Nonreciprocal Charge Transport

• Nonreciprocal charge transport is defined by electrical resistance depending on current direction, typically arising from symmetry-breaking effects such as inversion- and time-reversal-symmetry breaking.
• Experimental studies use second-harmonic voltage detection and nonlinear I–V characterizations to quantify the effect, often reporting coefficients in units of A⁻¹T⁻¹ or exhibiting bilinear magnetoresistance responses.
• Applications span semiconductors, superconductors, and topological materials, with tunable mechanisms including Rashba effects, asymmetric scattering, and non-Hermitian transport.

Searching arXiv for recent and foundational papers on nonreciprocal charge transport to ground the article in the literature. Nonreciprocal charge transport (NCT) denotes electrical transport in which the resistance or voltage response depends on current direction, so that opposite current polarities are not equivalent under otherwise fixed conditions. In the literature surveyed here, NCT appears in several phenomenological forms, including a resistance correction linear in both current and magnetic field, a second-order longitudinal voltage detected at $2\omega$, and, in superconductors, current-direction-dependent critical or depinning responses. Across these realizations, the central organizing theme is symmetry: many experimentally established cases require simultaneous inversion-symmetry breaking and time-reversal-symmetry breaking, whereas more recent theory and experiment have also identified longitudinal nonreciprocity in zero-field antiferromagnets, in time-reversal-symmetric noncentrosymmetric conductors through disorder-induced asymmetric scattering, and in open or non-Hermitian transport settings (Li et al., 2022, Nagahama et al., 11 Jul 2025, Varshney et al., 19 Mar 2026, Sudo et al., 8 Nov 2025).

1. Definition, phenomenology, and observables

A standard definition used in recent work is that NCT is a phenomenon where electrical resistance depends on the current direction (Nagahama et al., 11 Jul 2025). In weak-bias magnetochiral settings, this is commonly written as

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$

or, in simplified geometries, as a response proportional to $IB$ (Nagahama et al., 11 Jul 2025). Closely related formulations include

$R=R_0(1+\gamma BI),$

used for polar Dirac metals (Kondo et al., 13 Jan 2025), and

$R(I,B)=R_0\left(1+\beta B^2+\gamma BI\right),$

used for superconducting nonreciprocity in hydrogen-gradient SmFeAsO$_{1-x}$H$_x$ (Nagai et al., 8 Dec 2025).

In harmonic-transport experiments, NCT is typically isolated through a second-harmonic voltage or resistance. For an AC drive $I(t)=I_{\rm ac}\sin\omega t$, a nonlinear $BI$ term generates a $2\omega$ response, and low-frequency lock-in detection of $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$0 or $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$1 is the standard method in semiconductor heterostructures, superconductors, topological systems, and polar metals (Li et al., 2022, Nagai et al., 8 Dec 2025, Wu et al., 2022). Several papers define a nonreciprocal coefficient from the second-harmonic signal. In InSb/CdTe,

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$2

with the hallmark scaling

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$3

for bilinear magnetoresistance (Li et al., 2022). In Ti$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$4O$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$5/GaN,

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$6

while the phenomenological second-harmonic form is

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$7

(Dong et al., 2024).

The nonlinear $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$8-$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$9 viewpoint is equally common. A general expansion,

$IB$0

was developed for two-dimensional noncentrosymmetric superconductors, where $IB$1 is the leading nonreciprocal coefficient and its temperature and field dependence diagnose the operative mechanism (Hoshino et al., 2018). In zero-field antiferromagnetic NdRu$IB$2Al$IB$3, the response is written as

$IB$4

so NCT is encoded directly in the $IB$5 term (Sudo et al., 8 Nov 2025).

A common misconception is that any finite $IB$6 resistance is intrinsic NCT. Bulk FeSe provides a counterexample: substantial second-harmonic signals can arise from Joule heating at current contacts and thermoelectric voltages, including Seebeck and Nernst contributions, rather than genuine nonreciprocal transport (Terashima et al., 13 Feb 2025).

