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

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.

Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions

“…Therefore the small parameter in our theory is Ω Γ . The solution described below follows closely the ideas of previous authors 36,[56][57][58][59]63 . The exponential operators in Eqs.…”

“…Our aim here is to derive a Langevin-like equation to obtain the stochastic trajectory for the molecular junction geometry x = x(t). Our derivation follows the ideas introduced by von Oppen et al 36 , then later expanded upon by Subotnik and Dou 56,63 .…”

“…There are a number of varying methods for calculating the friction tensor and random force which are the main ingredients of the Langevin equation. These include the use of NEGF methods 36,54,56,[60][61][62][63] , which we will also employ in this paper, as well as scattering theory approaches 35,36,64,65 , path integral methods and influence functional methods [66][67][68] .…”

“…With a handful of exceptions 14,54,56,63,69,70 , all these theoretical approaches largely focus on nuclear motion localized in the central region; however, the motion at the molecule-electrode interface is at least equally important. Large amplitude conformational changes such as chemical reactions, switching between different geometries, localized heating, and electromigration of atoms predominantly occur on the interface in molecular electronic junctions.…”

Non-equilibrium Green’s function theory for non-adiabatic effects in quantum transport: Inclusion of electron-electron interactions

“…24,26,33 The scope of current theoretical work with simultaneous modeling electronic correlations and nuclear dynamics is, at present, limited and all these considering nuclear motion as harmonic vibrations around equilibrium geometry. [78][79][80] Recently, several authors have used gradient expansions, 81 a technique reaching back to work of Kadanoff and Baym, 82 in their theoretical approaches, 24,26,[63][64][65][66][67]83,84 where classically described nuclei are treated as a slow disturbance in non-equilibrium Green's functions. Our previous works expanded on this methodology, where we developed a transport theory in the non-equilibrium Green's function formalism that takes into account the non-adiabatic effects of nuclear motion.…”