Breakdown electron-hole symmetry in graphene structure with a semiconductor gate

The electron-hole symmetry in the structure graphene - insulating substrate -semiconductor gate is violated due to an asymmetrical drop of potential in the semiconductor gate under positive or negative biases. The gate voltage dependencies of concentration and conductivity are calculated for the case of SiO_2 substrate placed over low- (moderate-) doped p-Si. Similar dependencies of the optical conductivity are analyzed for the case of high-kappa substrates (AlN, Al_2O_3, HfO_2, and ZrO_2). The comparison of our results with experimental data shows a good agreement for both cases.