2. Symmetry principles and microscopic mechanisms

In many experimentally established normal-state realizations, NCT requires both inversion-symmetry breaking and time-reversal-symmetry breaking. In the InSb/CdTe heterostructure, inversion symmetry is broken by the asymmetric interface and its built-in electric field, while time-reversal symmetry is broken by an external magnetic field; together they generate a magnetochiral or bilinear magnetoresistance response (Li et al., 2022). The associated Rashba description is

$IB$7

with a second-order current

$IB$8

(Li et al., 2022). Related symmetry selection rules appear in polar metals as

$IB$9

so the signal is strongest when polarization, field, and current are mutually orthogonal (Kondo et al., 13 Jan 2025).

Microscopically, several distinct routes to NCT recur across the literature. In Rashba systems, interfacial electric fields produce antisymmetric spin-orbit coupling, spin-momentum locking, and asymmetric spin subband shifts under magnetic field (Li et al., 2022). In polar Dirac metals BaMn$R=R_0(1+\gamma BI),$0, the relevant texture is Zeeman-type spin-valley coupling in spin-polarized Dirac valleys rather than a simple Rashba splitting (Kondo et al., 13 Jan 2025). In magnetic topological insulators such as MnBi$R=R_0(1+\gamma BI),$1Te$R=R_0(1+\gamma BI),$2, NCT is tied to chiral edge transport and the hybridization of chiral edge channels with trivial or dissipative states, which produces asymmetric dispersion for opposite propagation directions (Zhang et al., 2022). In quantum Hall states of Sn-Bi$R=R_0(1+\gamma BI),$3Sb$R=R_0(1+\gamma BI),$4Te$R=R_0(1+\gamma BI),$5S, the proposed mechanism is asymmetric scattering between chiral quantum Hall edge states and broadened Landau-orbit states of the Dirac surface, with

$R=R_0(1+\gamma BI),$6

capturing the gate-dependent peak–valley structure through the derivative of the broadened Landau-level density of states (Li et al., 2023).

Theoretical work has broadened the symmetry landscape. A general theory for longitudinal NCT in crystalline materials, formulated within semiclassical Boltzmann transport, classifies all 122 magnetic point groups and identifies 42 magnetic point groups that allow intrinsic longitudinal NCT (Zhao et al., 2024). In that framework,

$R=R_0(1+\gamma BI),$7

and asymmetric band dispersion is the essential microscopic ingredient (Zhao et al., 2024). A later disorder-based theory shows that longitudinal NCT can remain finite even in time-reversal-symmetric, nonmagnetic, noncentrosymmetric conductors through skew scattering and side jump, with

$R=R_0(1+\gamma BI),$8

and identifies 42 point groups that permit this $R=R_0(1+\gamma BI),$9-even extrinsic mechanism (Varshney et al., 19 Mar 2026). This directly overturns the belief that longitudinal nonreciprocity necessarily requires magnetic order or an external magnetic field (Varshney et al., 19 Mar 2026).

3. Semiconductor, topological, magnetic, and polar-material realizations

A prominent room-temperature semiconductor realization is the lattice-matched InSb/CdTe heterostructure, which exhibits unidirectional magnetoresistance up to 298 K (Li et al., 2022). The key materials parameters reported are a built-in electric field

$R(I,B)=R_0\left(1+\beta B^2+\gamma BI\right),$0

localized near the interface with estimated width about 8 nm, a Rashba coefficient

$R(I,B)=R_0\left(1+\beta B^2+\gamma BI\right),$1

effective mass $R(I,B)=R_0\left(1+\beta B^2+\gamma BI\right),$2, in-plane $R(I,B)=R_0\left(1+\beta B^2+\gamma BI\right),$3, and $R(I,B)=R_0\left(1+\beta B^2+\gamma BI\right),$4 (Li et al., 2022). At 298 K the nonreciprocal coefficient reaches

$R(I,B)=R_0\left(1+\beta B^2+\gamma BI\right),$5

described as $R(I,B)=R_0\left(1+\beta B^2+\gamma BI\right),$6–$R(I,B)=R_0\left(1+\beta B^2+\gamma BI\right),$7 orders of magnitude larger than most non-centrosymmetric materials at room temperature, and top-gating through 50 nm Al$R(I,B)=R_0\left(1+\beta B^2+\gamma BI\right),$8O$R(I,B)=R_0\left(1+\beta B^2+\gamma BI\right),$9 modulates the UMR amplitude by about 40% (Li et al., 2022).

