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

2025/12/02 by G. Q. Garcia, D. C. Moreira, Garcia, G. Q. +5
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Non-Hermitian Physics #Topological Materials and Phenomena

paper · pdf · doi:10.48550/arxiv.2512.02949

openalex publication_date 2025/12/02 · openalex created_date 2025/12/04 · openalex updated_date 2026/07/28

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.

Citations

• When Adiabaticity Is Not Enough to Study Topological Phases in Solid-State Physics: Comparing the Berry and Aharonov-Anandan Phases in 2D Materials
• Landau levels for massive disclinated graphene-based topological insulator
• Observation of 2D Weyl Fermion States in Epitaxial Bismuthene
• Holographic Topological Semimetals
• Non-relativistic holography
• Large N field theories, string theory and gravity
• The Large N Limit of Superconformal Field Theories and Supergravity
• Significance of Electromagnetic Potentials in the Quantum Theory

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