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Biaxial strain tuned thermoelectric properties in monolayer $\mathrm{PtSe_2}$

Strain engineering is a very effective method to tune electronic, optical, topological and thermoelectric properties of materials. In this work, we systematically study biaxial strain dependence of electronic structures and thermoelectric properties (both electron and phonon parts) of monolayer $\mathrm{PtSe_2}$ with generalized gradient approximation (GGA) plus spin-orbit coupling (SOC) for electron part and GGA for phonon part. Calculated results show that compressive or tensile strain can induce conduction band minimum (CBM) or valence band maximum (VBM) transition, which produces important effects on Seebeck coefficient. It is found that compressive or tensile strain can induce significantly enhanced n- or p-type Seebeck coefficient at the critical strain of CBM or VBM transition, which can be explained by strain-induced band convergence. Another essential strain effect is that tensile strain can produce significantly reduced lattice thermal conductivity, and the room temperature lattice thermal conductivity at the strain of -4.02\% can decrease by about 60\% compared to unstrained one, which is very favorable for high $ZT$. To estimate efficiency of thermoelectric conversion, the figure of merit $ZT$ can be obtained by empirical scattering time $τ$. Calculated $ZT$ values show that strain indeed is a very effective strategy to achieve enhanced thermoelectric properties, especially for p-type doping. Tuning thermoelectric properties with strain also can be applied to other semiconducting transition-metal dichalcogenide monolayers $\mathrm{MX_2}$ (M=Zr, Hf, Mo, W and Pt; X=S, Se and Te).