Topological platforms display several distinct NCT regimes. In MnBi$_{1-x}$0Te$_{1-x}$1, the longitudinal resistance depends on current direction along a chiral edge, with the effect being magnetically switchable, edge-position sensitive, septuple-layer-number controllable, and gate tunable (Zhang et al., 2022). The phenomenology is written as

$_{1-x}$2

which makes the joint role of magnetization and edge dipole explicit (Zhang et al., 2022). In Sn-BSTS quantum Hall devices, NCT is strongest in plateau-transition regions rather than in the fully quantized plateau, reverses with the sign of $_{1-x}$3, and attains a giant coefficient

$_{1-x}$4

at $_{1-x}$5 K in the $_{1-x}$6 transition (Li et al., 2023).

Magnetic and chiral metals offer yet another route. Pt$_{1-x}$7MnGe thin films realize large NCT from 5 K to 400 K, interpreted as chirality-dependent asymmetric carrier scattering from a noncollinear magnetic state with nonzero vector spin chirality under in-plane field (Meng et al., 2022). The electrical magnetochiral anisotropy is expressed as

$_{1-x}$8

and the reported coefficient is

$_{1-x}$9

in the 200–400 K range (Meng et al., 2022). In PMG/Pt bilayers, the chirality can be reversed by a spin-polarized current generated through the spin Hall effect in the Pt layer (Meng et al., 2022).

Polar Dirac metals BaMnSb$_x$0 and BaMnBi$_x$1 demonstrate intrinsic bulk rectification tied to tunable spin-valley structure (Kondo et al., 13 Jan 2025). The bulk rectification coefficient is extracted as

$_x$2

after fitting

$_x$3

BaMnSb$_x$4 shows $_x$5 exceeding

$_x$6

at low temperature for $_x$7, whereas BaMnBi$_x$8 is reduced to about

$_x$9

and peaks around 60 K because multiple valley types partially cancel (Kondo et al., 13 Jan 2025).

4. Superconducting NCT: fluctuations, vortices, helical states, and diode physics

Superconductors constitute a major NCT class because the relevant energy scale is reduced from $I(t)=I_{\rm ac}\sin\omega t$0 to the superconducting gap or fluctuation scale, greatly enhancing nonlinear response (Hoshino et al., 2018). A unified theory for two-dimensional noncentrosymmetric superconductors writes

$I(t)=I_{\rm ac}\sin\omega t$1

and shows that above the mean-field transition $I(t)=I_{\rm ac}\sin\omega t$2,

$I(t)=I_{\rm ac}\sin\omega t$3

with $I(t)=I_{\rm ac}\sin\omega t$4 finite at $I(t)=I_{\rm ac}\sin\omega t$5; near the KT transition in in-plane-field systems, $I(t)=I_{\rm ac}\sin\omega t$6 (Hoshino et al., 2018). For transition-metal dichalcogenides under out-of-plane field, the theory distinguishes damping-anisotropy and ratchet-potential mechanisms by the field scaling of $I(t)=I_{\rm ac}\sin\omega t$7: $I(t)=I_{\rm ac}\sin\omega t$8 versus $I(t)=I_{\rm ac}\sin\omega t$9 (Hoshino et al., 2018).

Several experiments realize these regimes. In Ti$BI$0O$BI$1/GaN, NCT emerges in the superconducting transition regime around 3–3.5 K, with $BI$2 K and a large

$BI$3

around 3 K (Dong et al., 2024). The signal is maximal only when the magnetic field is in plane and perpendicular to current, and it disappears for tilts beyond roughly $BI$4, which is interpreted as a crossover from a symmetry-breaking helical state to a symmetric state (Dong et al., 2024). In 1T-CrTe$BI$5/FeTe, second-harmonic transport reveals strong NCT only in the transition regime $BI$6, with

$BI$7

for the $BI$8 heterostructure and

$BI$9

at $2\omega$0 K (Yan et al., 2024).

