Spontaneous Nonreciprocal Transport

• Spontaneous nonreciprocal transport is the emergence of asymmetric directional responses that arise from internal symmetry-breaking mechanisms such as magnetic, ferroelectric, or topological orders.
• It is characterized experimentally by a quadratic current dependence in second-harmonic voltage or resistance measurements, with clear signatures in angular, temperature, and field scans.
• Microscopic routes include asymmetric quasiparticle scattering, intrinsic band asymmetry, toroidal order, and quantum-geometric effects, leading to robust nonreciprocal responses in diverse quantum materials.

Searching arXiv for recent and related papers on spontaneous nonreciprocal transport. Spontaneous nonreciprocal transport is the appearance of direction-dependent transport generated by a system’s own ordered state rather than by an externally engineered diode geometry, patterned asymmetry, or purely extrinsic field configuration. In its most common electrical form, it means that the response for opposite current directions is unequal, $R(+I)\neq R(-I)$ or $V(+I)\neq V(-I)$, and the current–voltage relation acquires a second-order term such as $V = R_0 I + \gamma B I^2 + \dots$ or $E = \rho j + \gamma j^2$ (Ye et al., 2022, Sudo et al., 8 Nov 2025). In a broader sense, the same idea includes zero-bias bulk photovoltaic currents $j_a=\beta_{abc}E_bE_c$, superconducting diode behavior, and other directional transport phenomena whose sign and magnitude are fixed by intrinsic chirality, polarization, magnetism, toroidal order, or topology rather than by a conventional junction (Zhang et al., 15 Dec 2025, Kokkeler et al., 2023).

1. Definition and phenomenology

The defining operational criterion is directional asymmetry under reversal of the driving. For dissipative electrical transport, this is usually expressed as a second-order contribution to the voltage or resistivity, so that the linear Ohmic term is supplemented by a term even in the current magnitude but odd under current reversal through the overall response. In AC measurements with $I_\omega = I\sin(\omega t)$, the quadratic contribution produces a second-harmonic voltage $V^{2\omega}$, which is why nonreciprocal transport is commonly quantified through $V_{xx}^{2\omega}$, $V_{xy}^{2\omega}$, or the corresponding second-harmonic resistance (Ye et al., 2022).

“Spontaneous” does not denote a single experimental protocol. In strict zero-field realizations, the required symmetry breaking is entirely internal, as in the zero-magnetic-field nonreciprocal charge transport reported for the antiferromagnet NdRu$_2$Al$V(+I)\neq V(-I)$0 and in the ferromagnetic Rashba 2DEG at EuO/SrTiO$V(+I)\neq V(-I)$1 interfaces (Sudo et al., 8 Nov 2025, Lazrak et al., 21 Aug 2025). In other cases, external magnetic fields are used mainly to align domains or select a magnetic configuration, while the existence of the nonreciprocal tensor itself is rooted in spontaneous ferroelectric, antiferromagnetic, or topological order; the multiferroic Rashba semiconductor (Ge,Mn)Te is the clearest example of this distinction (Yoshimi et al., 2022).

The same phenomenology extends beyond dc charge transport. In layered hybrid perovskites, a structurally symmetric graphene–perovskite–graphene device exhibits a zero-bias photocurrent under illumination, with $V(+I)\neq V(-I)$2 mV and a dark-to-illuminated resistance change from $V(+I)\neq V(-I)$3 to $V(+I)\neq V(-I)$4 at $V(+I)\neq V(-I)$5W, identifying a spontaneous bulk photovoltaic response rather than junction rectification (Zhang et al., 15 Dec 2025). In superconducting structures, spontaneous nonreciprocity appears as a finite equilibrium supercurrent at zero phase difference and unequal positive and negative critical currents, $V(+I)\neq V(-I)$6, when gyrotropy and time-reversal breaking coexist (Kokkeler et al., 2023).

2. Symmetry requirements

At the symmetry level, nonreciprocal transport is a second-order response allowed only when the relevant tensors are not forced to vanish by inversion and time-reversal operations. A generic expansion is

$V(+I)\neq V(-I)$7

or, in polar conductors under magnetic control,

$V(+I)\neq V(-I)$8

showing that inversion breaking and time-reversal breaking enter on equal footing in the nonlinear coefficient (Yoshimi et al., 2022).

