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Z_2 topological invariant and solutions of the Dirac equation | | Shun-Qing Shen
; Wen-Yu Shan
; Hai-Zhou Lu
; | | Date: |
28 Sep 2010 | | Abstract: | We present a general description of topological insulators from the point of
view of the Dirac equation. The Z_2 index for the Dirac equation is always
zero, and thus the Dirac equation is topologically trivial. After the quadratic
Bp^2 term in momentum p is introduced to correct the band gap mv^2 of the Dirac
equation (v has the dimension of speed), the Z_2 index is modified as 1 for a
dimensionless parameter mB>0 and 0 for mB<0. For a fixed B there exists a
topological quantum phase transition from a topologically trivial system to a
non-trivial one system when the sign of the band gap mv^2 changes. A series of
solutions near the boundary in the modified Dirac equation are obtained, which
is characteristic of topological insulator. From the solutions of the bound
states and the Z_2 index we establish an explicit relation between the Dirac
equation and topological insulators. | | Source: | arXiv, 1009.5502 | | Services: | Forum | Review | PDF | Favorites | |
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