Eur. Phys. J. B (2018) 91: 118
https://doi.org/10.1140/epjb/e2018-90162-1

Regular Article

Time-dependent i-DFT exchange-correlation potentials with memory: applications to the out-of-equilibrium Anderson model^★

¹ Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Dpto. de Física de Materiales, Universidad del País Vasco UPV/EHU, Av. Tolosa 72, 20018 San Sebastián, Spain
² IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
³ Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, 20018 San Sebastián, Spain
⁴ Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
⁵ INFN, Sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy

^a e-mail: stefan.kurth@ehu.es

Received: 13 March 2018
Received in final form: 20 April 2018
Published online: 13 June 2018

Abstract

We have recently put forward a steady-state density functional theory (i-DFT) to calculate the transport coefficients of quantum junctions. Within i-DFT it is possible to obtain the steady density on and the steady current through an interacting junction using a fictitious noninteracting junction subject to an effective gate and bias potential. In this work we extend i-DFT to the time domain for the single-impurity Anderson model. By a reverse engineering procedure we extract the exchange-correlation (xc) potential and xc bias at temperatures above the Kondo temperature T_K. The derivation is based on a generalization of a recent paper by Dittmann et al. [N. Dittmann et al., Phys. Rev. Lett. 120, 157701 (2018)]. Interestingly the time-dependent (TD) i-DFT potentials depend on the system’s history only through the first time-derivative of the density. We perform numerical simulations of the early transient current and investigate the role of the history dependence. We also empirically extend the history-dependent TD i-DFT potentials to temperatures below T_K. For this purpose we use a recently proposed parametrization of the i-DFT potentials which yields highly accurate results in the steady state.