Bulk Photovoltaic Effect Overview

• BPVE is a dc photocurrent arising in noncentrosymmetric materials via second-order optical processes that leverage broken inversion symmetry and quantum geometry.
• It involves both ultrafast coherent shift currents and slower ballistic/injection currents, with defect-mediated scattering sustaining long-lived responses.
• Integrating nonlinear optics, ferroelectricity, and topology, BPVE research drives innovations in photovoltaic and optoelectronic materials design.

Searching arXiv for recent and foundational BPVE papers to ground the article in the latest literature. The bulk photovoltaic effect (BPVE) is a dc photocurrent generated in a homogeneous, noncentrosymmetric crystal under uniform illumination, without external bias or built-in interface fields. In contrast to conventional photovoltaic responses based on p–n junctions or Schottky contacts, BPVE originates intrinsically from crystal symmetry and quantum geometry, and it is expressed as a second-order optical rectification process in the bulk. Contemporary work places BPVE at the intersection of nonlinear optics, Berry-phase band geometry, scattering kinetics, ferroelectricity, topology, and magnetism; recent contactless spatiotemporal imaging in monodomain $\mathrm{BiFeO_3}$ has further shown that long-lived, symmetry-aligned photocurrent can persist on nanosecond scales in the absence of contacts, requiring a defect-mediated microscopic description beyond the canonical ultrafast mechanisms (Ganguly et al., 1 Sep 2025, Dai et al., 2022).

1. Definition, symmetry, and nonlinear-response framework

BPVE is allowed only when inversion symmetry is broken. In the standard nonlinear-optics description, the dc photocurrent density is written as

$$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$

where $\sigma_{ijk}$ is a second-order conductivity tensor that is finite only in noncentrosymmetric crystals. Broken inversion symmetry allows optical excitation to produce a net current in the bulk via second-order nonlinear processes that add coherently across the Brillouin zone; in centrosymmetric crystals, the second-order dc response vanishes by symmetry (Ganguly et al., 1 Sep 2025).

The best-known intrinsic contribution is the shift current, which is a coherent interband process tied to the Berry connections of Bloch states and the real-space shift of electronic wavefunctions during photoexcitation. A standard form is

$$\sigma_{abc}(0;\,\omega,-\omega) = \frac{\pi e^3}{\hbar^2}\sum_{n,m}\int\frac{d^3k}{(2\pi)^3}\,(f_n-f_m)\,r^{a}_{mn}(\mathbf{k})\,r^{b}_{nm}(\mathbf{k})\,R^{c}_{mn}(\mathbf{k})\,\delta\!\big(\omega_{mn}(\mathbf{k})-\omega\big),$$

with

$$R^{c}_{mn}(\mathbf{k}) = \partial_{k_c}\arg\!\big(r^{c}_{mn}(\mathbf{k})\big) - A_n^c(\mathbf{k}) + A_m^c(\mathbf{k}),$$

so the shift vector is a gauge-invariant combination of phase gradients and Berry connections. This formulation makes BPVE a direct probe of quantum geometry, rather than a purely transport-derived effect (Ganguly et al., 1 Sep 2025).

A distinct contribution is the ballistic or injection current, in which photoexcitation creates an asymmetric distribution in momentum space,

$$\mathbf{J} = e \sum_{\mathbf{k}} \mathbf{v}_{\mathbf{k}}\,\delta n_{\mathbf{k}}.$$

Its microscopic origin depends on symmetry. In time-reversal-symmetric nonmagnetic systems, intrinsic injection is tied to circular polarization, whereas magnetic order or magnetic crystalline symmetry can activate linearly driven injection-like responses and alter the polarization selection rules (Pi et al., 2023, Ezawa, 2024).

2. Canonical mechanisms and their extensions

Shift current is intrinsically ultrafast because it is generated during the optical transition itself and does not require scattering to rectify the field. Injection current, by contrast, is a transport effect that builds from an asymmetric nonequilibrium carrier distribution and is controlled by momentum relaxation. This distinction is central to current BPVE theory: the coherent shift contribution is scattering-insensitive, while ballistic and injection channels are explicitly kinetic and depend on carrier lifetimes, scattering amplitudes, or relaxation-time physics (Dai et al., 2022).

