Study of strain-mediated Dirac point shift in monolayer SbSSn by second harmonic generation

Strain provides a degree of freedom for effectively tailoring the electronic and optical properties of two-dimensional (2D) materials. Here, we theoretically demonstrate that the shift of two Dirac points under the tensile strain in the y direction εy can be detected by second harmonic generation (SHG) in monolayer SbSSn.With spin-orbit coupling (SOC), two Dirac points appear above and below the Fermi level at the high symmetry points Y and M, which are connected by two Kramers-like degenerate bands crossing the Fermi level. As the tensile strain εy increases, these two Dirac points shift downward and upward relative to the Fermi level, making two Dirac points closer to the Fermi level. The downward shift of the Dirac point at Y point is driven by the decrease of the Sn-S bonds, which enhances the bonding strength. In contrast, the upward shift of the Dirac point at M point is due to the elongation of the Sb-Sb, Sb-S, and Sb-Sn bonds, which weakens the bonding strength. All the above changes can be detected by SHG, where the first peak intensity of the interband transitions for both χyxx⁽²⁾ and χyyy⁽²⁾ components are enhanced. This is because the two Kramers degenerate bands connecting the two Dirac points are pushed away from each other and the corresponding transition channels between them are significantly enhanced. Due to the semimetal nature of SbSSn, the intraband contribution dominates χyxx⁽²⁾ and χyyy⁽²⁾. The response of intraband current to strain is nontrivial, mainly caused by PDOS of Sb-p and Sn-p orbitals near the Fermi level. Our findings demonstrate that SHG is a feasible means to detect the shift of Dirac points in 2D materials.