Driven Liouville-von Neumann Equation for Quantum Transport and Multiple-Probe Green's Functions

FRANCISCO RAMIREZ; DANIEL DUNDAS; CRISTIAN SANCHEZ; DAMIAN A SCHERLIS; TCHAVDAR TODOROV

JOURNAL OF PHYSICAL CHEMISTRY C

AMER CHEMICAL SOC

Lugar: Washington; Año: 2019 vol. 123 p. 12542 - 12555

1932-7447

The so-called driven Liouville−von Neumann equation is adynamical formulation to simulate a voltage bias across a molecular system and tomodel a time-dependent current in a grand-canonical framework. This approachintroduces a damping term in the equation of motion that drives the charge to areference, out of equilibrium density. Originally proposed by Horsfield and coworkers,further work on this scheme has led to different coexisting versions ofthis equation. On the other hand, the multiple-probe scheme devised by Todorovand collaborators, known as the hairy-probes method, is a formal treatment basedon Green?s functions that allows the electrochemical potentials in two regions ofan open quantum system to be fixed. In this article, the equations of motion ofthe hairy-probes formalism are rewritten to show that, under certain conditions,they can assume the same algebraic structure as the driven Liouville−vonNeumann equation in the form proposed by Morzan et al. (J. Chem. Phys. 2017, 146, 044110). In this way, a new formal groundis provided for the latter, identifying the origin of every term. The performances of the different methods are explored usingtight-binding time-dependent simulations in three trial structures, designated as ballistic, disordered, and resonant models. Inthe context of first-principles Hamiltonians, the driven Liouville−von Neumann approach is of special interest, because it doesnot require the calculation of Green?s functions. Hence, the effects of replacing the reference density based on the Green?sfunction by one obtained from an applied field are investigated, to gain a deeper understanding of the limitations and the rangeof applicability of the driven Liouville−von Neumann equation.