Investigating the effect of temperature dependent many-body interactions on electronic structures of SnTe in the Matsubara-time domain

Recently, SnTe has gained attention due to its non-trivial topological nature and eco-friendly thermoelectric applications. We report a detailed temperature dependent electronic structure of this compound using DFT and GW methods. The calculated values of bandgaps by using PBEsol and G₀W₀ methods are found to be in good agreement with the experiment, whereas mBJ underestimates the bandgap. The averaged value of diagonal matrix elements of fully screened Coulomb interaction ( $\bar{W}$ ) at ω = 0 eV for Sn (Te) 5p orbitals is ∼1.39 (∼1.70) eV. The nature of frequency dependent $\bar{W}\left(\omega \right)$ reveals that the correlation strength of this compound is relatively weaker and hence the excited electronic state can be properly studied by full-GW many-body technique. The plasmon excitation is found to be important in understanding this frequency dependent $\bar{W}\left(\omega \right)$ . The temperature dependent electron-electron interactions (EEI) reduces the bandgaps with increasing temperature. The value of bandgap at 300 K is obtained to be ∼161 meV. The temperature dependent lifetimes of electronic state along W-L-Γ direction are also estimated. This work suggests that EEI is important to explain the high temperature transport behaviour of SnTe.