Universal phase diagrams for the quantum spin Hall systems
Abstract
We describe how the three-dimensional (3D) 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.
- Publication:
-
Physical Review B
- Pub Date:
- October 2008
- DOI:
- 10.1103/PhysRevB.78.165313
- arXiv:
- arXiv:0806.3309
- Bibcode:
- 2008PhRvB..78p5313M
- Keywords:
-
- 85.75.-d;
- 72.25.Dc;
- 73.43.Nq;
- Magnetoelectronics;
- spintronics: devices exploiting spin polarized transport or integrated magnetic fields;
- Spin polarized transport in semiconductors;
- Quantum phase transitions;
- Condensed Matter - Mesoscopic Systems and Quantum Hall Effect
- E-Print:
- 10 pages, 8 figures, minor changes, to be published in Phys. Rev. B