Electric field and charged impurity doping effects on the Schottky anomaly of β12-borophene

Abstract

Due to the coexistence of Dirac and triplet fermions, monolayer β₁₂-borophene has recently attracted both experimental and theoretical researchers. In particular, various phase transitions have been recently reported in the structure, in the presence of dilute charged impurity and a perpendicular electric field, leading to interesting electronic heat capacity (HC). In this paper, we systematically examine the effects of charged impurity doping and electric field on the HC of monolayer β₁₂-borophene. To do this, we utilize the five-band tight-binding Hamiltonian model, the Green's function, T-matrix, and the Born approximation for different models considering the substrate effects. Numerical analysis reveals that the inversion symmetric model is the proper model in the pristine and perturbed metallic β₁₂-borophene, leading to a regular reduction of HC with both charged impurity and electric field. Moreover, the pristine and perturbed Schottky anomaly alterations are fully addressed. Unforeseeably, HC irregularly fluctuates with impurity in the homogeneous model. We believe that our results provide new physical insights into the thermal properties of monolayer β₁₂-borophene.