Universal phase diagrams for the quantum spin Hall systems

Abstract

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.

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

References in corpus (5)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Dissipationless Quantum Spin Current at Room Temperature
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Tuning phase transition between quantum spin Hall and ordinary insulating phases