It is shown that the integers found by Thouless et al. in the quantized Hall effect are the only quantized quantities associated with the energy bands. It is also proved that if two bands touch and then come apart as a parameter is varied, then their individual integers (conductances) may not be preserved but their sum is preserved.
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 ...
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 ...
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...
We investigate the electronic spectra and quantum Hall effect in twisted\nbilayer graphenes with various rotation angles under magnetic fields, using a\nmodel rigorously includi...
Quantum anomalous Hall goes intrinsic Quantum anomalous Hall effect—the appearance of quantized Hall conductance at zero magnetic field—has been observed in thin films of the to...
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