The object of the present work is to study the quantum Hall effect through its symmetries and topological aspects. We consider the model of an electron moving in a two-dimensional lattice in the presence of applied in-plain electric field and perpendicular magnetic field. We refer to this as the two dimensional electric-magnetic Bloch problem (EMB). The Hall conductivity quatizations beyond the linear response approximation is analyzed.
Oscillation of spin polarization in a two-dimensional hole gas under a perpendicular magnetic field
Spin edge helices in a perpendicular magnetic field
Generic suppression of conductance quantization of interacting electrons in graphene nanoribbons in a perpendicular magnetic field
