Electronic miniband structure, heat capacity and magnetic susceptibility of monolayer and bilayer silicene in TI, VSPM and BI regimes

In the current work, we theoretically study the electronic band structure (EBS), electronic heat capacity (EHC) and magnetic susceptibility (MS) of three structures including monolayer, AA-stacked and AB-stacked bilayer silicene based on the Kane-Mele Hamiltonian model and Green's function method. The particular attention of this study is paid to the effect of external electric field on the aforementioned physical properties. By variation of the electric field, three phases are found: Topological insulator (TI), valley-spin polarized metal (VSPM) and band insulator (BI). Marvellously, its electronic minibands show that the spin-up contribution of charge carriers with lowest energy bands behaves like relativistic Dirac fermions with linear (parabolic) energy dispersions in monolayer (bilayer) case near the Dirac points. An insightful analysis shows that the maximum and minimum value of EHC peak appear for (AA) AB-stacked bilayer and monolayer silicene in TI (BI) regime while in MS curves appear for (AB) AA-stacked bilayer and monolayer lattices in TI (BI) regime, respectively. Moreover, we have observed a phase transition from antiferromagnetic to ferromagnetic and paramagnetic in the monolayer and bilayer structures in the VSPM regime based on the MS findings, respectively.