Vibration-induced non-adiabatic geometric phase and energy uncertainty of fermions in graphene

¹  National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University Nanjing 210093, China
²  College of Physical Science and Technology, Nanjing Normal University - Nanjing 210097, China

Received: 18 June 2007
Accepted: 21 October 2007

Abstract

We investigate the geometric phase of fermion states under relative vibrations of two sublattices in graphene by solving the time-dependent Schödinger equation using the 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.