Non-Abelian properties of electron wave packets in Dirac semimetals A$_3$Bi (A=Na,K,Rb)

TL;DR

This paper investigates the non-Abelian Berry curvature effects on electron wave packet trajectories in Dirac semimetals A$_3$Bi, revealing how electromagnetic fields influence valley and chirality splitting due to their non-Abelian properties.

Contribution

It demonstrates the impact of non-Abelian Berry curvature on wave packet dynamics in Dirac semimetals, highlighting field-dependent valley and chirality splitting phenomena.

Findings

Valley splitting occurs in parallel electric and magnetic fields.

Chirality separation is prominent for initially polarized states.

Deviations from Abelian trajectories are observed in perpendicular fields.

Abstract

The motion of electron wave packets in the Dirac semimetals A$_3$Bi (A=Na,K,Rb) is studied in a semiclassical approximation. Because of the two-fold degeneracy of the Dirac points and a momentum-dependent gap term in the low-energy Hamiltonian, the associated Berry curvature is non-Abelian. In the presence of background electromagnetic fields, such a Berry curvature leads to a splitting of trajectories for the wave packets that originate from different Dirac points and chiral sectors. The nature of the splitting strongly depends on the background fields as well as the initial chiral composition of the wave packets. In parallel electric and magnetic fields, while a well pronounced valley splitting is achieved for any chirality composition, the chirality separation takes place predominantly for the initially polarized states. On the other hand, in perpendicular electric and magnetic fields, there are clear deviations from the conventional Abelian trajectories, albeit without a well-pronounced valley splitting.