Thermodynamic properties of electronic Lieb lattice with spin–orbit coupling: the magnetic field effects

In this paper, the electronic properties of a two-dimensional Lieb lattice that is a line-centered square lattice are investigated in the presence of magnetic field and spin–orbit coupling. Specially, we address the temperature dependence of the specific heat and paramagnetic spin susceptibility due to spin–orbit interaction. Using Green’s function approach, the temperature dependence of specific heat and spin susceptibility has been obtained in the context of Kane–Mele model Hamiltonian. Our results for density of states in the presence of spin–orbit coupling show that there are two critical magnetic fields where the phase transitions from semiconductor state to metallic one take place. The specific heat increases with increasing the temperature at low amounts of temperature due to the increasing thermal energy of charge carriers and excitation of them to the conduction bands. Also we have studied the temperature dependence of spin susceptibility of Lieb monolayer due to both spin–orbit coupling and magnetic field factors in detail. The results demonstrate that spin susceptibility decreases with temperature in the absence of magnetic field for each value of spin–orbit coupling and gap parameter.