Momentum-space dynamics of Dirac quasiparticles in correlated random potentials: Interplay between dynamical and Berry phases

TL;DR

This paper investigates how dynamical and Berry phases influence the momentum distribution of Dirac quasiparticles in correlated disordered lattices, revealing transient asymmetries and interference effects observable in cold atom experiments.

Contribution

It provides a combined numerical and theoretical analysis of Berry phase effects on Dirac quasiparticle dynamics in correlated disorder, highlighting the role of dynamical phases and symmetry breaking.

Findings

Backscattering dip in massless case vanishes due to trigonal warping.

Dynamical phase induces transient broken reflection symmetry.

Berry phase effects are observable in cold atom lattice experiments.

Abstract

We consider Dirac quasi-particles, as realized with cold atoms loaded in a honeycomb lattice or in a $\pi$-flux square lattice, in the presence of a weak correlated disorder such that the disorder fluctuations do not couple the two Dirac points of the lattices. We numerically and theoretically investigate the time evolution of the momentum distribution of such quasi-particles when they are initially prepared in a quasi-monochromatic wave packet with a given mean momentum. The parallel transport of the pseudo-spin degree of freedom along scattering paths in momentum space generates a geometrical phase which alters the interference associated with reciprocal scattering paths. In the massless case, a well-known dip in the momentum distribution develops at backscattering (respective to the Dirac point considered) around the transport mean free time. This dip later vanishes in the honeycomb case because of trigonal warping. In the massive case, the dynamical phase of the scattering paths becomes crucial. Its interplay with the geometrical phase induces an additional transient broken reflection symmetry in the momentum distribution. The direction of this asymmetry is a property of the Dirac point considered, independent of the energy of the wave packet. These Berry phase effects could be observed in current cold atom lattice experiments.