Renormalization of Fermi Velocity and Band Gap in a Two-Dimensional System near a Conducting Plate at Finite Temperature

In a recent work, it was demonstrated within the framework of Pseudo Quantum Electro-dynamics (PQED) at zero temperature that the logarithmic renormalization of the Fermi velocity in a graphene sheet is inhibited by the presence of a single parallel conducting plate. In the present study, aiming for a more general and realistic approach, we explore the renormalization of the Fermi velocity and mass (band gap) in a two-dimensional system influenced by a conducting plate at finite temperature, also in the context of PQED. Our findings refine previous results in the literature and provide valuable insights for future investigations on the effects of external conditions within PQED.