Photocurrents induced by k-linear terms in semiconductors and semimetals

Abstract

We develop a six-band $\mathbf{k} \cdot \mathbf{p}$ model to describe the electronic structure and optical response of chiral multifold semimetals, such as RhSi. By means of invariants method we construct the effective Hamiltonian describing the states near the $Γ$-point of the Brillouin zone where the spin-orbit coupling and $\mathbf{k}$-linear Rashba terms, which are crucial for circular photogalvanic effect, are taken into account. The model is parameterized using tight-binding calculations. We compute the interband absorption spectrum, showing a linear-in-frequency dependence at low energies and a resonant feature near the spin-orbit splitting energy. Furthermore, we calculate the circular photogalvanic effect. In agreement with previous works the current generation rate at low frequencies exhibits a quantized low-frequency response, governed by the universal value $|\mathcal{C}| = 4$ for the effective topological charge. Our results provide an analytical framework for understanding the role of Rashba coupling and topology in the optoelectronic properties of multifold chiral semimetals.

Figures (2)

• Figure 1: (a) Electron dispersion in RhSi found using the tight-binding method according to Ref. Hasan2017. The used tight-binding parameters in eV Hasan2017 are $v_1 = 0.55$, $v_2 = 0.16$, $v_p =-0.76$, $v_{r1} = 0$, $v_{r2} =-0.03$, $v_{r3} = 0.01$, $v_{s1} =-0.04$, $v_{s2} = v_{s3} = 0$. Dashed and solid lines show the calculation neglecting and including spin-orbit interaction. The inset shows the scheme of the first Brillouin zone with high-symmetry points labeled as $\Gamma$, X, M, and R. (b) Spectrum near the $\Gamma$ point calculated with spin-orbit interaction in the tight-binding method (dotted) and in the $\bm{k} \cdot \bm{p}$ model (solid curves). Arrows denote allowed optical transitions in $\sigma^+$ polarization (in the isotropic model). The parameters of the $\bm{k} \cdot \bm{p}$ model obtained by fitting the tight-binding calculation are given in Table \ref{['tab:kp']}.
• Figure 2: (a) Absorption spectrum for interband optical transitions calculated within the $\bm{k} \cdot \bm{p}$ model for the Fermi energy $E_F=0$. Dashed line shows the linear in $\omega$ extrapolation. (b) The CPGE excitation rate coefficient $\beta$ related to the quantized current constant. Thin horizontal line shows the universal value $-4$, see Eq. \ref{['universal']} and details in text. Inset shows a zoom-in at low frequencies.