Direct Measurement of Helicoid Surface States in RhSi Using Nonlinear Optics

Dylan Rees, Baozhu Lu, Yue Sun, Kaustuv Manna, Rüstem Özgür, Sujan Subedi, Horst Borrmann, Claudia Felser, J. Orenstein, and Darius H. Torchinsky

Phys. Rev. Lett. 127, 157405 – Published 8 October 2021

Abstract

Despite the fundamental nature of the edge state in topological physics, direct measurement of electronic and optical properties of the Fermi arcs of topological semimetals has posed a significant experimental challenge, as their response is often overwhelmed by the metallic bulk. However, laser-driven currents carried by surface and bulk states can propagate in different directions in nonsymmorphic crystals, allowing for the two components to be easily separated. Motivated by a recent theoretical prediction G. Chang et al., Phys. Rev. Lett. 124, 166404 (2020), we have measured the linear and circular photogalvanic effect currents deriving from the Fermi arcs of the nonsymmorphic, chiral Weyl semimetal RhSi over the 0.45–1.1 eV incident photon energy range. Our data are in good agreement with the predicted spectral shape of the circular photogalvanic effect as a function of photon energy, although the direction of the surface photocurrent departed from the theoretical expectation over the energy range studied. Surface currents arising from the linear photogalvanic effect were observed as well, with the unexpected result that only two of the six allowed tensor element were required to describe the measurements, suggesting an approximate emergent mirror symmetry inconsistent with the space group of the crystal.

Received 9 March 2021
Revised 2 August 2021
Accepted 15 September 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.157405

Physics Subject Headings (PhySH)

Edge states Fermi surface Optical & microwave phenomena Photogalvanic effect Photoinduced effect Topological materials Topological phases of matter Weyl fermions

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Dylan Rees ^1,2,*, Baozhu Lu ^3,*, Yue Sun^2,4, Kaustuv Manna^5,6, Rüstem Özgür⁷, Sujan Subedi ³, Horst Borrmann⁵, Claudia Felser⁵, J. Orenstein ^1,2,†, and Darius H. Torchinsky ^3,‡

¹Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
²Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
⁴Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
⁵Max Planck Institute for Chemical Physics of Solids, Dresden D-01187, Germany
⁶Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India
⁷Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA

^*These two authors contributed equally to this work.
^†jworenstein@lbl.gov
^‡dtorchin@temple.edu

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Vol. 127, Iss. 15 — 8 October 2021

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Images

Figure 1
(a) Unit cell displayed with the [111] direction pointing out of the page, showing the threefold rotational symmetry of the crystal. (b) Extended RhSi structure, showing two alternate unit cells (black and orange). When the unit cell marked by the black frame is rotated by 180° about the $z$ axis and displaced by $(1 / 2, 0, 1 / 2)$ , it is identical to the unit cell marked by the orange frame, illustrating the twofold screw symmetry. (c) When circularly polarized light is incident on RhSi, the bulk CPGE current will be directed perpendicular to the surface, with its sign determined by the incident light’s handedness. L and R refer to left- and right-handed circular polarization, and $j_{b}$ refers to the bulk CPGE current.
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Figure 2
(a) Schematic of experiment used to detect photogalvanic currents in RhSi via terahertz detection. Near infrared light with tunable wavelength and polarization is focused onto the [001] RhSi surface at normal incidence. Terahertz radiation is collected and collimated using off-axis parabolic mirrors. It passes through a wire-grid polarizer before being focused onto a ZnTe crystal. Light with $λ = 800 nm$ and variable time delay $Δ t$ copropagates through the ZnTe for electro-optical detection of the terahertz. PD, photodiode; WP, Wollaston prism; WGP wire-grid polarizer; $λ / 2$ , half-wave plate; $λ / 4$ , quarter-wave plate. (b) In one experimental configuration, the sample is kept fixed while the pump polarization is rotated by angle $θ$ . The sample axes are set such that [100] and [010] are horizontal and vertical in the lab frame respectively. (c) In the second configuration, the pump polarization is fixed at $θ = 0$ , and the sample is rotated by an angle $ϕ$ .
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Figure 3
(a) Amplitude of CPGE for horizontally and vertically polarized THz emission as a function of sample orientation $ϕ$ . (b) Schematic showing directions of bulk PGE ( $j_{b}$ , red) and surface PGE ( $j_{s}$ , green) with normally incident light on the 001 surface of RhSi with the resulting radiation patterns. In general $j_{s}$ has a component in $x$ and $y$ .
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Figure 4
(a) Schematic of surface helicoid bands including a photoexcitation of an electron at energy $ℏ ω$ (red arrow) and the induced current (green arrow). (b) CPGE spectral data for $β_{x z}$ and $β_{y z}$ compared with theory from Ref. [44]. (c) Experimental data compared with theory after rescaling of energy. Rescaling of the energy by a factor of 1.25 is seen when density functional theory - local density approximation theory is augmented by inclusion of a certain amount of Hartree-Fock exchange using hybrid density functionals, for example in the Heyd, Scuseria, and Ernzerhof approach.
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Figure 5
(a) Terahertz amplitude along $x$ and $y$ as a function of linear pump polarization angle $θ$ for $λ = 2000 nm$ . (b) Results of fitting data in (a) to general LPGE tensor $γ_{i j k}$ .
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