Phonon-assisted ballistic current provides a first-principles realization of this kinetic picture. For tetragonal $\mathrm{BaTiO_3}$, a perturbative treatment of intrinsic electron–phonon scattering gives a ballistic current

$$j_{\alpha\beta,\gamma}(\omega) = 2 e \tau_0 \sum_{cvk} \Gamma^{\alpha\beta,\mathrm{asym}}_{cv,k}(\omega)\,[v^{e,\gamma}_{ck} - v^{e,\gamma}_{vk}],$$

with the asymmetric generation rate derived from a second-order expansion of the momentum–momentum correlator in the electron–phonon interaction. In that system, the phonon-assisted ballistic current is comparable in magnitude to the shift current, has a jagged spectral structure, and improves agreement with measured photocurrent spectra, especially for the $xxZ$ tensor component (Dai et al., 2020).

Correlation effects extend the mechanism set further. In a ferroelectric excitonic insulator, explicit real-time dynamics show that a deformable electronic order parameter can produce strong sub-band-gap resonances from optically active collective modes and can generate an injection current under linearly polarized light even in a time-reversal-symmetric material, a channel absent in a rigid-band approximation. The injection contribution scales as $1/\gamma$ and can dominate the nonlinear conductivity in clean samples (Kaneko et al., 2020).

Moiré flat-band systems add another extension. In twisted bilayer graphene, the THz BPVE is dominated not by a conventional real-space shift contribution but by a “momentum-space shift current” associated with quantum-geometric structures beyond the quantum geometric tensor. The calculated response peaks in the $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$0–$$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$1 THz window and remains finite at room temperature, with the dominant term arising from a momentum-space displacement rather than a Berry-curvature-dipole mechanism or injection current (Kaplan et al., 2021).

Magnetic and topological systems impose still different selection rules. In a $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$2-wave altermagnet with Rashba interaction and an in-plane Néel vector, linearly polarized light generates injection current and circularly polarized light generates shift current, with the injection conductivity nearly constant over the window $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$3 (Ezawa, 2024). In the Haldane model, mirror-time symmetry and $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$4 symmetry separate a linearly driven shift current along one direction from a linearly driven injection current along the orthogonal direction, while circular BPVE vanishes; across the topological phase transition, injection does not change sign whereas shift current does (Lin et al., 17 Aug 2025).

3. Direct observation of intrinsic bulk BPVE in $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$5

A longstanding experimental problem is that BPVE is often measured through devices with interfaces and metal contacts, leaving open the question of whether observed signals are genuinely bulk or are contaminated by Schottky fields, band bending, or photothermoelectric gradients. A direct resolution was provided by contactless pump–probe reflection microscopy on single-crystal, monodomain $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$6, which mapped photoexcited carrier dynamics in space and time without contacts or junctions (Ganguly et al., 1 Sep 2025).

The sample is rhombohedral $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$7 in space group $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$8 with spontaneous ferroelectric polarization along the pseudocubic $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$9 axis; the surface normal is $\sigma_{ijk}$0, and the in-plane $\sigma_{ijk}$1 axis aligns with $\sigma_{ijk}$2. Raman spectroscopy, X-ray diffraction, and in-plane piezoresponse force microscopy verify a single domain with a well-defined polar axis. Pump pulses at $\sigma_{ijk}$3 nm and probe pulses at $\sigma_{ijk}$4 nm, both $\sigma_{ijk}$5 fs, are focused to sub-micron spots, with pump and probe cross-polarized relative to each other. The pump and probe fluences are $\sigma_{ijk}$6 and $\sigma_{ijk}$7, and the repetition rate is $\sigma_{ijk}$8 MHz (Ganguly et al., 1 Sep 2025).

