Spin-orbit coupling effects on transport properties of electronic Lieb lattice in the presence of magnetic field

In this paper, the transport 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 electrical and thermal conductivities as well as Seebeck coefficient due to spin-orbit interaction. We have exploited Green’s function approach in order to study thermoelectric and transport properties of Lieb lattice in the context of Kane–Mele model Hamiltonian. The results for Seebeck coefficient show the sign of thermopower is positive in the presence of spin-orbit coupling. Also the temperature dependence of transport properties indicates that the increase of spin-orbit coupling leads to decrease thermal conductivity however the decrease of gap parameter causes the reduction of thermal conductivity. There is a peak in temperature dependence of thermal conductivity for all values of magnetic fields and spin-orbit coupling strengths. Both electrical and thermal conductivities increase with increasing the temperature at low amounts of temperature due to the increasing of transition rate of charge carriers and excitation of them to the conduction bands. Also we have studied the temperature dependence of Seebeck coefficient of Lieb monolayer due to both spin orbit coupling and magnetic field factors in details.