Exploring temperature dependent electron-electron interaction of topological crystalline insulators (SnS and SnSe) within Matsubara-time domain

Abstract

Both experimental and theoretical studies show non-trivial topological behaviour in native rocksalt phase for SnS and SnSe and categorize these materials in topological crystalline insulators. Here, the detailed electronic structures studies of SnS and SnSe in the rocksalt phase are carried out using many-body GW based theory and density functional theory both for ground states and temperature dependent excited states. The estimated values of fundamental direct bandgaps around L-point using G0W0 (mBJ) are ∼0.27 (∼0.13) eV and ∼0.37 (∼0.17) eV for SnS and SnSe, respectively. The strength of hybridization between Sn 5p and S 3p (Se 4p) orbitals for SnS (SnSe) shows strong k-dependence. The behaviour of W (ω), which is the averaged value of diagonal matrix elements of fully screened Coulomb interaction, suggests to use full-GW method for exploring the excited states because the correlation effects within these two materials are relatively weak. The temperature dependent electronic structure calculations for SnS and SnSe provide linearly decreasing behaviour of bandgaps with rise in temperatures. The existence of collective excitation of quasiparticles in form of plasmon is predicted for these compounds, where the estimated values of plasmon frequency are ∼9.5 eV and ∼9.3 eV for SnS and SnSe, respectively. The imaginary part of self-energy and mass renormalization factor (Z k (ω)) due to electron-electron interaction (EEI) are also calculated along W-L-Γ direction for both the materials, where the estimated ranges of Z k (ω) are 0.70 to 0.79 and 0.71 to 0.78 for SnS and SnSe, respectively, along this k-direction. The present comparative study reveals that the behaviour of temperature dependent EEI for SnS and SnSe are the almost same and EEI is important for high temperature transport properties.

Evidence of phase stability, topological phonon and temperature-induced topological phase transition in rocksalt SnS and SnSe

“…The bandgaps of SnS are found to have lower values than SnSe for the studied temperature range. This is showing opposite behaviour of temperature dependent bandgaps due to EEI for both these materials 30 . Therefore, the bonding and anti-bonding strength between Sn 5p -S 3p orbitals are becoming more stronger (weaker) than Sn 5p -Se 4p orbitals at L-point, when EEI (EPI) is considered.…”

“…For investigating, the phononic structures of SnS and SnSe, the total forces of the atoms are estimated using full-potential linearized-augmented plane-wave (FP-LAPW) based WIEN2k code 40 with considering PBEsol exchangecorrelation (XC) functional 41 . The space group of these materials is F m-3m, which is utilized in present study along with the lattice parameters 5.753 Å and 5.955 Å for SnS and SnSe, respectively 30 . 5×5×5 k-mesh size is set to perform the present calculation together with fixing the Wyckoff positions at (0.0, 0.0 ,0.0) and (0.5, 0.5, 0.5) for Sn and S (Se), respectively.…”

“…al. 30 that PBEsol is failed to provide the semiconducting bandgap in case of SnS, but mBJ and G0W0 methods have shown the bandgap. However, the behaviour of the bands are almost similar for PBEsol, mBJ and G0W0 methods.…”

“…Therefore in present case, for obtaining more realistic semiconducting dispersion curve of SnS from PBEsol functional, a rigid shifting for VB (CB) towards lower (higher) energy with respect to EF is given. It is known that the bandgap of these two materials are found near the high-symmetric L-point 30 . Thus, we have focused to study the effect of EPI at L-point of valence band maxima (VBL) and conduction band minima (CBL).…”

“…It is known that increment of temperature will directly affect the electron-phonon interaction (EPI) within the material along with electronelectron interaction (EEI). The temperature effect on the EEI of SnS, SnSe and SnTe are discussed in literature, where GW method in Matsubara-time domain is used for considering the temperature effect 29,30 . Recently, Querales-Flores et.…”