The Effects of Electric and Exchange Magnetic Fields on Spin Energy Dispersion, Electronic Heat Capacity and Magnetic Susceptibility of Monolayer Silicene

Abstract

The Kane-Mele model and Green’s function technique help us to describe and survey the influences of electric and exchange magnetic fields (EF and EMF) on the dynamics of Dirac fermions in the monolayer silicene by studying the energy dispersion (ED), electronic heat capacity (EHC) and Pauli magnetic susceptibility (MS). Spin band gaps show three phases including topological insulator (TI), valley-spin polarized metal (VSPM) and band insulator (BI) in the presence of external EF. The maximum value for EHC and MS have been observed in the VSPM phase. Also, ED evolution with EMF shows that the Fermi level decreases. Interestingly, two critical temperatures have been found in the VSPM regime of 0.5 and 2 in terms of spin-orbit coupling (SOC) strength in the EHC and MS curves, respectively. In addition, remarkable point in the VSPM regime is the observed phase transition from antiferromagnetic to paramagnetic in MS curves. Competition between thermal and quantum effects is the main reason of these critical points which these findings can control the thermal properties of silicene-based devices.