Electronic and thermal properties of quasi - free non - relativistic and ultra - relativistic electrons

Abstract

The purpose of this work is to provide a brief description of the transport of the particles and heat energy in the non-relativisti c and ultra -relativistic 2DEG in the low temperature limit where linear response theory wo rks. A viable basis of the Landau er theory wi ll be provided to understand the transport of the non-relativistic and ultra relativistic quasi-free particles and energy . The electrical conductance and thermal conductance quantum will be found by using Landauer theory. This also provides a gateway to find Seebeck and Peltier coeffi cient. Moreover, we examine the behavior of a 2DEG that is subj ected to both a perpendi cul ar magnetic field and spatially va ryin g internal electri c fi elds. We choose one of the two guiding centre to be diago nal. This makes energy a loca l fun ction of the position, allowin g for an easy visualization of the transverse response to externally imposed fi elds, as we ll as the spatial distribution of the (transverse) Hall current inside the sampl e. Further, in this model, we apply a thermal gradient vvhi ch results into the quantized thermal current flowin g through the sample.