The spatiotemporal $\sigma_{ijk}$9 maps show a clear asymmetry of carrier spreading along the in-plane component of the polar axis $$\sigma_{abc}(0;\,\omega,-\omega) = \frac{\pi e^3}{\hbar^2}\sum_{n,m}\int\frac{d^3k}{(2\pi)^3}\,(f_n-f_m)\,r^{a}_{mn}(\mathbf{k})\,r^{b}_{nm}(\mathbf{k})\,R^{c}_{mn}(\mathbf{k})\,\delta\!\big(\omega_{mn}(\mathbf{k})-\omega\big),$$0, while perpendicular directions remain symmetric. Rotating the crystal by $$\sigma_{abc}(0;\,\omega,-\omega) = \frac{\pi e^3}{\hbar^2}\sum_{n,m}\int\frac{d^3k}{(2\pi)^3}\,(f_n-f_m)\,r^{a}_{mn}(\mathbf{k})\,r^{b}_{nm}(\mathbf{k})\,R^{c}_{mn}(\mathbf{k})\,\delta\!\big(\omega_{mn}(\mathbf{k})-\omega\big),$$1 flips the asymmetry consistently with the reversal of the polarization direction, ruling out miscut or alignment artifacts. By decomposing $$\sigma_{abc}(0;\,\omega,-\omega) = \frac{\pi e^3}{\hbar^2}\sum_{n,m}\int\frac{d^3k}{(2\pi)^3}\,(f_n-f_m)\,r^{a}_{mn}(\mathbf{k})\,r^{b}_{nm}(\mathbf{k})\,R^{c}_{mn}(\mathbf{k})\,\delta\!\big(\omega_{mn}(\mathbf{k})-\omega\big),$$2 into a symmetric diffusion term and an asymmetric drifting Gaussian, the measurements yield a symmetric diffusivity $$\sigma_{abc}(0;\,\omega,-\omega) = \frac{\pi e^3}{\hbar^2}\sum_{n,m}\int\frac{d^3k}{(2\pi)^3}\,(f_n-f_m)\,r^{a}_{mn}(\mathbf{k})\,r^{b}_{nm}(\mathbf{k})\,R^{c}_{mn}(\mathbf{k})\,\delta\!\big(\omega_{mn}(\mathbf{k})-\omega\big),$$3 and a drift of the asymmetric component’s center at $$\sigma_{abc}(0;\,\omega,-\omega) = \frac{\pi e^3}{\hbar^2}\sum_{n,m}\int\frac{d^3k}{(2\pi)^3}\,(f_n-f_m)\,r^{a}_{mn}(\mathbf{k})\,r^{b}_{nm}(\mathbf{k})\,R^{c}_{mn}(\mathbf{k})\,\delta\!\big(\omega_{mn}(\mathbf{k})-\omega\big),$$4 along the polar axis. The asymmetric drift persists to at least $$\sigma_{abc}(0;\,\omega,-\omega) = \frac{\pi e^3}{\hbar^2}\sum_{n,m}\int\frac{d^3k}{(2\pi)^3}\,(f_n-f_m)\,r^{a}_{mn}(\mathbf{k})\,r^{b}_{nm}(\mathbf{k})\,R^{c}_{mn}(\mathbf{k})\,\delta\!\big(\omega_{mn}(\mathbf{k})-\omega\big),$$5 ns. Time-domain $$\sigma_{abc}(0;\,\omega,-\omega) = \frac{\pi e^3}{\hbar^2}\sum_{n,m}\int\frac{d^3k}{(2\pi)^3}\,(f_n-f_m)\,r^{a}_{mn}(\mathbf{k})\,r^{b}_{nm}(\mathbf{k})\,R^{c}_{mn}(\mathbf{k})\,\delta\!\big(\omega_{mn}(\mathbf{k})-\omega\big),$$6 at spatial overlap shows a step at $$\sigma_{abc}(0;\,\omega,-\omega) = \frac{\pi e^3}{\hbar^2}\sum_{n,m}\int\frac{d^3k}{(2\pi)^3}\,(f_n-f_m)\,r^{a}_{mn}(\mathbf{k})\,r^{b}_{nm}(\mathbf{k})\,R^{c}_{mn}(\mathbf{k})\,\delta\!\big(\omega_{mn}(\mathbf{k})-\omega\big),$$7 followed by a slow decay exceeding $$\sigma_{abc}(0;\,\omega,-\omega) = \frac{\pi e^3}{\hbar^2}\sum_{n,m}\int\frac{d^3k}{(2\pi)^3}\,(f_n-f_m)\,r^{a}_{mn}(\mathbf{k})\,r^{b}_{nm}(\mathbf{k})\,R^{c}_{mn}(\mathbf{k})\,\delta\!\big(\omega_{mn}(\mathbf{k})-\omega\big),$$8 ps, and transient photoluminescence gives biexponential lifetimes $$\sigma_{abc}(0;\,\omega,-\omega) = \frac{\pi e^3}{\hbar^2}\sum_{n,m}\int\frac{d^3k}{(2\pi)^3}\,(f_n-f_m)\,r^{a}_{mn}(\mathbf{k})\,r^{b}_{nm}(\mathbf{k})\,R^{c}_{mn}(\mathbf{k})\,\delta\!\big(\omega_{mn}(\mathbf{k})-\omega\big),$$9 ns and $$R^{c}_{mn}(\mathbf{k}) = \partial_{k_c}\arg\!\big(r^{c}_{mn}(\mathbf{k})\big) - A_n^c(\mathbf{k}) + A_m^c(\mathbf{k}),$$0 ns, establishing long carrier lifetimes on the same scale as the observed asymmetric transport (Ganguly et al., 1 Sep 2025).

