Strong intervalley electron-phonon couplings in monolayer antimonene: revisited studies on the band-convergence stategy to enhance thermoelectricity

The stategy of band convergence of multi-valley conduction bands or multi-peak valence bands has been successfully used to understand or further improve the high thermoelectric performance in good thermoelectric materials, or helps to discover new thermoelectric materials. However, the phonon-assisted intervalley scatterings due to multiple band degeneracy are generally neglected in the traditional context of band-convergence stategy, for computational simplifications or experimental difficulties, which may play key role in determining the electronic parts of thermoelectric figure of merits. In this work, by using first-principles method, we investigated in details the (thermo)electric properties of monolayer $\beta$- and $\alpha$-antimonene (Sb) considering full electron-phonon interactions. Our calculations reveal strong intervally-scatterings among the nearly degenerate valley electrons for both $\beta$- and $\alpha$-Sb, and the deformation potential approximation based on the coupling between valley electrons and longitudinal acoustic phonons no longer works accurately for these multi-valley non-polar systems. As a result, by considering full electron-phonon interactions based on the rigid-band approximation, the maximum thermoelectric figure of merit of $zT$ value at room temperature reduces to 0.37 in $\beta$-Sb, by almost 5.7 times smaller than that calculated based on the constant relaxiation-time approximation, while $zT$ increases to 1.25 for $\alpha$-Sb along $a$ direction. Our work not only provides a more accurate method to theoretically investigate the thermoelectric performance of materials, but also manifests the key role of intervalley scatterings in determining the electronic transport properties, which may help clarify the validation scope of the band-convergence stategy for the enhancement of thermoelectricity.