Asymptotic self-consistency in quantum transport calculations

Abstract

Ab-initio simulations of quantum transport commonly focus on a central region which is considered to be connected to infinite, periodic leads through which the current flows. The electronic structure of these distant leads is normally obtained from an equilibrium calculation, ignoring the self-consistent response of the leads to the current. We examine the consequences of this, and show that the electrostatic potential, ∆φ, is effectively being approximated by the difference between electrochemical potentials, ∆µ, and that this approximation is incompatible with asymptotic charge neutrality. In a test calculation for a simple metal-vacuum-metal junction, we find large errors in the non-equilibrium properties calculated with this approximation, in the limit of small vacuum gaps. We provide a simple scheme by which these errors may be corrected.

An accurate and efficient self-consistent approach for calculating electron transport through molecular electronic devices: including the corrections of electrodes

“…At zero bias, the energy integration of the retarded Green's function gives the density matrix (equation ( 6)); at nonzero bias, the density matrix can be obtained by performing the energy integration of the matrix correlation function, entering the regime of the non-equilibrium Green's function (NEGF). In practical implementations of the NEGF + DFT method [4,5,[11][12][13], the electrodes are usually assumed to be in local equilibrium but not in equilibrium with each other, and the self-energies are also obtained from an equilibrium calculation, ignoring the self-consistent response of the electrodes to the current [25]. Therefore, we expect our approach to be correct at least at low bias when the current is not too large.…”

Bound states inab initioapproaches to quantum transport: A time-dependent formulation

“…Equations (32,36,40) and the following discussion (including Section V) are the main results of this work.…”

“…7,8 The use of TDDFT in quantum transport is gaining ground 7,8,10,17,18,19,20,21,22,23,24,25,26,27,28,29 and several properties of the time-dependent exchangecorrelation potential and kernel have recently been discussed. 30,31,32,33,34 In a previous work 6 we have shown how a steady current develops under the influence of a constant bias. For non-interacting electrons we also proved that the steady current is independent of the history of the applied bias and agrees with the steady current calculated in the contacting approach.…”

Current-constraining variational approaches to quantum transport

“…The electrons are taken to be non-interacting while in the leads. This construction, however, leads to violation of local charge neutrality in the non-interacting regions as discussed elsewhere 9 . Neither does it clarify the relation between the total and induced electric field.…”

“…typically the electronic structure of the leads are taken as that of the leads in equilibrium. The errors included this way can be assessed and calculations for representative systems suggest them to be no more than a few percent 9 . A second source of discrepancies between the experimental and theoretical work comes from the ambiguity of the geometry of the molecular junction one employs.…”