the exact eigenstate basis of the scattering potential, we obtain a version of the Floquet state theory in the Green's functions language. The formalism is checked for cases such as a simple model of a double barrier in a strong electric field. Furthermore, an exact relation between the inelastic scattering rate due to the microwave and the AC conductivity of the system is derived which in particular holds near or at a metal-insulator transition in disordered systems.

to appear in Phys. Rev. B., 21 pages, 3 figures (ps-files)

References in corpus (6)

• Charging Effects in Ultrasmall Quantum Dots in the Presence of Time-Varying Fields
• Dynamical Franz-Keldysh effect
• Localization Effects in ac-driven Tight-Binding Lattices
• Coherent and sequential photoassisted tunneling through a semiconductor double barrier structure
• Coherent resonant tunneling in ac fields
• Boltzmann equation approach for transport in systems subject to microwave irradiation

Cited by in corpus (18)

• Driven quantum transport on the nanoscale
• Photon-assisted transport in semiconductor nanostructures
• Semiconductor Superlattices: A model system for nonlinear transport
• Current Switch by Coherent Trapping of Electrons in Quantum Dots
• Shot noise control in ac-driven nanoscale conductors
• Role of electronic structure in photoassisted transport through atomic-sized contacts
• Self-consistent ac quantum transport using nonequilibrium Green functions
• Photon-assisted resonant Andreev reflections: Yu-Shiba-Rusinov and Majorana states
• Impact ionization processes in the steady state of a driven Mott insulating layer coupled to metallic leads
• Nonlinear response of quantum cascade structures
• Timescale separation solution of Kadanoff-Baym equations for quantum transport in time-dependent fields
• Full counting statistics for electron transport in periodically driven quantum dots
• Dynamic Stimulation of Quantum Coherence in Lattice Bosons
• Transport signatures in topological systems coupled to AC fields
• Renormalization approach for quantum-dot structures under strong alternating fields
• Quantum transport in driven systems with vibrations: Floquet nonequilibrium Green's functions and the GD approximation
• Higher harmonics and ac transport from time dependent density functional theory
• Quantum circuit refrigerator based on quantum dots coupled to normal-metal and superconducting electrodes