Circular Photogalvanic Effect in Quantum Materials

Updated 10 January 2026

Circular Photogalvanic Effect is a nonlinear optical phenomenon generating helicity-dependent dc currents in inversion-broken materials via injection, shift, and Berry curvature mechanisms.
The effect is experimentally observed in systems such as Rashba interfaces, topological insulators, and Weyl semimetals, providing insights into band topology and symmetry constraints.
Applications include polarization-sensitive photodetectors, spin current generation, and topological charge diagnostics, with quantized responses linking theory and experiments.

The circular photogalvanic effect (CPGE) is a second-order nonlinear optical phenomenon in which illumination by circularly polarized light generates a helicity-dependent dc photocurrent in materials lacking inversion symmetry. In such systems, the direction and magnitude of the photocurrent are determined by the light's helicity (right- or left-circular polarization), electronic band structure, symmetry of the crystal lattice, and spin-orbit coupling. CPGE is a key tool for probing the interplay of symmetry, topology, and spin–momentum locking in a wide range of quantum materials, including Rashba interfaces, topological insulators, chiral Weyl semimetals, two-dimensional heterostructures, and magnetic systems.

1. Microscopic Origin and Tensor Structure

CPGE arises from a second-order nonlinear process where the interaction of circularly polarized light with electronic or magnonic states in a noncentrosymmetric (inversion-broken) medium generates a dc current. The effect can be phenomenologically described by a third-rank pseudo-tensor as

$J_i = \sum_{jk} \gamma_{ijk} E_j(\omega) E_k^*(\omega),$

where $J_i$ is the current density, $E_j(\omega)$ is the complex amplitude of the incident electric field, and $\gamma_{ijk}$ is the CPGE tensor, constrained by the crystal symmetry. For circularly polarized light, the key quantity is $i (E \times E^*)$ , which is odd under time-reversal and helicity. The tensorial form and allowed nonzero components of $\gamma$ (or equivalently second-rank contracted forms) depend on the point group: only noncentrosymmetric, mirror-odd (typically chiral) groups allow a nonzero trace of the CPGE tensor (Le et al., 2021).

Microscopically, prominent mechanisms entail:

Injection current (ballistic): Circular photons selectively inject electrons into spin-split bands with opposite velocities, generating a helicity-dependent photocurrent.
Shift current (displacement): Optical transitions induce net real-space displacements due to asymmetric wavefunction shifts.
Berry curvature–mediated mechanisms: The Berry curvature and associated monopole (Chern) charge play central roles, especially in topological semimetals (Juan et al., 2016, Le et al., 2021).

In Rashba-type systems, the spin–momentum locking near interfaces normal to $\hat{z}$ allows circular polarization to excite carriers with net spin polarization $\langle S \rangle \parallel \pm (\hat{k} \times \hat{z})$ , leading to a directional perpendicular dc current (Hirose et al., 2018, Taniuchi et al., 2023).

2. Symmetry Constraints, Band Topology, and Quantization

The absence of inversion symmetry is necessary, but further symmetry constraints (e.g., mirror symmetry) dictate which CPGE tensor components survive. In noncentrosymmetric, chiral point groups (e.g., C $_1$ , C $_2$ , T, O), the diagonal trace of the tensor can be nonzero, enabling isotropic CPGE responses (Le et al., 2021).

In chiral multifold semimetals and Weyl systems without inversion and mirror symmetries, the CPGE trace is quantized: the rate of photocurrent generation is determined solely by the monopole (Chern) charge of the underlying band crossing,

$\mathrm{Tr}\, \beta(\omega) = i \pi e^3/h^2\, C$

for frequencies where only a single node contributes. This quantization is robust against disorder (which affects only the linear growth time window) and small nonlinear corrections, but is sensitive to perfect linear dispersion and energy separation from other bands (Juan et al., 2016, Le et al., 2021, Pal et al., 2023).

The trace quantization enables direct measurement of topological invariants of the band structure via nonlinear optical transport experiments, as observed or predicted in materials such as CoSi, RhSi, and their family (Ni et al., 2020, Le et al., 2021).

3. Experimental Realizations and Material Platforms

CPGE has been observed across a wide range of materials, each leveraging different microscopic mechanisms and symmetry properties:

Material Class	Key Mechanism	Symmetry/Topology
Rashba interfaces (e.g., Cu/Bi, Tl-Pb/Si)	Interfacial Rashba spin–orbit bands	Local interface inversion breaking
Topological insulators (e.g., BSTS)	Surface Dirac spin–momentum locking	Time-reversal preserving, inversion breaking
Weyl/multifold semimetals (CoSi, RhSi, CeAlSi)	Berry curvature monopole, chirality	Chiral point group, broken I/T
2D TMDs/van der Waals heterostructures	Valley-selective interband transitions, field-tunable asymmetry	Local inversion breaking, C $_{3v}$ or field-induced breaking
Perovskites (e.g., MAPI)	Rashba-induced spin–momentum lock	Bulk or surface inversion breaking
AFM insulators (spin-CPGE/MCPGE)	Injection of pure spin or magnon current	PT symmetry, inversion and/or T breaking
Quantum wells (HgTe/CdHgTe, CdHgTe)	Rashba, Elliott–Yafet, Drude-shift	Quantum-well and strain-induced symmetry breaking

