Large second-harmonic generation and linear electro-optic effect in trigonal selenium and tellurium

Trigonal selenium and tellurium crystalize in helical chainlike structures and thus possess interesting properties such as nontrivial band topology, gyrotropic effects, and nonlinear optical responses. By performing systematic density-functional-theory calculations with the generalized gradient approximation plus scissors correction, we study their linear and nonlinear optical (NLO) properties. We find that both materials exhibit large second-harmonic generation (SHG) and linear electro-optic (LEO) effect. In particular, tellurium has the huge SHG coefficient (χxxx(2)) in the photon energy range of 0∼3eV with the maximum magnitude being about 16 times larger than that of GaN, a widely used NLO material. Tellurium is also found to possess the gigantic static SHG coefficient χxyz(2), which is up to 100 times larger than that of GaN. On the other hand, selenium exhibits the large LEO coefficient rxxx(0), which is more than six times larger than that of GaN. Thus, tellurium and selenium may find valuable applications in NLO and LEO devices such as frequency conversion, electro-optical switches, and light signal modulators. Interestingly, our calculations also reveal that for each material, the χxxx(2) values for the two helical structures are equal but the χxyz(2) values differ in sign, suggesting that the SHG spectroscopy is a useful probe of their chirality. The calculated static and optical dielectric constants as well as SHG coefficients at the CO2 laser frequency are in good agreement with the available experiments. Finally, much stronger NLO responses of selenium and tellurium compared with the semiconductors with similar band gaps are attributed to their quasi-one-dimensional structures with directional covalent bonding and lone-pair electrons. These findings will help the search for new materials with large NLO coefficients.