Vortex motion is a recurring mechanism. In the hydrogen-gradient Sm1111:H superconductor, a depthwise H-concentration gradient acts as a polar axis and creates an asymmetric pinning landscape. NCT appears only near the superconducting transition, with $2\omega$1 K in the gradient sample, and the antisymmetric $2\omega$2 peak–valley structure around $2\omega$3 is identified as the canonical fingerprint of superconducting nonreciprocal transport (Nagai et al., 8 Dec 2025). The work attributes the signal to vortex-motion nonreciprocity rather than paraconductivity and states that vortex-origin NCT is observed above 40 K, representing the highest temperature reported to date among single bulk materials without an artificially hetero-layered structure (Nagai et al., 8 Dec 2025). In CsV$2\omega$4Sb$2\omega$5, second-harmonic voltages develop with both in-plane and out-of-plane magnetic fields in the vortex-flow regime, split into several peak series, and some reverse sign with field or current, suggesting strong asymmetry not readily explained by the centrosymmetric crystal structure alone (Wu et al., 2022).

The superconducting diode limit is treated most explicitly in voltage-biased Josephson junctions involving helical superconductors with finite Cooper-pair momentum $2\omega$6 (Zazunov et al., 2023). In equilibrium, the diode efficiency is

$2\omega$7

with maximal reported $2\omega$8 in the optimal ballistic low-temperature case (Zazunov et al., 2023). Under voltage bias, multiple Andreev reflection on Doppler-shifted gaps $2\omega$9 yields richer subharmonic structure, and in the low-voltage ballistic limit the rectification efficiency can reach

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$00

(Zazunov et al., 2023).

5. Zero-field, time-reversal-symmetric, ballistic, and non-Hermitian extensions

Although the canonical picture ties NCT to simultaneous inversion and time-reversal breaking, several recent developments establish broader classes of longitudinal nonreciprocity.

A striking experimental example is the zero-magnetization antiferromagnet NdRu$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$01Al$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$02, which exhibits spontaneous NCT at zero magnetic field below

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$03

(Sudo et al., 8 Nov 2025). The effect is attributed to antiferromagnetic order interpretable as magnetic toroidal dipole order, which breaks time reversal and spatial inversion while preserving the symmetry conditions that forbid a zero-field anomalous Hall effect yet allow nonreciprocal longitudinal transport (Sudo et al., 8 Nov 2025). The reported average second-order nonlinear conductivity is

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$04

described as orders of magnitude larger than many field-induced cases (Sudo et al., 8 Nov 2025). The sign of $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$05 depends on the antiferromagnetic domain, suggesting electrical sensitivity to domain spin configuration (Sudo et al., 8 Nov 2025).

A complementary theoretical route keeps time reversal intact. In nonmagnetic, noncentrosymmetric conductors, skew scattering and side-jump processes can generate a finite $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$06-even nonlinear longitudinal current through asymmetric impurity scattering (Varshney et al., 19 Mar 2026). The theory decomposes the scattering probability as

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$07

with $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$08 responsible for the asymmetric part, and expresses the nonlinear conductivity as

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$09

In $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$10-symmetric systems, $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$11 vanishes but $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$12 and $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$13 remain finite (Varshney et al., 19 Mar 2026). Bernal bilayer graphene under displacement field is proposed as a concrete realization, with theoretical nonreciprocity factors up to $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$14 and experimentally extracted values around $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$15 at accessible fields $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$16 V/mm (Varshney et al., 19 Mar 2026).

Ballistic and open-system formulations introduce still different mechanisms. In gauge-invariant nonlinear ballistic transport, asymmetric band structures lead to unequal injectivities,

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$17

so the self-consistent Coulomb potential satisfies

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$18

yielding a second-order conductance

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$19

and a generalized reciprocity relation

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$20

rather than simple antisymmetry under bias reversal (Zou et al., 2023). In mesoscopic heterojunctions with a coherently coupled reservoir, the effective Hamiltonian becomes non-Hermitian, with direction-dependent lifetimes

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$21

point-gap spectral topology, and nonreciprocal conductance

$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$22

as a transport signature of the non-Hermitian skin effect (Geng et al., 2022). Open quantum wires with balanced gain and loss in the bulk provide a further linear-response NCT setting in which parity breaking plus inelastic scattering are essential; the nonreciprocity saturates in the strongly inelastic regime and can oscillate with system length when coherence is retained (Bag et al., 2024).

