Field-unmasked quantum geometry in a symmetry-forbidden photocurrent

Abstract

Frequency- and polarization-resolved photocurrents provide a sensitive probe of hidden symmetry and band geometry in quantum materials. Here we study a chiral cubic sillenite whose global crystal symmetry forbids a longitudinal odd-in-B magneto-photocurrent in the Voigt geometry. Nevertheless, we observe a pronounced longitudinal response across the visible range that is predominantly linear in magnetic field, persists below the band gap, and exhibits strong helicity selectivity, with the circular channel exceeding the linear one and reversing sign upon switching light helicity. We resolve this apparent contradiction by identifying defect-enabled, field-selected spin ordering as the mechanism that lowers the effective magnetic symmetry without altering the global crystal structure. First-principles calculations show that O vacancies generate in-gap bound states and localized magnetic moments on neighboring Bi-O units, stabilized by strong SOC. Although symmetry-related vacancy configurations remain energetically degenerate and preserve the macroscopic T symmetry at zero field, an applied magnetic field selects a time-reversal-broken sector of the defect ensemble and reduces the effective magnetic symmetry to the subgroup that leaves B invariant, thereby lifting the longitudinal selection rule. Importantly, this field-selected symmetry reduction does more than activate a nominally forbidden photocurrent: it unmasks latent quantum-geometric responses encoded in the electronic structure. Momentum-resolved calculations show that the dominant circular and linear magneto-photocurrent channels spatially correlate with Berry-curvature-rich and quantum-metric-rich regions of the Brillouin zone, respectively. Our results establish field-selected defect symmetry lowering as a route to revealing hidden quantum geometry and activating forbidden nonlinear photocurrents in chiral quantum materials.

Figures (8)

• Figure 1: (a) Crystal structure of Bi$_{12}$SiO$_{20}$: atomic model (Si blue, Bi grey, and O red) and a simplified tetrahedral diagram highlighting its chiral cubic symmetry $T$ with two-fold and three-fold symmetry (space group $I23$). (b) Measurement geometry in the Voigt configuration for longitudinal photocurrent under magnetic field: Photocurrent $\mathbf{J} \parallel \hat{z}$, magnetic field $\mathbf{B} \parallel \hat{y}$, and light propagates along $\mathbf{k} \parallel \hat{z}$. (c) Magneto-optical photocurrent $J_{z}$ versus quarter-wave-plate angle $\psi$ at $\lambda=568$ nm; color encodes magnetic field $B$ (T; $+\hat{y}$ positive; $-0.6 \rightarrow 0.6$ in 0.1 T steps). (d) Magnetic field dependence of $J_z$ ($\Delta J_z$) at $\lambda=568$ nm for quarter-wave plate angles $\psi\in[0,\pi]$. (e) Magnetic sensitivity $\partial J_z/\partial B$ versus light-polarization state for all measured wavelengths. (f) Spectra of the magneto-photocurrent change $\Delta J_{z}(B)\equiv J_{z}(B)-J_{z}(B=0)$ for left circularly (left), linearly (middle), and right circularly (right) polarized light. The blue dashed line marks the pristine BSO band gap ($\approx 387$ nm).
• Figure 2: (a) Room-temperature Raman spectrum of Bi12SiO20 collected via a back-scattering configuration under 457 nm excitation with a parallel polarization geometry. Raman spectra exhibit peaks at 61.0, 69.6, 92.3, 132.4, 147.7, 170.1, 212.2, 280.5, 331.5, 462.5, and 542.7 cm$^{-1}$. (b) Photoluminescence spectrum of Bi12SiO20 with an excitation wavelength of 457 nm depending on helicity of light (RCP, black-solid; LCP blue-dashed lines). (c) Total energies of symmetry-related neutral oxygen-vacancy configurations $\left(\mathrm{V}_{\mathrm O}^{\times}\right)$, grouped by the distance to the nearest Si site (N/NN/NNN). (d) Defect formation energy of Bi12SiO20 with an oxygen vacancy as a function of the Fermi level; the slope of each segment equals the charge state $q$. Shaded regions indicate the valence-band (VB) and conduction-band (CB) energy ranges. (e,f) Spin-resolved density of states (DOS) for Bi12SiO20 containing $\mathrm{V}_{\mathrm O}^{\mathop{\mathrm{\scalerel*{\cdot}{\bigodot}}}\limits}$: (e) a magnetic solution with total magnetization $M \approx 1\,\mu_{\mathrm B}$ per supercell and (f) a (nearly) nonmagnetic solution with $M \approx 0$, highlighting a defect-related feature near $E_{\mathrm F}$ (circled). (g) Supercell view and local atomic environment around $\mathrm{V}_{\mathrm O}^{\mathop{\mathrm{\scalerel*{\cdot}{\bigodot}}}\limits}$, illustrating vacancy-induced spin polarization on neighboring Bi atoms (arrow indicates the spin/magnetization direction).
• Figure 3: (a,b) Calculated spectral magneto-photocurrent of (a) defective BSO (defect ensemble) and (b) pristine BSO for $B\parallel[010]$ and $k\parallel[001]$. (c) Calculated magnetic field dependence of $\Delta J_z$ at $\lambda=568$ nm for quarter-wave angles $\psi\in[0,\pi]$ with fitting. (d) Magnetic sensitivity $\partial J_z/\partial B$ versus light-polarization state for all measured wavelengths fitting using Eq. \ref{['J_fitting']}. (e-h) Decomposition photocurrent of the defect ensemble into (e) linear shift, (f) circular injection, (g) circular shift, and (h) linear injection currents.
• Figure 4: (a,b) Two-dimensional (2D) momentum-resolved distribution of (a) circular shift and (b) linear injection currents of the 568 nm peak in the first Brillouin zone (BZ) of the defect ensemble Bi_12SiO_20 at $k_z=0$ plane. (c,d) Corresponding 2D momentum-resolved distribution of (c) Berry curvature and (d) Quantum metric map in the first BZ of the defect ensemble Bi_12SiO_20 at $k_z=0$ plane.
• Figure S1: Measured variation in the longitudinal photocurrent vs. QWP angle for various magnetic fields. Individual traces fit using eq. \ref{['J_fitting']}.