An Antisymmetric Berry Frictional Force At Equilibrium in the Presence of Spin-Orbit Coupling

TL;DR

This paper analytically demonstrates that electronic friction near a metal surface with spin-orbit coupling includes a significant antisymmetric Berry force component at equilibrium, which can dominate dissipation and influence spin-dependent chemical processes.

Contribution

It reveals the presence of an antisymmetric Berry frictional force at equilibrium in systems with complex electronic Hamiltonians due to spin-orbit coupling.

Findings

Friction tensor is not symmetric at equilibrium when spin-orbit coupling is present.

The friction tensor includes a Berry pseudomagnetic force component.

Berry force can surpass dissipative forces, affecting spin-polarized currents.

Abstract

We analytically calculate the electronic friction tensor for a molecule near a metal surface in the case that the electronic Hamiltonian is complex-valued, e.g. the case that there is spin-orbit coupling and/or an external magnetic field. In such a case, even at equilibrium, we show that the friction tensor is not symmetric. Instead, the tensor is the real-valued sum of one positive definite tensor (corresponding to dissipation) plus one antisymmetric tensor (corresponding to a Berry pseudomagnetic force). Moreover, we find that this Berry force can be much larger than the dissipational force, suggesting the possibility of strongly spin-polarized chemicurrents or strongly spin-dependent rate constants for systems with spin-orbit coupling.