Electronic specific heat and thermal conductivity of bilayer graphene with pristine and parametrically doped layers: A study in the low-energy regime

We theoretically study thermal properties of bilayer graphene with one pristine and one 50 % doped layer. In the doped layer, hopping energy is tuned by a dimensionless parameter, reducing its Fermi velocity relative to pristine bilayer. Considering interlayer interactions, analytical expressions are derived for the energy spectrum, number of states, and density of states per particle. These expressions are employed to compute thermodynamic quantities in the low-energy and low-temperature regimes, including internal energy, electronic specific heat, and electronic thermal conductivity per unit cell. Results show that doping induces a flattening of the low-energy bands near the Fermi level, leading to an increased low-energy density of states. This enhancement increases in the electronic specific heat, particularly within the low temperature regime. The predominant contribution from the enhanced electronic specific heat leads to an overall rise in the electronic thermal conductivity. Findings suggest routes to tune graphene heterostructure thermal properties via doping.