Linear Photogalvanic Effect (LPGE) Overview

• LPGE is a second-order nonlinear optical effect where linearly polarized light in non-centrosymmetric media induces a DC current, characterized by a third-rank tensor.
• It leverages symmetry considerations and harmonic analysis to distinguish its contributions from the circular photogalvanic effect in various material platforms.
• Microscopic mechanisms including shift current, asymmetric scattering, and hydrodynamic responses provide insights into optimizing optoelectronic devices.

Searching arXiv for recent and foundational LPGE papers to support the encyclopedia entry. Tool call: arxiv_search.query {"search_query":"all:\"linear photogalvanic effect\" OR all:LPGE","start":0,"max_results":10,"sort_by":"submittedDate","sort_order":"descending"} The linear photogalvanic effect (LPGE) is a second-order nonlinear optical response in which linearly polarized radiation generates a dc electric current in a non-centrosymmetric medium. In its most general form, the current is quadratic in the optical field and is described by a third-rank tensor, $j_i=\sum_{jk}\chi_{ijk}E_jE_k^*$, with the LPGE distinguished from the circular photogalvanic effect (CPGE) by its dependence on the linear-polarization sector of the optical field rather than on helicity (Wittmann et al., 2010). Across contemporary literature, LPGE encompasses several microscopic realizations—including shift current, ballistic or disorder-assisted current, Drude-like rectification, and hydrodynamic analogues—whose relative importance depends on symmetry, band structure, scattering, and excitation regime (0904.1917).

1. Constitutive description and relation to polarization

A standard decomposition expresses the dc photocurrent as the sum of a symmetric, linear-polarization-driven part and an antisymmetric, helicity-driven part. In HgTe/CdHgTe quantum wells, the phenomenological form is written as

$$j_i=\sum_{jk}\chi_{ijk}E_jE_k^*+\sum_\beta \gamma_{i\beta}\hat e_\beta P_{\mathrm{circ}}|E|^2,$$

where $\chi_{ijk}$ describes LPGE, $\gamma_{i\beta}$ describes CPGE, $\hat e$ is the propagation direction inside the medium, and $P_{\mathrm{circ}}$ is the radiation helicity (Wittmann et al., 2010). In terms of Stokes parameters,

$$S_1=|E_x|^2-|E_y|^2,\qquad S_2=E_xE_y^*+E_yE_x^*,\qquad S_3=i(E_xE_y^*-E_yE_x^*),$$

LPGE is governed by $S_1$ and $S_2$, whereas CPGE scales with $S_3$ (Wittmann et al., 2010).

In many modern treatments, especially for interband responses, LPGE is also written as a second-order conductivity: $$j_i=\sum_{jk}\chi_{ijk}E_jE_k^*+\sum_\beta \gamma_{i\beta}\hat e_\beta P_{\mathrm{circ}}|E|^2,$$0 with $$j_i=\sum_{jk}\chi_{ijk}E_jE_k^*+\sum_\beta \gamma_{i\beta}\hat e_\beta P_{\mathrm{circ}}|E|^2,$$1 interpreted as a shift-conductivity tensor (Zheng et al., 2023). This language is exact when the dominant LPGE channel is a shift current; however, it is narrower than the full LPGE taxonomy, because other works explicitly retain ballistic, disorder-assisted, and hydrodynamic contributions within the same linear-polarization-driven dc response (Leppenen et al., 2022).

The angular dependence follows directly from symmetry. For linearly polarized light in low-symmetry quantum wells, LPGE often appears as

$$j_i=\sum_{jk}\chi_{ijk}E_jE_k^*+\sum_\beta \gamma_{i\beta}\hat e_\beta P_{\mathrm{circ}}|E|^2,$$2

where $$j_i=\sum_{jk}\chi_{ijk}E_jE_k^*+\sum_\beta \gamma_{i\beta}\hat e_\beta P_{\mathrm{circ}}|E|^2,$$3 is the polarization-plane angle with respect to a crystallographic axis (Wittmann et al., 2010). On topological-insulator surfaces with $$j_i=\sum_{jk}\chi_{ijk}E_jE_k^*+\sum_\beta \gamma_{i\beta}\hat e_\beta P_{\mathrm{circ}}|E|^2,$$4 symmetry, the linear regime yields the familiar second harmonic in the polarization angle, while the nonlinear saturation regime can generate fourth harmonics through the ballistic channel (Leppenen et al., 2022).

