Vibration Induced Non-adiabatic Geometric Phase and Energy Uncertainty of Fermions in Graphene

TL;DR

This paper explores how vibrations in graphene induce non-adiabatic geometric phases and energy uncertainties in fermions, revealing regions of stable and chaotic phase behavior with implications for transport properties.

Contribution

It introduces a Floquet-based method to analyze vibrational effects on fermion geometric phases in graphene, highlighting non-adiabatic and chaotic phenomena.

Findings

Geometric phases depend on fermion momentum during vibrations.

Identification of adiabatic and chaotic regions in momentum space.

Vibrations cause energy spikes indicating dephasing mechanisms.

Abstract

We investigate geometric phase of fermion states under relative vibrations of two sublattices in graphene by solving time-dependent Sch\"{o}dinger equation using Floquet scheme. In a period of vibration the fermions acquire different geometric phases depending on their momenta. There are two regions in the momentum space: the adiabatic region where the geometric phase can be approximated by the Berry phase and the chaotic region where the geometric phase drastically fluctuates in changing parameters. The energy of fermions due to vibrations shows spikes in the chaotic region. The results suggest a possible dephasing mechanism which may cause classical-like transport properties in graphene.