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

G. Q. Garcia; D. C. Moreira; E. Cavalcante; C. Furtado

doi:10.1209/0295-5075/ae44c7

Issue		EPL Volume 153, Number 4, February 2026


Article Number		46001
Number of page(s)		6
Section		Condensed matter and materials physics
DOI		https://doi.org/10.1209/0295-5075/ae44c7
Published online		20 February 2026

EPL, 153 (2026) 46001

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

G. Q. Garcia¹ (This email address is being protected from spambots. You need JavaScript enabled to view it. ), D. C. Moreira¹ (This email address is being protected from spambots. You need JavaScript enabled to view it. ), E. Cavalcante² (This email address is being protected from spambots. You need JavaScript enabled to view it. ) and C. Furtado³ (This email address is being protected from spambots. You need JavaScript enabled to view it. )

¹ Centro de Ciências, Tecnologia e Saúde, Universidade Estadual da Paraíba - 58233-000, Araruna, PB, Brazil
² Centro de Ciências e Tecnologia, Universidade Estadual da Paraíba - 58429-500, Campina Grande, PB, Brazil
³ Departamento de Física, Universidade Federal da Paraíba - 58051-970, João Pessoa, PB, Brazil

Received: 2 December 2025
Accepted: 11 February 2026

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.

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