2. Symmetry conditions and selection rules

Broken inversion symmetry is the essential requirement for LPGE. In centrosymmetric crystals the second-order conductivity vanishes by inversion symmetry, which is why LPGE is absent in pristine bilayer graphene but becomes allowed once a gate voltage imposes opposite on-site potentials on the two layers (Zheng et al., 2023). The same logic underlies surface-enabled LPGE in centrosymmetric bulk systems: inversion is forbidden in the bulk but broken at a surface, allowing a surface photocurrent (Shah et al., 13 May 2026).

The detailed tensor structure is fixed by point-group symmetry. In $$j_i=\sum_{jk}\chi_{ijk}E_jE_k^*+\sum_\beta \gamma_{i\beta}\hat e_\beta P_{\mathrm{circ}}|E|^2,$$5-grown HgTe/CdHgTe quantum wells with $$j_i=\sum_{jk}\chi_{ijk}E_jE_k^*+\sum_\beta \gamma_{i\beta}\hat e_\beta P_{\mathrm{circ}}|E|^2,$$6 symmetry, the relevant in-plane LPGE tensor elements are $$j_i=\sum_{jk}\chi_{ijk}E_jE_k^*+\sum_\beta \gamma_{i\beta}\hat e_\beta P_{\mathrm{circ}}|E|^2,$$7 and $$j_i=\sum_{jk}\chi_{ijk}E_jE_k^*+\sum_\beta \gamma_{i\beta}\hat e_\beta P_{\mathrm{circ}}|E|^2,$$8, so a nonzero $$j_i=\sum_{jk}\chi_{ijk}E_jE_k^*+\sum_\beta \gamma_{i\beta}\hat e_\beta P_{\mathrm{circ}}|E|^2,$$9 is required. Consequently, for in-plane current detection, LPGE vanishes at normal incidence and appears only at oblique incidence (Wittmann et al., 2010). In $\chi_{ijk}$0-grown HgTe/CdHgTe wells, the symmetry is $\chi_{ijk}$1, so all $\chi_{ijk}$2 components are allowed and LPGE is present already at normal incidence, with currents flowing along arbitrary in-plane directions (Wittmann et al., 2010).

The same $\chi_{ijk}$3 logic governs inverted GaSb/InAs quantum wells. There the allowed LPGE tensor components are $\chi_{ijk}$4 and $\chi_{ijk}$5, and the effect requires simultaneous in-plane and out-of-plane field components, so the bulk LPGE vanishes at normal incidence and changes sign with the incidence angle through the $\chi_{ijk}$6 factors in the theory (Plank et al., 2016).

Other material classes realize different symmetry patterns. Gated AB-stacked bilayer graphene has $\chi_{ijk}$7 symmetry and supports in-plane LPGE even at normal incidence through a nonzero $\chi_{ijk}$8, whereas gated AA-stacked bilayer graphene has $\chi_{ijk}$9 symmetry, which forces $\gamma_{i\beta}$0 and therefore requires oblique incidence for in-plane LPGE (Zheng et al., 2023). In buckled group-V monolayers with point group $\gamma_{i\beta}$1, mirror symmetry $\gamma_{i\beta}$2 enforces an orientation dichotomy: charge LPGE is allowed along the armchair direction, while spin-LPGE is allowed along the zigzag direction for the polarization configurations considered (Zhang et al., 2023). On the surface of magnetic Co$\gamma_{i\beta}$3Sn$\gamma_{i\beta}$4S$\gamma_{i\beta}$5, inversion is broken at the surface, $\gamma_{i\beta}$6 constrains the in-plane second-order tensor, and an antiunitary mirror $\gamma_{i\beta}$7 forces several intrinsic LPGE tensor elements to vanish (Shah et al., 13 May 2026).

