Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by Thouless, Kohmoto, Nightingale, and den Nijs to the situation where many-body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect, we draw the conclusion that there must be a symmetry breaking in the many-body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also discussed.
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. The existence of the quantum Hall effect requires ...
The spin Hall effect in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings is studied numerically. Integer quantized spin...
Recent theories predict dissipationless spin current induced by an electric field in doped semiconductors. Nevertheless, the charge current is still dissipative in these systems...
The Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential $U$. The Kubo formula is written in a form...
We propose models of two dimensional paramagnetic semiconductors where the\nintrinsic spin Hall effect is exactly quantized in integer units of a\ntopological charge. The model ...
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