Energy spectra and quantized Hall conductance in a 2D lattice subjected to light irradiation

Abstract

We make an in-depth analysis of the phenomenon of integer quantum Hall effect, considering a two-dimensional (2D) square lattice in presence of light irradiation. Following the well known Landauer-Buttiker multi-probe formalism we compute transverse conductance in a four-probe setup where the irradiation effect is incorporated through a minimal coupling scheme based on the Floquet-Bloch approach. The energy spectrum gets significantly modified with the irradiation which thus directly affects the quantum Hall plateaus. Moreover, we also put an emphasis on how to get an effective one-dimensional Harper equation from the 2D Hall system. Several characteristic features emerge from our analysis that might be interesting and important as well.