These examples show that LPGE is not a single universal angular law but a family of symmetry-governed responses. A plausible implication is that photogalvanic measurements can function as a sensitive diagnostic of hidden surface, interface, and structural asymmetries.

3. Microscopic mechanisms

Several microscopic channels produce LPGE. In semiclassical transport theory, the 2009 treatment of nonlinear transport in non-centrosymmetric media showed that LPGE and nonlinear $\gamma_{i\beta}$8-$\gamma_{i\beta}$9 characteristics are governed mainly by skew scattering, whereas CPGE is governed by Berry-curvature and side-jump terms (0904.1917). In this picture, asymmetric scattering rectifies the ac-driven anisotropy of the distribution function into a dc current.

In quantum wells driven in the THz Drude regime, the dominant LPGE mechanism is often orbital. In HgTe/CdHgTe wells, LPGE is attributed phenomenologically to second-order response in a non-centrosymmetric structure where structural inversion asymmetry and strong Rashba spin-orbit coupling permit asymmetric scattering and anisotropic momentum relaxation; in the THz regime, orbital mechanisms dominate, while under MIR interband excitation LPGE is compatible with anisotropic photoexcited-carrier distributions and asymmetric scattering (Wittmann et al., 2010). In GaSb/InAs wells, the microscopic theory is a Boltzmann ratchet mechanism: the in-plane ac field drives carriers, the out-of-plane field modulates scattering and mobility, and the phase-shifted product rectifies into a dc current containing both LPGE and CPGE pieces (Plank et al., 2016).

In topological-insulator surface states, both shift and ballistic channels can contribute at the same order. For direct optical transitions between TI surface states, the shift contribution is set by coordinate shifts of wavepackets during interband absorption, while the ballistic contribution is caused by interference of optical absorption and scattering by disorder; the two are generally of the same order of magnitude, but only the ballistic part has a frequency dependence and only the ballistic part generates the nontrivial fourth-harmonic polarization dependence in the nonlinear regime (Leppenen et al., 2022).

In first-principles quantum kinetics, LPGE as a shift current is explicitly tied to quantum geometry. The clean-limit excitation shift current depends on the shift vector

$\hat e$0

while the 2026 density-matrix theory further shows that phonon-mediated scattering can contribute significantly to the shift current in BaTiO$\hat e$1, resolving earlier underestimation of the experimental photocurrent (Yu et al., 3 Jan 2026). In semi-Dirac systems, the LPGE shift conductivity is governed by the symplectic connection, and specific tensor components track the Lifshitz transition (Ghosh et al., 24 Feb 2026).

This literature also clarifies a frequent misconception: LPGE is not reducible to one mechanism. Depending on the system, it can be dominated by shift current, by skew/disorder-assisted transport, by orbital Drude rectification, or even by hydrodynamic nonlinearities.

4. Experimental signatures and separation from CPGE

A central experimental task is separating LPGE from CPGE. In HgTe/CdHgTe wells illuminated with elliptically polarized light controlled by a quarter-wave element, CPGE appears as a $\hat e$2 harmonic, whereas LPGE contributes $\hat e$3, $\hat e$4, and, in $\hat e$5 symmetry, a polarization-independent offset: $\hat e$6 with $\hat e$7, $\hat e$8, and $\hat e$9 identified as LPGE (Wittmann et al., 2010). For purely linearly polarized light in the same $P_{\mathrm{circ}}$0 wells, the photocurrent follows

$P_{\mathrm{circ}}$1

which isolates LPGE (Wittmann et al., 2010).

GaSb/InAs quantum wells exhibit the same separation strategy. Under $P_{\mathrm{circ}}$2-plate rotation at oblique incidence,

$P_{\mathrm{circ}}$3

so the longitudinal component is purely LPGE in that geometry (Plank et al., 2016). The angle-of-incidence reversal further changes the sign of both LPGE and CPGE through the same $P_{\mathrm{circ}}$4 factor (Plank et al., 2016).