For many metallic and semiconducting cases, both $V(+I)\neq V(-I)$9 and $V = R_0 I + \gamma B I^2 + \dots$0 must be broken. In MnBi$V = R_0 I + \gamma B I^2 + \dots$1Te$V = R_0 I + \gamma B I^2 + \dots$2/Pt, the even-layer bulk is centrosymmetric, but the surface and interface necessarily break inversion symmetry, while antiferromagnetic order below $V = R_0 I + \gamma B I^2 + \dots$3 breaks time reversal; this permits spontaneous surface-confined nonreciprocity although the ideal bulk moment is compensated (Ye et al., 2022). In NdRu$V = R_0 I + \gamma B I^2 + \dots$4Al$V = R_0 I + \gamma B I^2 + \dots$5, local inversion symmetry breaking on zigzag chains and antiferromagnetic toroidal dipole order break $V = R_0 I + \gamma B I^2 + \dots$6 and $V = R_0 I + \gamma B I^2 + \dots$7 individually while preserving $V = R_0 I + \gamma B I^2 + \dots$8, which suppresses anomalous Hall response at zero field but allows a large second-order conductivity (Sudo et al., 8 Nov 2025).

There are important variations on this symmetry logic. Shift current in noncentrosymmetric crystals requires broken inversion but may preserve time reversal, because the relevant tensor is the second-order optical conductivity $V = R_0 I + \gamma B I^2 + \dots$9 rather than a dissipative magnetochiral coefficient (Zhang et al., 15 Dec 2025). Conversely, antiferromagnetic nonlinear transport need not rely on relativistic spin–orbit coupling at all: on triangular and breathing kagome lattices, local scalar spin chirality and spin-induced electric polarization can generate Drude-type and Berry-curvature-dipole-type second-order transport once magnetic order lowers the symmetry appropriately (Hayami et al., 2022).

A recurrent misconception is that spontaneous nonreciprocity requires a globally noncentrosymmetric bulk crystal. Surface, interface, local-site, or domain-level inversion breaking can be sufficient, provided it couples to an internal order parameter that breaks time reversal or generates a fixed polar/toroidal axis. This is the organizing principle behind surface Dirac systems, toroidal antiferromagnets, impurity-driven mechanisms, and gyrotropic superconducting hybrids (Ye et al., 2022, Isobe et al., 2022, Kokkeler et al., 2023).

3. Microscopic mechanisms

One major route is asymmetric quasiparticle scattering. In MnBi$E = \rho j + \gamma j^2$0Te$E = \rho j + \gamma j^2$1/Pt, spin-momentum-locked Dirac surface electrons couple to magnons, and the resulting emission and absorption processes differ for opposite current directions because spin flip and momentum transfer are locked together on the Fermi contour. The hallmark is a second-harmonic voltage that scales as $E = \rho j + \gamma j^2$2, emerges below $E = \rho j + \gamma j^2$3 K for 4 SL MnBi$E = \rho j + \gamma j^2$4Te$E = \rho j + \gamma j^2$5, and shows non-monotonic field dependence characteristic of asymmetric scattering (Ye et al., 2022). In (Ge,Mn)Te, inelastic electron–magnon scattering likewise dominates the observed nonreciprocal resistance, with the signal enhanced at low hole density where a single spin-momentum-locked Fermi surface is realized (Yoshimi et al., 2022).

A second route is intrinsic band asymmetry. In conical or helical magnets, exchange coupling to a chiral spin background can make $E = \rho j + \gamma j^2$6 even without explicit relativistic spin–orbit coupling. For Co$E = \rho j + \gamma j^2$7Zn$E = \rho j + \gamma j^2$8Mn$E = \rho j + \gamma j^2$9, the nonreciprocal resistivity was separated into a fluctuation-driven contribution and a band-asymmetry contribution; the latter is largest in the conical phase and persists toward low temperature, consistent with an intrinsic mechanism tied to asymmetric electronic dispersion in the chiral magnetic texture (Nakamura et al., 2024). In EuO/SrTiO$j_a=\beta_{abc}E_bE_c$0, gate tuning changes the occupation of Rashba-split $j_a=\beta_{abc}E_bE_c$1 subbands, reshapes the Berry-curvature distribution, and drives even a sign reversal of the anomalous Hall effect while the spontaneous nonlinear magnetoresistive response remains linked to ferromagnetic order in the 2DEG (Lazrak et al., 21 Aug 2025).