Several controls eliminate extrinsic explanations. The spatial asymmetry tracks the monodomain polarization direction and reverses upon crystal rotation; it is absent in the transverse direction; and $$R^{c}_{mn}(\mathbf{k}) = \partial_{k_c}\arg\!\big(r^{c}_{mn}(\mathbf{k})\big) - A_n^c(\mathbf{k}) + A_m^c(\mathbf{k}),$$1 scales linearly with pump power, showing that the signal tracks carrier density rather than a nonlinear optical artifact. Complementary device measurements under cw illumination show open-circuit voltage $$R^{c}_{mn}(\mathbf{k}) = \partial_{k_c}\arg\!\big(r^{c}_{mn}(\mathbf{k})\big) - A_n^c(\mathbf{k}) + A_m^c(\mathbf{k}),$$2 V, slightly exceeding the optical band gap, and a strong dependence on light polarization relative to the crystal polarization, reinforcing a bulk interpretation (Ganguly et al., 1 Sep 2025).

4. Why ultrafast BPVE mechanisms are insufficient for the long-lived response

The nanosecond-scale drift in $$R^{c}_{mn}(\mathbf{k}) = \partial_{k_c}\arg\!\big(r^{c}_{mn}(\mathbf{k})\big) - A_n^c(\mathbf{k}) + A_m^c(\mathbf{k}),$$3 is inconsistent with the standard ultrafast BPVE channels. Shift current is a coherent process during photoexcitation and decays with the electronic decoherence time, which in ferroelectrics is typically a few to $$R^{c}_{mn}(\mathbf{k}) = \partial_{k_c}\arg\!\big(r^{c}_{mn}(\mathbf{k})\big) - A_n^c(\mathbf{k}) + A_m^c(\mathbf{k}),$$4 fs. Ballistic currents based on an initial momentum-space asymmetry decay with momentum relaxation times typically below $$R^{c}_{mn}(\mathbf{k}) = \partial_{k_c}\arg\!\big(r^{c}_{mn}(\mathbf{k})\big) - A_n^c(\mathbf{k}) + A_m^c(\mathbf{k}),$$5 ps in oxide ferroelectrics. In $$R^{c}_{mn}(\mathbf{k}) = \partial_{k_c}\arg\!\big(r^{c}_{mn}(\mathbf{k})\big) - A_n^c(\mathbf{k}) + A_m^c(\mathbf{k}),$$6, reported upper bounds are $$R^{c}_{mn}(\mathbf{k}) = \partial_{k_c}\arg\!\big(r^{c}_{mn}(\mathbf{k})\big) - A_n^c(\mathbf{k}) + A_m^c(\mathbf{k}),$$7 fs for decoherence and $$R^{c}_{mn}(\mathbf{k}) = \partial_{k_c}\arg\!\big(r^{c}_{mn}(\mathbf{k})\big) - A_n^c(\mathbf{k}) + A_m^c(\mathbf{k}),$$8 ps for momentum relaxation. Neither shift current nor phonon-assisted ballistic current can therefore sustain an asymmetric drift over multi-nanosecond timescales after carriers have cooled near the band minima (Ganguly et al., 1 Sep 2025).