6. Tunability, diagnostics, and open issues

A major trend across the field is the use of electrostatic, compositional, thickness, and geometry control to tune either the sign or the magnitude of NCT. In InSb/CdTe, top-gate voltage redistributes transport between the interfacial Rashba channel and the bulk InSb channel, producing about 40% modulation of the UMR amplitude from 1.5 K to 298 K (Li et al., 2022). In topological-insulator/superconductor heterostructures $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$23, tuning the Sb composition moves the topological surface-state Fermi level across the charge neutral point: the NCT prefactor $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$24 is negative for $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$25, positive for $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$26, and changes sign between $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$27 and $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$28, consistent with a proximitized TSS model including a quadratic correction (Nagahama et al., 11 Jul 2025). Reducing the FST thickness from 8 nm to 2 nm enhances $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$29 by about $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$30 in BT/FST and about an order of magnitude in ST/FST, which is attributed to inversion-symmetry breaking in the superconducting layer itself adjacent to the TI (Nagahama et al., 11 Jul 2025).

Thickness, layer number, and edge choice act as additional knobs. In MnBi$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$31Te$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$32, 5-septuple-layer devices show finite zero-field NCT whereas 4-septuple-layer devices do not, reflecting the difference between uncompensated and compensated magnetic states; left and right edges display opposite trends, demonstrating edge-controlled chirality (Zhang et al., 2022). In CsV$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$33Sb$$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$34, the multipeak, sign-changing $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$35 is stronger for in-plane than out-of-plane field and decreases when current exceeds about 0.2 mA, consistent with current-induced weakening of vortex pinning (Wu et al., 2022). In PMG/Pt, the sign of the EMCA coefficient can be switched by sufficiently large current density through spin-Hall-induced chirality reversal (Meng et al., 2022).

The field also faces methodological issues. The most important experimental diagnostic remains the combination of symmetry selection, current scaling, field scaling, and artifact rejection. Genuine magnetochiral signals typically exhibit $$R = R_0\left[1+\gamma\,(\hat{\mathbf z}\times \mathbf I)\cdot \mathbf B\right],$$36, geometry-specific angular dependence, and sign reversal under the symmetry operation appropriate to the platform (Li et al., 2022, Yan et al., 2024, Kondo et al., 13 Jan 2025). The FeSe study shows why these criteria are necessary but not always sufficient: contact-configuration dependence, correlation with contact resistance, sensitivity to the helium thermal environment, and frequency-dependent phase lag all point to thermoelectric artifacts rather than intrinsic NCT (Terashima et al., 13 Feb 2025). This suggests that contact engineering and thermal diagnostics are not auxiliary issues but central parts of NCT metrology.

At the conceptual level, two open tensions structure the present literature. First, some studies interpret strong superconducting NCT as evidence for helical superconductivity or unconventional order-parameter symmetry, whereas others attribute comparable second-harmonic signals to asymmetric vortex dynamics or ratchet-like pinning (Dong et al., 2024, Wu et al., 2022, Nagai et al., 8 Dec 2025). Second, the boundary between intrinsic band-structure mechanisms and extrinsic scattering mechanisms has become less rigid: asymmetric band dispersion, disorder-induced skew scattering, self-consistent Coulomb potentials, and reservoir-engineered non-Hermiticity all generate longitudinal nonreciprocity in settings that were previously treated separately (Zhao et al., 2024, Varshney et al., 19 Mar 2026, Zou et al., 2023, Geng et al., 2022). A plausible implication is that “nonreciprocal charge transport” now functions less as a single mechanism than as a symmetry-defined transport class spanning crystalline, superconducting, topological, mesoscopic, and open-system regimes.