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

The strategy of band convergence of multi-valley conduction bands or multi-peak valence bands has been successfully used to understand or help researchers design more efficient thermoelectric materials, or guide the discovery of 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, owning to computational simplifications or experimental difficulties. However, the electron-phonon coupling may play the key role in determining the electronic part 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 mode-resolved electron-phonon interactions. Our calculations reveal strong intervally-scattering between the nearly degenerate electronic valley states in both $\beta$- and $\alpha$-Sb, and the deformation potential approximation based on the coupling between valley electrons and longitudinal acoustic phonons fails to describe accurately the electron-phonon scattering and thermoelectric transport properties in these multi-valley non-polar systems. As a result, by considering full electron-phonon interactions based on the rigid-band approximation, the maximum value of thermoelectric figure of merit $zT$ at room temperature reduces to 0.37 in $\beta$-Sb, by a factor of 5.7 comparing to what is predicted based on the constant relaxiation-time approximation. Our work shows that the band convergence of multi-valley is less beneficial in materials where the intervalley scattering is strong.