Temperature and doping effects on the electronic and magnetic properties in two-dimensional graphene honeycomb lattices

Abstract Electron–electron interactions in honeycomb lattices have attracted attention because of the intensive research on two-dimensional (2D) graphene. We investigated the finite-temperature electronic properties of honeycomb lattices using the single-band Hubbard model and the canonical partition function. The calculations were performed on a small cluster unit cell with N = 6 atoms. The half-filled band (one electron per) and hole-doped (one and two holes) honeycomb lattices were studied as a function of the intensity ratio between the on-site Coulomb repulsion ( U ) and the nearest-neighbor electronic hopping ( t ). The magnetization, magnetic susceptibility, spin–spin correlation functions, spin-resolved specific heat, magneto-caloric effect (MCE), local magnetic moments, charge, and spin gaps were analyzed. In the half-filled band, the antiferromagnetic (AFM) insulator behavior developed as U/t increased; the one-hole-doping case showed AFM order, presumably resonating valence bond states, and ferromagnetic (FM) insulator behavior as the U/t strength increased. The entropy under external magnetic fields was calculated to determine the MCE. The magnetic field dependence of the total spin S was also analyzed. The honeycomb lattice with a half-filled band underwent a negative-positive MCE as the temperature increased. In contrast, the hole-doped systems exhibited a positive MCE, regardless of the U/t strength. Our findings from a small cluster within the Hubbard model could help to further understand the electronic and magnetic properties of real 2D materials. However, it is important to note that the critical U/t values for spin transitions and magnetic ordering could be size-dependent owing to the finite-size effects.