Notable experimental features include:

Sign and magnitude of CPGE current reverses with the helicity of incident light.
Oblique incidence is typically required to break in-plane symmetry and project angular momentum into the sample plane.
Current directionality is determined by the symmetry and geometry (e.g., perpendicular to plane of incidence in Cu/Bi (Hirose et al., 2018)).
Enhancement and tunability via structural design (metamaterials (Sun et al., 2020), strain, thickness, gating (Nishijima et al., 2024, Rasmita et al., 2019)).
Quantitative observation of CPGE trace quantization in chiral semimetals at peaks matching theoretical values (Ni et al., 2020, Le et al., 2021).

4. Analytical Models and Quantitative Expressions

The theoretical formalism for CPGE covers several regimes:

Nonlinear optical tensor formulation:

$j_i = \gamma_{ijk} E_j E_k^*$

where the antisymmetric part in $j$ and $k$ relates to helicity.

Injection current (velocity-gauge):

$\frac{dj_i}{dt} = \beta_{ijk}(\omega) E_j(\omega) E_k^*(\omega)$

or, in contracted notation,

$\frac{dj_i}{dt} = \beta_{ij}(\omega) [E(\omega) \times E^*(\omega)]_j$

(Juan et al., 2016).

Quantized CPGE in Weyl semimetals:

$\mathrm{Tr}\, \beta(\omega) = i \pi e^3 / h^2\, C$

for clean, two-band nodes within the appropriate energy window.

Phenomenological fitting in experiments:

$J(\alpha) = C \sin 2(\alpha + \alpha_0) + L_1 \sin 4(\alpha + \alpha_0) + L_2 \cos 4(\alpha + \alpha_0) + D$

where $C$ is the CPGE amplitude (helicity-dependent), $L_{1,2}$ are linear and photon-drag terms, $D$ is background (Hirose et al., 2018, Taniuchi et al., 2023).

In 2D and quantum well systems, explicit formulas for current density, tensor elements, and their dependence on incident polarization state, incidence angle, and material parameters are available, and fitting parameters can be extracted from polarization-dependent photocurrent measurements (Wittmann et al., 2010, Nishijima et al., 2024, Taniuchi et al., 2023).

5. Extensions: Magnon and Spin Circular Photogalvanic Effects

The CPGE paradigm extends beyond charge transport into spin and magnon systems:

Magnon CPGE (MCPGE): In antiferromagnetic insulators, circularly polarized light via two-magnon Raman processes drives a pure magnonic current, governed by higher-rank Raman nonlinearities and detectable electrically via the inverse spin Hall effect in adjacent heavy metals. MCPGE inherits the CPGE symmetry structure but operates on magnon population, not electrons (Boström et al., 2021).
Spin CPGE (spin-CPGE): In PT-symmetric antiferromagnets, circularly polarized excitation injects pure spin currents with zero net charge flow. The effect is robust to spin–orbit strength and achieves sizable helicity-controlled spin currents at room temperature (Fei et al., 2021).

These extensions underscore the universality of the symmetry and topology principles underpinning CPGE and its derivatives.

6. Applications and Outlook

The circular photogalvanic effect has become a central tool in opto-spintronics, ultrafast photodetection, and topological matter research:

Polarization-sensitive photodetectors: Devices leveraging the high helicity discrimination ( $\rho_\mathrm{circ}$ ) in engineered metamaterials and thin films operate at room temperature and in low-bias configurations (Sun et al., 2020).
Spin current generation: All-optical routes to spin current and spin–orbit–torque effects benefit from the pronounced CPGE in noncentrosymmetric metals and 2D materials (e.g., Cu/Bi, Tl-Pb/Si) (Hirose et al., 2018, Taniuchi et al., 2023).
Topological charge diagnostics: Quantized CPGE rates in chiral Weyl and multifold semimetals serve as bulk probes of the Berry monopole charge, complementing ARPES and optical conductivity (Juan et al., 2016, Le et al., 2021, Ni et al., 2020).
Valleytronics and spin–valley logic: Electrically tunable CPGE in TMD-based heterostructures enables gate-controlled valley-polarized current injection and logic operations (Rasmita et al., 2019).
Nonlinear optoelectronics: The robust nonlinearity and quantized responses in exotic topological semimetals indicate potential for ultrafast and quantized nonlinear photonic devices (Pal et al., 2023).

Adjustable parameters—such as strain, gating, thickness, twist angle, substrate engineering, and metamaterial structuring—provide a rich parameter space to maximize and control the CPGE response for both fundamental studies and technological applications.

References

For detailed derivations, explicit experimental data, and comprehensive theoretical developments, see (Hirose et al., 2018, Juan et al., 2016, Sun et al., 2020, Taniuchi et al., 2023, Le et al., 2021, Ni et al., 2020, Nishijima et al., 2024, Rasmita et al., 2019, Boström et al., 2021, Fei et al., 2021, Hubmann et al., 2019, Wittmann et al., 2010, 2332.03159).