Anisotropic electronic heat capacity and electrical conductivity of monolayer biased impurity-infected black phosphorus

We theoretically investigate the electron-impurity interaction effects on the direction-dependent electronic heat capacity (EHC) and electrical conductivity (EC) of single-layer biased black phosphorus (BP) as a function of temperature. By means of the Born approximation besides the continuum approximation of the tight-binding Hamiltonian and the Green's function approach, we obtain a significant difference in the x− and y−direction EHC and EC. Inherent higher value of the y−direction density of states around the Fermi energy in the valence band exhibits interesting anisotropic EHC and EC results. The Schottky anomaly in EHC quantity decreases slightly with impurity in x−direction of unbiased BP, whereas there is no change in y−direction. On the other hand, the probability of transition between energy levels provided by the decreased critical temperature decreases with impurity in x−direction EC and similarly there is no alteration in y−direction EC. We show that the Drude weight in EC appears with impurity in both directions. Furthermore, we study the influence of bias voltage on the EHC and EC of impurity-infected BP. Our findings showcase the increased (decreased) EHC (EC) of disordered BP and disappeared the Drude weight of EC in the presence of bias voltage.