To explain the persistence of the drift, the proposed mechanism is asymmetric defect scattering under nonequilibrium illumination. In this picture, defects with electronic states intrinsically asymmetric with respect to the polar axis scatter carriers with direction-dependent probability even after hot-carrier cooling, so repeated scattering events maintain a net drift without external bias. This is ballistic in the sense of a momentum-space asymmetry, but it is not the ideal-crystal phonon ballistic current; the asymmetry is supplied by defect potentials aligned with the polarization (Ganguly et al., 1 Sep 2025).

The kinetic Monte Carlo model contains two channels. The first is symmetric electron–acoustic phonon scattering with $$R^{c}_{mn}(\mathbf{k}) = \partial_{k_c}\arg\!\big(r^{c}_{mn}(\mathbf{k})\big) - A_n^c(\mathbf{k}) + A_m^c(\mathbf{k}),$$9, so $$\mathbf{J} = e \sum_{\mathbf{k}} \mathbf{v}_{\mathbf{k}}\,\delta n_{\mathbf{k}}.$$0 fs. The second is asymmetric defect scattering with a directional modulation and representative oxygen-vacancy density $$\mathbf{J} = e \sum_{\mathbf{k}} \mathbf{v}_{\mathbf{k}}\,\delta n_{\mathbf{k}}.$$1 for $$\mathbf{J} = e \sum_{\mathbf{k}} \mathbf{v}_{\mathbf{k}}\,\delta n_{\mathbf{k}}.$$2 oxygen vacancies, $$\mathbf{J} = e \sum_{\mathbf{k}} \mathbf{v}_{\mathbf{k}}\,\delta n_{\mathbf{k}}.$$3, and defect cross section in the $$\mathbf{J} = e \sum_{\mathbf{k}} \mathbf{v}_{\mathbf{k}}\,\delta n_{\mathbf{k}}.$$4–$$\mathbf{J} = e \sum_{\mathbf{k}} \mathbf{v}_{\mathbf{k}}\,\delta n_{\mathbf{k}}.$$5 range, yielding $$\mathbf{J} = e \sum_{\mathbf{k}} \mathbf{v}_{\mathbf{k}}\,\delta n_{\mathbf{k}}.$$6 ps. Including asymmetric scattering produces a nonzero average velocity of $$\mathbf{J} = e \sum_{\mathbf{k}} \mathbf{v}_{\mathbf{k}}\,\delta n_{\mathbf{k}}.$$7 and a linear drift over many nanoseconds in the presence of frequent symmetric phonon scattering, in quantitative agreement with the measured $$\mathbf{J} = e \sum_{\mathbf{k}} \mathbf{v}_{\mathbf{k}}\,\delta n_{\mathbf{k}}.$$8 and persistence to $$\mathbf{J} = e \sum_{\mathbf{k}} \mathbf{v}_{\mathbf{k}}\,\delta n_{\mathbf{k}}.$$9 ns. Without asymmetric scattering there is no sustained drift; stronger asymmetric cross section increases the drift; and an out-of-equilibrium carrier population is required, but an initially asymmetric distribution is not, because the defects themselves generate and maintain the asymmetry after excitation (Ganguly et al., 1 Sep 2025).