Topological-insulator surface states offer another diagnostic. In $P_{\mathrm{circ}}$5Te, normal-incidence LPGE follows a pure $P_{\mathrm{circ}}$6 dependence, and the current is unchanged when illumination switches from front to back. That front/back invariance rules out a photon-drag origin proportional to $P_{\mathrm{circ}}$7 and identifies the response as LPGE of the surface states (Doneva et al., 2017). In magnetic Co$P_{\mathrm{circ}}$8Sn$P_{\mathrm{circ}}$9S$$S_1=|E_x|^2-|E_y|^2,\qquad S_2=E_xE_y^*+E_yE_x^*,\qquad S_3=i(E_xE_y^*-E_yE_x^*),$$0, the total LPGE current reverses sign at symmetry-selected polarization angles upon flipping the magnetization, and in that configuration the CPGE vanishes identically because $$S_1=|E_x|^2-|E_y|^2,\qquad S_2=E_xE_y^*+E_yE_x^*,\qquad S_3=i(E_xE_y^*-E_yE_x^*),$$1 enforces $$S_1=|E_x|^2-|E_y|^2,\qquad S_2=E_xE_y^*+E_yE_x^*,\qquad S_3=i(E_xE_y^*-E_yE_x^*),$$2 (Shah et al., 13 May 2026).

This body of work suggests that LPGE identification rests on a combination of harmonic analysis, incidence-angle dependence, surface-versus-bulk tests, and symmetry-controlled sign reversals rather than on amplitude alone.

5. Material platforms and spectral regimes

Quantum wells remain a canonical LPGE platform. HgTe/CdHgTe structures show LPGE under both MIR interband excitation and THz intrasubband absorption, with polarization laws that track the symmetry class and with substantial LPGE terms in $$S_1=|E_x|^2-|E_y|^2,\qquad S_2=E_xE_y^*+E_yE_x^*,\qquad S_3=i(E_xE_y^*-E_yE_x^*),$$3 samples (Wittmann et al., 2010). In inverted GaSb/InAs quantum wells, LPGE and CPGE are of comparable magnitude at room temperature under oblique THz excitation, and both decrease with frequency in a Drude-like manner (Plank et al., 2016).

Surface states of topological materials form a second major platform. In $$S_1=|E_x|^2-|E_y|^2,\qquad S_2=E_xE_y^*+E_yE_x^*,\qquad S_3=i(E_xE_y^*-E_yE_x^*),$$4Te topological insulators, LPGE dominates the photocurrent over 0.6–60 THz, exhibits a low-frequency Drude-like spectrum $$S_1=|E_x|^2-|E_y|^2,\qquad S_2=E_xE_y^*+E_yE_x^*,\qquad S_3=i(E_xE_y^*-E_yE_x^*),$$5, and even allows extraction of room-temperature surface mobilities despite residual bulk impurities (Doneva et al., 2017). The same TI literature predicts direct inter-surface-state LPGE controlled by warping, with shift and ballistic contributions of the same order (Leppenen et al., 2022). In Weyl systems, confinement and surface boundary conditions can enable LPGE in otherwise symmetry-forbidden situations, and in Co$$S_1=|E_x|^2-|E_y|^2,\qquad S_2=E_xE_y^*+E_yE_x^*,\qquad S_3=i(E_xE_y^*-E_yE_x^*),$$6Sn$$S_1=|E_x|^2-|E_y|^2,\qquad S_2=E_xE_y^*+E_yE_x^*,\qquad S_3=i(E_xE_y^*-E_yE_x^*),$$7S$$S_1=|E_x|^2-|E_y|^2,\qquad S_2=E_xE_y^*+E_yE_x^*,\qquad S_3=i(E_xE_y^*-E_yE_x^*),$$8 the surface LPGE is dominated by extrinsic contributions associated with Fermi-arc surface states (Steiner et al., 2021, Shah et al., 13 May 2026).

