The universality of electronic friction II: Equivalence of the quantum-classical Liouville equation approach with von Oppen's nonequilibrium Green's function methods out of equilibrium

TL;DR

This paper demonstrates the equivalence of the quantum-classical Liouville equation approach with von Oppen's nonequilibrium Green's function methods for electronic friction, extending the universality of the friction tensor to out-of-equilibrium systems with multiple metal surfaces.

Contribution

It proves the equivalence between QCLE and NEGF methods for electronic friction in out-of-equilibrium multi-surface systems, confirming the universality of the electronic friction tensor.

Findings

Established equivalence of QCLE and NEGF approaches out of equilibrium.

Extended the universality of the electronic friction tensor to multiple metal surfaces.

Confirmed the single universal electronic friction tensor from the Born-Oppenheimer approximation.

Abstract

In a recent publication [W. Dou, G. Miao, and J. E. Subotnik, Phys. Rev. Lett. 119, 046001 (2017)], using the quantum-classical Liouville equation (QCLE), we derived a very general form for the electronic friction felt by a molecule moving near one or many metal surfaces. Moreover, we have already proved the equivalence of the QCLE electronic friction with the Head-Gordon--Tully model as well as a generalized version of von Oppen's nonequilibrium Green's function (NEGF) method at equilibrium [W. Dou and J. E. Subotnik, Phys. Rev. B 96, 104305 (2017)]. In the present paper, we now further prove the equivalence between the QCLE friction and the NEGF friction for the case of multiple metal surfaces and an out-of-equilibrium electronic current. The present results conclude our recent claim that there is only one universal electronic friction tensor arising from the Born-Oppenheimer approximation.