Condensed Matter and Biological Physics Seminars

The Quantum Spin Hall is a newly conjectured state of matter that does not brake any discrete symmetries such as time reversal or parity. The state requires spin-orbit coupling and is protected by a Z_2 topological invariant. Initial proposals for such a state in graphene, strained semiconductors, and later Bismuth have proven to be unrealistic due to the small value of spin-orbit coupling and the failure of the tight-binding approximation to match realistic band structures. We predict that a non-trivial topological band-insulator that gives rise to a Quantum Spin Hall state must exist in a series of quantum wells of the inverted band structure variety such as HgTe. A k=0, the inverted band structure in HgTe/CdTe Quantum Wells gives rise to a single Dirac Fermion without the doubling problem, and it can be proved that the Quantum Spin Hall state exists in a range of the quantum well thickness. The interplay of the anomalous Quantum Hall effect and the Quantum Hall effect arising from an external magnetic field is also analized and the structure of the edge states is derived.