Download Localized Wave Function of the 2D Topological Insulator in a

Localized Wave Function of the 2D Topological Insulator in a Graphene Structure
(Talk/poster #: to be completed by the Organizer)
A. Hyeonjin Doh1,*, Gun Sang Jeon2
1
Department of Physics, Konkuk University, Seoul, Republic of Korea
2
Department of Physics, Ewha Womans University, Seoul, Republic of Korea
*Email of Presenting Author: [email protected]
We investigate the edge state of the Quantum Spin Hall effects which appears in a
honeycomb lattice described by the Kane-Mele (KM) model[1]. It is well know that the KM
model with a finite spin-orbit interaction is suggested for a 2D topological insulator[2] which
shows an insulating gap in a bulk state and a metallic state on the boundary. This metallic
edge state is attributed to the Z2 topological nature of the bulk gap and is protected by the
time reversal symmetry. We build coupled equations for the energy and the localized wave
functions of the edge state through Harper’s equation of the KM model. We obtain the
explicit dependencies of the localization of the wave function and the energy dispersion of
the edge state on the momentum and spin-orbit interaction. Our results show the wave
function of the edge state is well-localized and robust up to a certain parameter range.
Beyond the critical values of the parameters, however, the localization length of the wave
function increases quickly and finally diverges to become the bulk state. We also discuss the
control of the localization length by changing the gate voltage in experiments.
References:
[1] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
[2] B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006)