First-principles calculations identify oxygen vacancies as the relevant microscopic defect. In a $\mathrm{BaTiO_3}$0-atom $\mathrm{BaTiO_3}$1 supercell treated with Quantum ESPRESSO and PBE+$\mathrm{BaTiO_3}$2 with $\mathrm{BaTiO_3}$3 eV on Fe $\mathrm{BaTiO_3}$4, a single oxygen vacancy produces one in-gap state whose electronic density is highly asymmetric and oriented along $\mathrm{BaTiO_3}$5, the polar axis. Oxygen vacancies are described as the predominant defects in $\mathrm{BaTiO_3}$6, with acceptor-like levels $\mathrm{BaTiO_3}$7 eV below the band gap. The anisotropic defect wavefunction furnishes a microscopic origin for direction-dependent scattering matrix elements and thus for the observed persistent drift (Ganguly et al., 1 Sep 2025).

This defect-assisted interpretation clarifies the timescale hierarchy of BPVE in polar oxides: ultrafast shift and ideal-crystal injection channels dominate during and immediately after excitation, whereas long-lived macroscopic transport can be governed by asymmetric defect scattering once coherence and hot-carrier asymmetry have decayed (Ganguly et al., 1 Sep 2025).

5. Materials classes and symmetry-engineered realizations

The BPVE materials landscape spans ferroelectrics, Weyl semimetals, van der Waals crystals, magnetic semiconductors, chiral systems, and low-dimensional ferroelectrics. A central theme across this literature is that the measurable response is determined not only by broken inversion symmetry, but by how symmetry selects tensor components, which bands dominate optical transitions, and whether scattering, topology, or magnetic order enhances particular channels.

In the Weyl semimetal TaAs, room-temperature measurements established a mid-infrared BPVE dominated by shift current. The reflectance-corrected second-order photoconductivity reaches $\mathrm{BaTiO_3}$8 at $\mathrm{BaTiO_3}$9m, while theory gives $$j_{\alpha\beta,\gamma}(\omega) = 2 e \tau_0 \sum_{cvk} \Gamma^{\alpha\beta,\mathrm{asym}}_{cv,k}(\omega)\,[v^{e,\gamma}_{ck} - v^{e,\gamma}_{vk}],$$0, dominated by Weyl-band transitions. The measured Glass coefficient is $$j_{\alpha\beta,\gamma}(\omega) = 2 e \tau_0 \sum_{cvk} \Gamma^{\alpha\beta,\mathrm{asym}}_{cv,k}(\omega)\,[v^{e,\gamma}_{ck} - v^{e,\gamma}_{vk}],$$1, and polarization-phase analysis separates the intrinsic $$j_{\alpha\beta,\gamma}(\omega) = 2 e \tau_0 \sum_{cvk} \Gamma^{\alpha\beta,\mathrm{asym}}_{cv,k}(\omega)\,[v^{e,\gamma}_{ck} - v^{e,\gamma}_{vk}],$$2 contribution from photothermal $$j_{\alpha\beta,\gamma}(\omega) = 2 e \tau_0 \sum_{cvk} \Gamma^{\alpha\beta,\mathrm{asym}}_{cv,k}(\omega)\,[v^{e,\gamma}_{ck} - v^{e,\gamma}_{vk}],$$3 terms (Osterhoudt et al., 2017).

Single-layer group-IV monochalcogenides provide a visible-range 2D BPVE platform. For GeS, GeSe, SnS, and SnSe, first-principles calculations predict strong visible absorption and effective three-dimensional shift-current peaks of order $$j_{\alpha\beta,\gamma}(\omega) = 2 e \tau_0 \sum_{cvk} \Gamma^{\alpha\beta,\mathrm{asym}}_{cv,k}(\omega)\,[v^{e,\gamma}_{ck} - v^{e,\gamma}_{vk}],$$4. Their large spontaneous effective three-dimensional polarization, reaching $$j_{\alpha\beta,\gamma}(\omega) = 2 e \tau_0 \sum_{cvk} \Gamma^{\alpha\beta,\mathrm{asym}}_{cv,k}(\omega)\,[v^{e,\gamma}_{ck} - v^{e,\gamma}_{vk}],$$5 in GeS, correlates with the integrated shift-current response for small polar distortion, though the dependence becomes nonmonotonic at large polarization because increasing shift vector competes with reduced optical matrix elements (Rangel et al., 2016).

