Thermal Layer Polarization in Asymmetric Doped Bilayer Graphene

We present a minimal model that isolates the effect of hopping asymmetry on the thermal redistribution of particles in a bilayer graphene system composed of one pristine and one doped layer. The behavior of the system is governed by a single control parameter α, which uniformly reduces the intralayer hopping in the doped sheet and defines the only source of spectral asymmetry. Particle conservation fixes the total density at all temperatures, so thermal effects appear exclusively as a redistribution relative to the zero-temperature reference state. This redistribution is quantified by the temperature-induced change of the layer populations, which measures how thermal occupation modifies the particle density in each layer without creating or destroying carriers. With this, the difference between the thermal population corrections of the doped and pristine layers defines the polarization. Thus, thermal excitations probe the asymmetric spectrum, exposing the intrinsic layer imbalance. Results show that for 0<α < 1, band deformation produces unequal occupations between doped and pristine layers, and temperature amplifies this imbalance. The resulting polarization increases monotonically with temperature and systematically with hopping reduction, establishing a direct quantitative link between microscopic spectral asymmetry and macroscopic thermally induced layer imbalance.