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 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.

Close

PrevNext

View figure in article

• Anomalous Hall effect
• Berry curvature
• Dirac fermions
• Quantum transport
• Topological insulators
• Boltzmann theory
• Semiclassical methods