SbSI illustrates phase-selective BPVE in a visible-gap ferroelectric. In the ferroelectric phase, the dominant shift photoconductivity is $$j_{\alpha\beta,\gamma}(\omega) = 2 e \tau_0 \sum_{cvk} \Gamma^{\alpha\beta,\mathrm{asym}}_{cv,k}(\omega)\,[v^{e,\gamma}_{ck} - v^{e,\gamma}_{vk}],$$6 at $$j_{\alpha\beta,\gamma}(\omega) = 2 e \tau_0 \sum_{cvk} \Gamma^{\alpha\beta,\mathrm{asym}}_{cv,k}(\omega)\,[v^{e,\gamma}_{ck} - v^{e,\gamma}_{vk}],$$7 eV and $$j_{\alpha\beta,\gamma}(\omega) = 2 e \tau_0 \sum_{cvk} \Gamma^{\alpha\beta,\mathrm{asym}}_{cv,k}(\omega)\,[v^{e,\gamma}_{ck} - v^{e,\gamma}_{vk}],$$8 at $$j_{\alpha\beta,\gamma}(\omega) = 2 e \tau_0 \sum_{cvk} \Gamma^{\alpha\beta,\mathrm{asym}}_{cv,k}(\omega)\,[v^{e,\gamma}_{ck} - v^{e,\gamma}_{vk}],$$9 eV; in the antiferroelectric phase, the dominant response rotates to $xxZ$0 at $xxZ$1 eV and $xxZ$2 at $xxZ$3 eV. The circular photogalvanic effect tracks the change from a Rashba–Dresselhaus-like spin texture in the ferroelectric phase to a Dresselhaus–Weyl-like texture in the antiferroelectric phase, so BPVE functions simultaneously as an optoelectronic response and a phase diagnostic (Cuono et al., 2024).

Atomically thin $xxZ$4 provides a lateral van der Waals realization in which intrinsic BPVE is isolated from contact effects by graphite electrodes and hBN encapsulation. The extracted in-plane tensor components at $xxZ$5 nm in a bilayer device are $xxZ$6, $xxZ$7, and $xxZ$8, with intrinsic responsivities of $xxZ$9 mA/W at $1/\gamma$0 nm in the bilayer and $1/\gamma$1 mA/W at $1/\gamma$2 nm and $1/\gamma$3 mA/W at $1/\gamma$4 nm in a four-layer device. Scanning photocurrent microscopy separates contact-localized signals from a uniform channel-centered BPVE (Ramos et al., 2024).

Magnetic systems expand BPVE far beyond the conventional linear-polarization shift-current paradigm. In monolayer $1/\gamma$5-$1/\gamma$6, where spatial inversion, time reversal, and space-time reversal are all broken, linearly polarized light generates coexisting injection-like and shift-like photocurrents that propagate in different directions. The peak photoconductance reaches $1/\gamma$7, the photo-spin-conductance $1/\gamma$8, and the photo-orbital-conductance $1/\gamma$9; magnetization rotation switches the injection currents and the shift-type spin and orbital currents (Liu et al., 2023). In bilayer antiferromagnetic $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$00, even-layer stacking breaks inversion symmetry and makes BPVE a probe of magnetic structure: AFM-$$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$01 allows only linear injection with $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$02, whereas AFM-$$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$03 and AFM-$$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$04 additionally allow circular shift responses and distinct tensor patterns that can be distinguished with circularly polarized light (Pi et al., 2023).

