Zitterbewegung velocity in semiclassical electron dynamics

TL;DR

This paper introduces a new Zitterbewegung velocity in semiclassical electron dynamics, derived from the quantum Liouville equation, explaining phenomena like position shifts and minimum conductivity in Dirac fermions.

Contribution

It identifies a novel Zitterbewegung velocity involving quantum geometric tensor components, enhancing semiclassical models of electron behavior in solids.

Findings

Resolves the position-shift paradox in electron dynamics.

Links Zitterbewegung velocity to minimum conductivity in Dirac fermions.

Provides a new framework for semiclassical electron dynamics.

Abstract

Zitterbewegung plays a major role in electron dynamics in solids, yet is not captured in conventional semiclassical treatments. Here, starting from the quantum Liouville equation, I identify a new Zitterbewegung velocity, which involves the symmetric and antisymmetric components of the quantum geometric tensor oscillating out of phase. The Zitterbewegung velocity resolves the position-shift paradox, recovering the field-induced shift in an electron's position by integrating the semiclassical equations, and is directly related to the famous minimum conductivity of massless Dirac fermions.