Are current-induced forces conservative?

TL;DR

This paper investigates whether current-induced forces are conservative, combining theoretical derivations and first-principles calculations to challenge existing assumptions and provide new insights into their fundamental nature.

Contribution

It offers a detailed analysis and physical mechanisms that question the conservativeness of current-induced forces, supported by first-principles calculations.

Findings

Force can be derived from first principles without assuming conservativeness.

Arguments suggesting non-conservativeness are invalidated by proposed mechanisms.

Results advance understanding but do not definitively resolve the question.

Abstract

The expression for the force on an ion in the presence of current can be derived from first principles without any assumption about its conservative character. However, energy functionals have been constructed that indicate that this force can be written as the derivative of a potential function. On the other hand, there exist compelling specific arguments that strongly suggest the contrary. We propose physical mechanisms that invalidate such arguments and demonstrate their existence with first-principles calculations. While our results do not constitute a formal resolution to the fundamental question of whether current-induced forces are conservative, they represent a substantial step forward in this direction.