Two-dimensional interlayer-sliding ferroelectrics demonstrate that BPVE need not track ferroelectric reversal in a uniform way. When the $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$05 and $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$06 states are related by a horizontal mirror $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$07 rather than inversion, in-plane BPVE tensor components are unswitchable while out-of-plane light-induced polarization is switchable. First-principles calculations on bilayer $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$08 and bilayer $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$09 validate this symmetry-based distinction and show that interlayer sliding can selectively reverse only tensor elements containing $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$10 indices (Xiao et al., 2022).

Hydrogenated Zintl compounds $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$11 offer a low-gap polar-semiconductor route. Across this family, calculated GGA band gaps range from $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$12 to $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$13 eV, and predicted maximum shift-current responses are up to eight times greater than that calculated for $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$14, with strong response down to substantially lower photon energies (Brehm, 2017).

6. Many-body corrections, theoretical controversies, and efficiency limits

A major theoretical development has been the recognition that quantitative BPVE prediction requires many-body and nonequilibrium corrections. In bulk $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$15 and monolayer SnSe, $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$16 quasiparticles shift and stretch the shift-current spectra to higher energies and reduce magnitudes by redistributing spectral weight, while excitons strongly reshape the near-gap optical response in bulk $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$17 but have only a small net effect in monolayer SnSe because the thin-film geometry suppresses attenuation. For $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$18, the direct gap increases from $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$19 eV at GGA to $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$20 eV at GW; for monolayer SnSe, the gap increases from $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$21 to $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$22 eV (Fei et al., 2018).

Another unresolved issue is whether steady-state BPVE can be reduced to equilibrium nonlinear optics. A nonequilibrium treatment with electron–phonon interactions shows that the nonlinear dc response contains three operator correlation functions, one of which is out-of-time-ordered and cannot be computed by equilibrium field theory. In a semiclassical picture, the BPVE can be interpreted as the dipole moment of generated excitons, while a quantum master equation shows that the scattering rate has a strong implicit effect on the nonlinear dc response and that spatially inhomogeneous excitation produces a strongly nonlocal response (Barik et al., 2019).

This nonequilibrium emphasis aligns with a methodological critique of shift-current-only descriptions. One line of argument holds that the widespread starting relation for the shift current, taken as a complete dc BPVE theory, is incomplete because it ignores kinetic processes of relaxation and recombination of photoexcited electrons and misses substantial ballistic contributions from asymmetric momentum distributions. In that view, the total current should be decomposed as $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$23, with both excitation and recombination contributions retained for the shift channel, and any steady-state theory must satisfy the equilibrium benchmark $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$24 in the absence of nonequilibrium driving (Sturman, 2019). A plausible implication is that different experimental regimes weight the coherent and kinetic channels very differently, so “BPVE” is not synonymous with “shift current.”

A second misconception is that photovoltages exceeding the band gap imply high photovoltaic efficiency. BPVE is not constrained by junction thermodynamics and can yield open-circuit voltages larger than $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$25, but practical conversion efficiency is subject to more stringent limits. For a monochromatic absorber, energy conservation gives

$$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$26

and for ballistic or injection transport the bound becomes

$$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$27

so realistic efficiencies are strongly suppressed by intrinsic conductivity, momentum-relaxation constraints, and the trade-off between high resistivity and long ballistic length. Under room-temperature conditions, intrinsic carriers collapse the photovoltage as the band gap becomes small, and practical BPVE efficiencies are argued to lie orders of magnitude below the Shockley–Queisser limit, despite the possibility of above-gap photovoltages (Pusch et al., 2022).

The resulting research program is therefore twofold. On the microscopic side, BPVE theory increasingly combines quantum geometry, scattering, excitons, topology, and magnetism rather than isolating a single channel. On the materials side, current design strategies target large shift vectors, favorable interband dipoles, strong polar distortion, symmetry-permitted tensor components, flat-band or Weyl-enhanced geometry, and, as the $$J_i = \sigma_{ijk}(0;\,\omega,-\omega)\,E_j(\omega)\,E_k(-\omega),$$28 results make clear, controlled defect types, densities, and orientations for long-lived photoresponses (Dai et al., 2022, Ganguly et al., 1 Sep 2025).