[Paper Review] Direct Measurement of Helicoid Surface States in RhSi using Nonlinear Optics

Dylan Rees, Baozhu Lu+7 more|arXiv (Cornell University)|Mar 16, 2021

Topological Materials and PhenomenaPhysics and Astronomy53 references30 citations

TL;DR

This study directly measures helicoid surface states in the chiral Weyl semimetal RhSi using nonlinear optical techniques, specifically the linear and circular photogalvanic effects (LPGE and CPGE). By probing the [001] surface with tunable, polarized light, the researchers isolate surface photocurrents from bulk contributions, observing a CPGE response consistent with theoretical predictions in magnitude but inconsistent in direction. Unexpectedly, only two of six expected LPGE tensor elements were needed to describe the data, suggesting emergent mirror symmetry not present in the crystal's space group (P213).

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 \cite{chang20}, 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 magnitude 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.

Motivation & Objective

• To directly probe the electronic and optical properties of Fermi arc surface states in topological Weyl semimetals, which are typically masked by bulk responses.
• To overcome the experimental challenge of separating surface photocurrents from dominant bulk contributions in nonsymmorphic crystals.
• To test theoretical predictions of quantized circular photogalvanic effect (CPGE) in chiral Weyl semimetals like RhSi using nonlinear optical response.
• To investigate the symmetry constraints of photogalvanic tensors on the (001) surface of RhSi, where bulk and surface responses are expected to differ fundamentally from (111) surfaces.
• To determine whether emergent symmetries arise in surface photocurrents despite the absence of mirror symmetry in the bulk crystal structure.

Proposed method

• Employed tunable near-infrared (800 nm) laser pulses with variable linear and circular polarization incident on the RhSi [001] surface at normal incidence.
• Used terahertz time-domain spectroscopy to detect and measure the second-order nonlinear photocurrents generated via the photogalvanic effect (PGE).
• Applied two experimental configurations: (1) rotating the pump polarization while keeping the sample fixed, and (2) fixing the pump polarization and rotating the sample to extract the nonlinear conductivity tensor elements.
• Modelled the photocurrent using the phenomenological PGE equation: $ J_i = \gamma_{ijk} E_j E_k + i\beta_{ij} (E \times E^*)_{j} $, where $ \gamma_{ijk} $ and $ \beta_{ij} $ are the linear and circular photogalvanic response tensors.
• Performed symmetry analysis using the space group P213 (No. 198), which predicts only $ \gamma_{xyz} $ and $ \beta_{ij} = \beta \delta_{ij} $ as non-zero elements, implying CPGE current parallel to the light wavevector.
• Conducted atomic force microscopy (AFM) to rule out surface topography-induced anisotropy in the optical measurements.

Experimental results

Research questions

• RQ1 Can the Fermi arc surface states in RhSi be directly probed using nonlinear optical techniques, despite overwhelming bulk contributions?
• RQ2 Does the circular photogalvanic effect (CPGE) on the RhSi (001) surface exhibit the theoretically predicted quantized response and directional dependence?
• RQ3 Are the measured nonlinear optical tensor elements consistent with the bulk crystal symmetry (space group P213), or do they indicate emergent symmetries?
• RQ4 Why does the observed CPGE current direction deviate from theoretical predictions based on bulk symmetry?
• RQ5 To what extent do the measured LPGE tensor elements reflect the actual symmetry of the surface, given that only two of six expected components are required to fit the data?

Key findings

• The measured circular photogalvanic effect (CPGE) magnitude agrees well with theoretical predictions across the 0.45–1.1 eV photon energy range, confirming the presence of topologically protected surface states.
• The direction of the CPGE current deviates from theoretical expectations based on bulk symmetry, indicating that the surface response is not fully governed by the bulk crystal's space group.
• Only two of the six possible LPGE tensor elements were required to fit the experimental data, suggesting an emergent mirror symmetry not present in the bulk RhSi crystal structure.
• The observed symmetry reduction implies that surface states may break or effectively restore symmetries not present in the bulk, leading to unexpected selection rules.
• No surface topographic features were detected via AFM that could explain the observed anisotropy, ruling out artifacts from surface morphology.
• The results demonstrate that second-order nonlinear optics provides a selective probe of surface state physics in Weyl semimetals, enabling isolation of topological surface currents from bulk contributions.