Parallel magnetic field driven quantum phase transition in a thin topological insulator film

@article{Zyuzin2011ParallelMF,
  title={Parallel magnetic field driven quantum phase transition in a thin topological insulator film},
  author={Alexander A. Zyuzin and Michael David Hook and Anton A. Burkov},
  journal={Physical Review B},
  year={2011},
  volume={83}
}
It is well-known that helical surface states of a three-dimensional topological insulator (TI) do not respond to a static in-plane magnetic field. Formally this occurs because the in-plane magnetic field appears as a vector potential in the Dirac Hamiltonian of the surface states and can thus be removed by a gauge transformation of the surface electron wavefunctions. Here we show that when the top and bottom surfaces of a thin film of TI are hybridized and the Fermi level is in the… 

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