Time-dependent bond-current functional theory for lattice Hamiltonians: fundamental theorem and application to electron transport

TL;DR

This paper develops a time-dependent bond-current functional theory for lattice Hamiltonians, establishing a fundamental theorem and demonstrating its application to electron transport, especially in systems exhibiting Coulomb blockade.

Contribution

It introduces TDBCFT as an alternative to TDDFT for lattice systems, proving a one-to-one correspondence between TD Peierl's phases and bond-currents, and applies it to electron transport scenarios.

Findings

Discontinuities in Kohn-Sham Peierl's phases affect steady-state achievement.

TDBCFT effectively describes Coulomb blockade phenomena.

Explicit time propagation demonstrates the formalism's applicability.

Abstract

The cornerstone of time-dependent (TD) density functional theory (DFT), the Runge-Gross theorem, proves a one-to-one correspondence between TD potentials and TD densities of continuum Hamiltonians. In all practical implementations, however, the basis set is discrete and the system is effectively described by a lattice Hamiltonian. We point out the difficulties of generalizing the Runge-Groos proof to the discrete case and thereby endorse the recently proposed TD bond-current functional theory (BCFT) as a viable alternative. TDBCFT is based on a one-to-one correspondence between TD Peierl's phases and TD bond-currents of lattice systems. We apply the TDBCFT formalism to electronic transport through a simple interacting device weakly coupled to two biased non-interacting leads. We employ Kohn-Sham Peierl's phases which are discontinuous functions of the density, a crucial property to describe Coulomb blockade. As shown by explicit time propagations, the discontinuity may prevent the biased system from ever reaching a steady state.