On the in-plane electronic thermal conductivity of biased nanosheet $\beta_{12}$-borophene

Unique physical and chemical properties of $\beta_{12}$-borophene stem from the coexistence of the Dirac and triplet fermions. The metallic phase of $\beta_{12}$--borophene transits to the semiconducting one when it is subjected to a perpendicular electric filed or bias voltage. In this work, with the aid of five-band tight-binding Hamiltonian, the Green’s function approach and the Kubo-Greenwood formalism, the electronic thermal conductivity (ETC) of the semiconducting phase of $\beta_{12}$-borophene is studied. Two homogeneous (H) and inversion symmetric (IS) models are considered depending on the interaction of substrate and boron atoms. In addition, due to the anisotropic structure of $\beta_{12}$-borophene, the swapping effect of bias poles is addressed. First of all, we find the pristine ETCIS < ETCH independent of the temperature. Further, a decrease of 74.45% (80.62%) is observed for ETCH (ETCIS) when the strong positive bias voltages are applied, while this occurs as much as 25.2% (47.48%) when applying the strong negative bias voltages. Moreover, the shoulder temperature of both models increases (fluctuates) with the positive (negative) bias voltage. Our numerical results pave the way for setting up the future experimental thermoelectric devices in order to achieve the highest performance.