Zero modes and geometric phase for 2D Weyl fermions on Lifshitz backgrounds

TL;DR

This paper explores the properties of Weyl fermions in 2D Lifshitz backgrounds, focusing on geometric phases and zero modes, revealing how geometry influences fermionic behavior.

Contribution

It provides an analytical study of Weyl fermions in Lifshitz spacetimes, deriving geometric phases and exact zero mode solutions using the Dirac phase method and supersymmetric equations.

Findings

Geometric phases arise from fermion-Lifshitz geometry coupling

Exact zero mode solutions are obtained analytically

Fermionic zero modes are well-behaved in the studied backgrounds

Abstract

Here we investigate analytical properties of Weyl fermions in (2+1)-dimensional Lifshitz spacetimes. In particular, we are interested in obtaining geometric phases and verifying the existence of well-behaved fermionic zero modes. Using the Dirac phase method, we show how geometric phases naturally arise from the coupling between the fermionic fields and the Lifshitz geometry. We also present exact solutions of the zero modes by rewriting the Weyl equation as a system of supersymmetric equations.