Direction-dependent electronic thermal conductivity and thermopower of single-layer black phosphorus in the presence of bias voltage and dilute charged impurity

By using the Green's function and the tight-binding model within the Born approximation, we obtain the electronic thermal conductivity (TC) and Seebeck coefficient [or thermopower (TP)] of monolayer black phosphorus (BP) under charged impurity doping. The results show that the TC and TP along the y−direction are larger than the x−direction in clean BP due to the inherent higher value of the electronic density of states in y−direction. Furthermore, the TC linearly decreases with low impurity concentrations in both directions, whereas it decreases and does not change with low impurity scattering potentials in x− and y−direction, respectively. On the other hand, TP increases (decreases) with very dilute impurity concentrations and scattering potentials in x−(y−)direction. To be a complete work, we also studied these properties in impurity-infected biased BP. We found that the TC of BP in the presence of impurity gradually increases with bias voltage in both directions and TP has a decreasing (increasing) treatment in x−(y−)direction. Our findings move the thermoelectric (TE) applications of BP into promising TE materials.