Unconventional Photocurrents from Surface Fermi Arcs in Topological Chiral Semimetals

The nonlinear optical responses from topological semimetals are crucial in both understanding the fundamental properties of quantum materials and designing next-generation light sensors or solar cells. However, previous work focused on the optical effects from bulk states only, disregarding the responses from topological surface states. In this Letter, we propose a new surface-only photocurrent response from chiral Fermi arcs. Using the ideal topological chiral semimetal RhSi as a representative, we quantitatively compute the photogalvanic currents from Fermi arcs on different surfaces. By rigorous crystal symmetry analysis, we demonstrate that Fermi arc photogalvanic currents can be perpendicular to the bulk injection currents regardless of the choice of materials surface. We then generalize this finding to other cubic chiral space groups and predict material candidates. Our theory reveals a powerful notion where common crystalline symmetry can be used to completely disentangle bulk and surface optical responses in many conducting material families.

Figure 1

Spiral Fermi arcs on the (001) surface of RhSi. (a) Electronic structure of RhSi in the presence of SOC. (b) ARPES-measured (001)-surface states of RhSi at 20 meV below the Fermi level. The Fermi arc surface states (indicated by the black dot line) stretch across the entire surface BZ along the $xy$ direction. The white box indicates the first surface BZ. The color bar indicates the high ($H$) and low ($L$) spectral weight distributions on the surface. (c) First-principles calculations of (001)-surface states of RhSi at the Fermi level. Our calculations match the experimental measurements in panel (b). (d) The energy dispersion along the red dashed line indicated in panel (c). The white line indicates the Fermi level, and the cyan arrow shows a possible light-absorption channel between the Fermi arcs at different energies. (e) Helicoid Fermi arc structures around $\overline{M}$ at different energies. Fermi arcs spiral clockwise with increasing of energy, which induce the potential light-absorption channel indicated by the cyan arrow.

Figure 2

CPGE in RhSi with laser normal to the (001) surface. (a) The momentum-resolved circular light absorption of RhSi at the $k_z=0.1\pi /a$ plane. The $S_{2z}=\{C_{2z}|0.5,0,0.5\}$ rotation axis induces twofold light absorption from the bulk cone. (b) Schematics of photocurrent in the $xy$ plane from the bulk Weyl cone. The cyan arrows indicate circularly polarized photons propagating along the $z$ direction, and the purple arrows indicate light-induced photocurrents. Because of the existence of $S_{2z}$ rotation symmetry in bulk, the photocurrent perpendicular to the laser $J_{\perp }^b$ vanishes. (c) The light absorption of the Fermi arc on the (001) surface in RhSi. Only time-reversal symmetry is still preserved. (d) Schematics of photocurrent from chiral Fermi arc surface states. The red and blue surfaces are two chiral Fermi arc surface states. A circularly polarized laser can only pump one side of the chiral arc, and thus generate a net nonvanishing photocurrent. (e) (001)-surface Fermi arcs induced CPGE photocurrents along the $x$ and $y$ directions in RhSi, respectively. ${\beta }_0=\pi e^3/h^2$, where $e$ and $h$ are the electron charge and the Planck constant, respectively. The calculated CPGE photocurrents are obtained from the top four unit cells where Fermi arcs locate. When the light is not normal to the surface, the in-plane bulk photocurrent will be switched on. Because of the deep penetration of the laser [28], the in-plane bulk photocurrents can be much larger than the surface photocurrents.

Figure 3

CPGE from Fermi arcs on generic surfaces of RhSi. (a) (110)-surface states of RhSi at the Fermi level. Long Fermi arcs connecting projected chiral fermions at $\overline{\mathrm{\Gamma }}$ and $\overline{Z}$ are observed. (b) Energy dispersions cutting through the Fermi arcs on panel (a). The cyan arrow indicates the possible light absorption between the (110)-surface Fermi arc surface states. (c) Numerical calculations reveal nonzero CPGE photocurrents from the (110)-surface Fermi arcs in RhSi under a laser perpendicular to the surface. The calculated CPGE photocurrents are obtained from the top four unit cells. (d) For any generic ($lmn$) surface of RhSi, under the circularly polarized laser perpendicular to the surface, the Fermi-arcs-induced CPGE photocurrents ($J_{\perp }^s$) are always perpendicular to the bulk CPGE photocurrents from chiral fermions ($J_{\parallel }^b$). The color bar indicates the high ($H$) and low ($L$) carrier density distributions from Fermi arc surface states. The photocurrents from the Fermi arcs should also be bounded on the surface, due to the surface localization of the Fermi arcs.