Vibration-induced non-adiabatic geometric phase and energy uncertainty of fermions in grapheneShi-Jie Xiong1 and Ye Xiong2
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 in final form 21 October 2007; published December 2007
published online 13 November 2007
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.
03.65.Vf - Phases: geometric; dynamic or topological.
73.21.-b - Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems.
81.05.Uw - Carbon, diamond, graphite.
© EPLA 2007