Fig. 3: Theoretical analysis of second-order rectification current in NiTe₂.

a The experimental ARPES spectrum (left panel) along the \({\bar{{\Gamma }}} - {\bar{\mathrm{M}}}\) direction with red and blue areas depicting the oppositely spin-polarized states, along with the corresponding calculations for the spin-polarized surface spectral function (right panel). Theoretical predictions capture the observed topological surface states (TSS), along with the measured spin texture reasonably well. b Orbital-resolved band structure and different band inversions along the Γ - A direction, along with the irreducible representations of the involved electronic states. The bulk Dirac point (BDP) and a pair of inverted band-gaps (IBG1 and IBG2) can be clearly seen. c Schematic of the spin-polarized TSSs at the Fermi energy in NiTe₂ which also show helical spin-momentum locking. d Trigonal crystal-field scattering of chiral surface Bloch-electrons driven by different ac electric field components, generating a net photocurrent. e Schematics of a rectifier based on four-terminal sector antenna under electromagnetic radiation with the polarization angle θ. f Derivatives of rectified photocurrent at different incident polarization, generated (i) by the skew scattering of chiral Bloch electrons and (ii) by the photothermal effect generated by the non-equilibrium distribution of the carriers. Comparisons for theoretical results of local distributions of rectified current at specific polarization angle θ = 0° and θ = 90° are shown in g for trigonal skew-scattering and in h for photothermal effect. The gradual color contour reflects the localized electric-field enhancement strength distribution. The THz output source direction in which the light polarization direction is parallel to the c–d direction is defined as 0°, and the light polarization direction moves counterclockwise. The scale bar is 5 μm.