Nonlinear optical response in kagome lattice with inversion symmetry breaking

Abstract

The kagome lattice is a fundamental model structure in condensed matter physics and materials science featuring symmetry-protected flat bands, saddle points, and Dirac points. This structure has emerged as an ideal platform for exploring various quantum physics. By combining effective model analysis and first-principles calculations, we propose that the synergy among inversion symmetry breaking, flat bands, and saddle point-related van Hove singularities within the kagome lattice holds significant potential for generating strong second-order nonlinear optical response. This property provides an inspiring insight into the practical application of the kagome-like materials, which is helpful for a comprehensive understanding of kagome lattice-related physics. Moreover, this work offers an alternative approach for designing materials with strong a second-order nonlinear optical response.

Figures (4)

• Figure 1: Schematic of second-order nonlinear optical response and band structures of ideal and distorted kagome lattices. (a) A net photocurrent is absent in an ideal kagome lattice with inversion symmetry. (b) A non-zero net photocurrent is allowed in a distorted kagome lattice. (c) Calculated second-order nonlinear optical conductivity for the lattice structure in (b). (d) Energy dispersion for lattice structure (b) over the entir Brillouin zone. (e) Energy dispersion for an ideal kagome lattice. (f) Energy dispersion for a distorted kagome lattice after consideration of SOC and inversion symmetry breaking. (g) Second-order nonlinear optical conductivity density distribution in momentum space with transition energy lying at $\hbar\omega$ = 2.1 eV. The parameters $t_{1}$ = -1.0 eV, $t_{2}$ = 0.0 eV, and $\lambda_{SOC}$ = -0.2 eV were used.
• Figure 2: Geometry schematic and electronic structures of Mo$_5$Te$_8$. (a) Crystal structure of $2 \times 2$ supercell of Mo$_5$Te$_8$. (b) The parent ideal kagome structure for Mo$_5$Te$_8$ can be derived from (a) by moving the atoms along the arrows. (c) Energy dispersion and density of states of Mo$_5$Te$_8$.
• Figure 3: Optical responses in monolayer Mo$_5$Te$_8$. (a) Shift current spectrum of $\sigma_{xxx}$ tensor component, (b) absorption coefficient, and (c) Glass coefficient.
• Figure 4: Relation between the second-order nonlinear optical conductivity density distribution of $\tilde{\chi}_{xxx}(\textbf{k}; \omega)$ and electronic band structures. (a-c) The distribution of $\tilde{\chi}_{xxx}(\textbf{k}; \omega)$ with photon energy at 0.74 eV, 1.43 eV and 1.95 eV, respectively. (d-f) Light excitation between occupied bands and non-occupied bands corresponding to (a-c).