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

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.

11 pages, 7 figures

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• Density-potential mappings in quantum dynamics
• Some open questions in TDDFT: Clues from Lattice Models and Kadanoff-Baym Dynamics
• Interacting fermions in 1D disordered lattices: Exploring localization and transport properties with lattice density-functional theories
• Disorder and interactions in systems out of equilibrium: The exact independent-particle picture from density functional theory
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