Fig. 3: Contribution of Berry connection to the SHG response of Te nanoflake.
From: Topologically enhanced giant broadband second-harmonic generation in Weyl semiconductor tellurium
a The experimentally extracted \({\chi }^{(2)}\) spectrum of Te nanoflakes as a function of SH energy and the theoretically calculated result with Fermi energy \({E}_{f}=-10\) meV. The pink, purple and orange shaded areas labeled with W1, W2 and W3 mark a peak and two shoulders in the response spectrum, respectively. Error bars indicate standard deviations from measurements on multiple samples. b Schematic band structure of Te around the high-symmetry H and L points of the Brillouin zone with spin-orbit coupling. The inset shows the first Brillouin zone of Te crystal. The pink, purple and orange arrows mark the two-photon transition energies at three different Weyl nodes (W1, W2 and W3), which correspond to the three shade areas marked in (a). c The modulus of in-plane interband Berry connection (\({|{{\boldsymbol{r}}}}_{{cv}{{\boldsymbol{k}}}}^{{||}}|\)) between the highest two valence bands \({{\rm{\nu }}}={v}_{1}({blue}),{v}_{2}({red})\) and the lowest two conduction bands \({c=c}_{1}({red}),{c}_{2}({blue})\) in the LHKM plane of the Brillouin zone. The high symmetry points are marked. The horizontal and vertical axes are along the L-H and K-H directions, respectively; the color scale indicates the modulus of in-plane Berry connection.
