Lorentz violation and momentum-space geometric phases

TL;DR

This paper explores how Lorentz violation influences geometric phases in momentum space for Weyl fermions, revealing topological features and invariants that emerge under significant Lorentz-violating conditions.

Contribution

It demonstrates the presence of adiabatic geometric phases in momentum space for Lorentz-violating Weyl fermions and derives related topological invariants.

Findings

Berry curvature and Chern number calculated for large Lorentz violation cases

Topological phases linked to the physical vacuum in certain scenarios

Alternative topological invariants identified

Abstract

Geometric phases can manifest when a relativistic quantum particle moves cyclically along a loop in parameter space. The phase can be affected by the presence of a background field and can be accompanied by nontrivial topological features. The appearance of adiabatic geometric phases in momentum space is demonstrated for a Lorentz-violating Weyl fermion, where the role of the background is played by the coefficients for Lorentz violation. As explicit examples, the Berry curvature and the first Chern number are derived for two cases with large Lorentz violation, one incorporating CPT violation and one preserving CPT symmetry. Some alternative topological invariants are also obtained. In certain scenarios with large Lorentz violation, the physical vacuum is associated with a topological phase.