Quantum Hall effect and Quantum spin Hall effect

The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductivity σ takes on the quantized values

σ =ν e2/h( ν multiplied by e square divided by h)

where e is the elementary charge and h is Planck's constant. The prefactor ν is known as the "filling factor", and can take on either integer ( ν = 1, 2, 3, etc...) or rational fraction ( ν = 1/3, 1/5, 5/2, 12/5 etc...) values. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction respectively. The integer quantum Hall effect is very well understood,and can be simply explained in terms of single particle orbitals of an electron in a magnetic field The fractional quantum Hall effect, however, is more complicated, and its existence relies fundamentally on electron-electron interactions.[...]

Quantum spin Hall effect:The quantum spin Hall state is a state of matter proposed to exist in special, two-dimensional, semiconductors with spin-orbit coupling. The quantum spin Hall state of matter is the cousin of the integer quantum Hall state, but, unlike the latter, it does not require the application of a large magnetic field. The quantum spin Hall state does not break any discrete symmetries (such as time-reversal or parity). It has been recently proposed and subsequently experimentally realized in mercury (II) telluride (HgTe) semiconductors.
The first proposal for the existence of a quantum spin Hall state was developed by Kane and Mele who adapted an earlier model for graphene by Haldane which exhibits an integer quantum Hall effect. The Kane and Mele model is two copies of the Haldane model such that the spin up electron exhibits a chiral integer quantum Hall Effect while the spin down electron exhibits and anti-chiral integer quantum Hall effect. Overall this idealized model has a charge-Hall conductance of exactly zero but a spin-Hall conductance of exactly σ(spin xy)=2 (in units of e/4pi). Independently, a quantum spin Hall model was proposed by Bernevig and Zhang in an intricate strain architecture which engineers, due to spin-orbit coupling, a magnetic field pointing upwards for spin-up electrons and a magnetic field pointing downwards for spin-down electrons. The main ingredient is the existence of spin-orbit coupling, which can be understood as a momentum-dependent magnetic field coupling to the spin of the electron.

Novel Quantum Effect, Quantum Spin Hall Effect, Directly Observed And Explained:Physicists has succeeded in gaining an in-depth insight into a most unusual phenomenon. They succeeded for the first time in directly measuring the spin of electrons in a material that exhibits the quantum spin Hall effect, which was theoretically predicted in 2004 and first observed in 2007. Astonishingly, the spin currents flow without any external stimulus as a result of the internal structure of the material. The electrons mimic the presence of a magnetic field.[...]