Universal phase diagrams for the quantum spin Hall systems

Details Universal phase diagrams for the quantum spin Hall systems Universal phase diagrams for the quantum spin Hall systems

2008-06-20

arxiv.org/abs/0806.3309v2

Phys. Rev. B 78, 165313 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

10 pages, 8 figures, minor changes, to be published in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.78.165313

We describe how the three-dimensional quantum spin Hall phase arises from the insulator phase by changing an external parameter. In 3D systems without inversion symmetry, a gapless phase should appear between the two phases with a bulk gap. The gapless points are monopoles and antimonopoles (in k space), whose topological nature is the source of this gapless phase. In general, when the external parameter is changed from the ordinary insulator phase, two monopole-antimonopole pairs are created and the system becomes gapless. The gap-closing points (monopoles and antimonopoles) then move in the k space as the parameter is changed further. They eventually annihilate in pairs, with changing partners from the pair creations, and the system opens a gap again, entering into the quantum spin Hall phase.

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