Temperature-dependent many-body effects in Dirac-Weyl materials: Interacting compressibility and quasiparticle velocity

We calculate, within the single-loop or equivalently the Hartree-Fock approximation (HFA), the finite-temperature interacting compressibility for three-dimensional (3D) Dirac materials and renormalized quasiparticle velocities for 3D and two-dimensional (2D) Dirac materials. We find that in the extrinsic (i.e., doped) system, the inverse compressibility (incompressibility) and renormalized quasiparticle velocity at k = 0 show nonmonotonic dependences on temperature. At low temperatures, the incompressibility initially decreases to a shallow minimum with a T-2 ln T dependence. As the temperature increases further, the incompressibility rises to a maximum and beyond that it decreases with increasing temperature. On the other hand, the renormalized quasiparticle velocity at k = 0 for both 2D and 3D Dirac materials first increases with T-2, rises to a maximum, and after reaching the maximum it decreases with increasing temperature. We also find that within the HFA, the leading-order temperature correction to the low-temperature renormalized extrinsic Fermi velocity for both 2D and 3D doped Dirac materials is ln(1/T).