Abstract
The valley Hall conductivity, having opposite signs between the K and K′ valleys, is calculated in disordered monolayer graphene with gap. In ideal graphene without disorder, it is quantized into ±e2/2h within the gap and its absolute value decreases in proportion to the inverse of the Fermi energy in the band continuum. In the presence of scatterers, the Hall conductivity in the band continuum is strongly enhanced. This enhancement depends on explicit form of scattering potential even in the clean limit where the concentration and strength of scatterers are vanishingly small. Numerical calculations performed within the self-consistent Born approximation for scatterers with Gaussian potential and for charged impurities show that the valley Hall conductivity remains appreciable in the presence of large disorder and exhibits double-peak structure near zero energy.
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