Current-induced forces in nanosystems: A hierarchical equations of motion approach

TL;DR

This paper introduces a hierarchical equations of motion approach to accurately compute current-induced forces in nanosystems, enabling analysis of complex transport scenarios with strong interactions.

Contribution

It develops a quantum mechanical framework that derives a classical Langevin equation for vibrational dynamics influenced by electronic forces, improving upon previous models.

Findings

The approach accurately calculates electronic friction in various nanosystems.

It demonstrates the method's effectiveness in systems with strong interactions.

The formalism aligns with existing expressions for electronic friction.

Abstract

A new approach to calculating current-induced forces in charge transport through nanosystems is introduced. Starting from the fully quantum mechanical hierarchical equations of motion formalism, a timescale separation between electronic and vibrational degrees of freedom is used to derive a classical Langevin equation of motion for the vibrational dynamics as influenced by current-induced forces, such as the electronic friction. The resulting form of the friction is shown to be equivalent to previously derived expressions. The numerical exactness of the hierarchical equations of motion approach, however, allows the investigation of transport scenarios with strong intrasystem and system-environment interactions. As a demonstration, the electronic friction of three example systems is calculated and analyzed: a single electronic level coupled to one classical vibrational mode, two electronic levels coupled to one classical vibrational mode, and a single electronic level coupled to both a classical and quantum vibrational mode.