Two-dimensional materials have broadened the LPGE landscape. Gated AB-stacked bilayer graphene exhibits large, gate-tunable LPGE starting at the gate-induced band gap; for $$S_1=|E_x|^2-|E_y|^2,\qquad S_2=E_xE_y^*+E_yE_x^*,\qquad S_3=i(E_xE_y^*-E_yE_x^*),$$9 eV, intensity $S_1$0 GW/cm$S_1$1, normal incidence, and width $S_1$2m, the predicted LPGE current is about $S_1$3 mA (Zheng et al., 2023). In contrast, gated AA-stacked bilayer graphene supports a much narrower spectral window and weaker magnitudes (Zheng et al., 2023). In monolayer WTe$S_1$4, LPGE is large and nearly constant in the radio region, begins to decrease in the microwave region, and is dominated by interband-3 contributions in the 50–100 THz range; the maximum frequency at which the Berry-curvature-dipole mechanism for the nonlinear Hall effect plays a major role is about $S_1$5 THz (Liu et al., 2023). In buckled As, Sb, and Bi monolayers, LPGE can generate either net charge current or pure spin current depending on crystal orientation and polarization, with a giant anisotropy ratio $S_1$6 reported for As at $S_1$7 (Zhang et al., 2023). In nickel–phosphorene–nickel devices, mechanically increased $S_1$8 asymmetry enhances zero-bias LPGE by up to $S_1$9 under tension and about $S_2$0 under bending (Zhao et al., 2020).

Unconventional regimes also exist. A hydrodynamic analogue of LPGE appears in nonreciprocal electron liquids with broken inversion and time-reversal symmetry, where the dc current scales quadratically with the ac drive and exhibits super-extensive low-frequency scaling $S_2$1 (Kirkinis et al., 9 Jul 2025). In a gated 2D electron strip under perpendicular magnetic field, magnetoplasmon excitation by linearly polarized light yields a resonant dc current and photovoltage through the nonlinear convective term of hydrodynamics (Rodionov et al., 11 Dec 2025).

6. Conceptual scope, methodological issues, and outlook

Two methodological conclusions recur across the literature. First, clean-limit formulas are often insufficient. In monolayer WTe$S_2$2, the theories in the clean limit fail once realistic femtosecond-scale relaxation times and small interband splittings are considered, and quantum kinetics with scattering becomes necessary (Liu et al., 2023). In BaTiO$S_2$3, phonon-mediated scattering contributes significantly to the shift current, and including it explains why previous first-principles work underestimated the experimental LPGE (Yu et al., 3 Jan 2026). Second, first-principles and quantum-kinetic approaches increasingly replace purely phenomenological descriptions when quantitative comparison to experiment is required (Hornung et al., 2020, Yu et al., 3 Jan 2026).

A second conceptual point concerns topology. Strong spin–orbit coupling, band inversion, or surface Fermi arcs can enhance or reshape LPGE, but LPGE itself does not require topological band features. In HgTe quantum wells, the phenomenology is tied to non-centrosymmetric symmetry and anisotropic scattering rather than to topology as such (Wittmann et al., 2010). Conversely, in surface-sensitive systems such as Weyl semimetals and topological insulators, the boundary can be the decisive symmetry-breaking element that makes LPGE observable at all (Doneva et al., 2017, Steiner et al., 2021).

The contemporary view therefore treats LPGE as a broad family of symmetry-allowed rectification phenomena. It serves simultaneously as a probe of $S_2$4 and $S_2$5, a diagnostic of inversion asymmetry and surface symmetry, a route to extracting transport parameters such as mobility and relaxation time, and a platform for charge-, spin-, and magnetization-controlled optoelectronics [(Wittmann et al., 2010); (Doneva et al., 2017); (Zhang et al., 2023); (Zheng et al., 2023)]. Further work on time-resolved photogalvanics, scattering-inclusive first-principles theory, and symmetry-engineered surfaces suggests that the most informative LPGE observables will continue to be not just magnitude, but tensor structure, polarization harmonics, and their dependence on geometry, disorder, and quantum geometry.