A third route is toroidal and multipolar order. In NdRu$j_a=\beta_{abc}E_bE_c$2Al$j_a=\beta_{abc}E_bE_c$3, antiferromagnetic order on locally noncentrosymmetric zigzag chains acts as a magnetic toroidal dipole. The resulting c–f exchange generates a strong sublattice-dependent effective field on itinerant electrons, shifting spin-polarized Fermi surfaces in the same direction and producing a large zero-field second-order conductivity, $j_a=\beta_{abc}E_bE_c$4 (Sudo et al., 8 Nov 2025). An extrinsic analogue is provided by magnetic impurities placed off inversion centers: the local toroidal moment $j_a=\beta_{abc}E_bE_c$5 enters the impurity potential through a term $j_a=\beta_{abc}E_bE_c$6, generating a second-order conductivity in otherwise centrosymmetric metals (Isobe et al., 2022).

A fourth route is quantum-geometric transport. In $j_a=\beta_{abc}E_bE_c$7, linearly polarized light drives a shift current

$j_a=\beta_{abc}E_bE_c$8

with the microscopic origin encoded in the shift vector of interband transitions. Because the relevant response depends on Berry connections and phases of optical matrix elements rather than on group velocity, a spontaneous cross-plane photocurrent can appear even where the out-of-plane bands are nearly flat (Zhang et al., 15 Dec 2025). This establishes that spontaneous nonreciprocity is not confined to magnetochiral metals: it can be a quantum-geometric property of the wavefunctions themselves.

4. Experimental diagnostics and identification strategies

The standard metrology is harmonic transport under AC drive. In electrical systems one measures the first harmonic $j_a=\beta_{abc}E_bE_c$9 or $I_\omega = I\sin(\omega t)$0 as the linear response and the second harmonic $I_\omega = I\sin(\omega t)$1 or $I_\omega = I\sin(\omega t)$2 as the nonlinear component. When the nonreciprocal term is quadratic in current, $I_\omega = I\sin(\omega t)$3, and angular, field, and temperature dependences of $I_\omega = I\sin(\omega t)$4 become the primary means of identifying the mechanism (Ye et al., 2022, Yoshimi et al., 2022).

Temperature scans are especially diagnostic because spontaneous nonreciprocity tracks internal ordering temperatures. In MnBi$I_\omega = I\sin(\omega t)$5Te$I_\omega = I\sin(\omega t)$6/Pt the second-harmonic transverse voltage becomes negligible above $I_\omega = I\sin(\omega t)$7 K, directly linking the effect to antiferromagnetic order (Ye et al., 2022). In (Ge,Mn)Te the nonreciprocal resistance vanishes around 30 K, near the relevant ferromagnetic transition, while its field dependence changes from low-field enhancement to high-field suppression as the magnon spectrum is gapped (Yoshimi et al., 2022). In NdRu$I_\omega = I\sin(\omega t)$8Al$I_\omega = I\sin(\omega t)$9, the zero-field coefficient appears only below $V^{2\omega}$0 K and flips sign between antiferromagnetic domains, which makes the response itself a domain-sensitive probe (Sudo et al., 8 Nov 2025).

Angular dependence is often what separates competing explanations. In MnBi$V^{2\omega}$1Te$V^{2\omega}$2/Pt, the longitudinal and transverse second-harmonic signals in the $V^{2\omega}$3 plane show a fixed $V^{2\omega}$4 offset, while the $V^{2\omega}$5 and $V^{2\omega}$6 plane signals are much smaller; this rules out standard spin–orbit-torque scenarios in Pt alone and supports magnon-mediated asymmetric scattering on topological surface states (Ye et al., 2022). In (Ge,Mn)Te, the nonreciprocal signal is maximized when $V^{2\omega}$7 is orthogonal to both current and polarization, precisely as required by $V^{2\omega}$8 (Yoshimi et al., 2022). In EuO/SrTiO$V^{2\omega}$9, the nonlinear longitudinal resistance exhibits the same coercive field as the anomalous Hall effect and anisotropic magnetoresistance, which ties the second-harmonic response to the ferromagnetic Rashba state rather than to heating or contact asymmetry (Lazrak et al., 21 Aug 2025).

These diagnostic patterns correct another common misconception: a second-harmonic voltage is not by itself evidence for spontaneous nonreciprocal transport. Joule heating, thermoelectric pickup, and spin–orbit-torque-driven magnetization oscillations can also generate $V_{xx}^{2\omega}$0 signals. The decisive evidence comes from their symmetry, phase, domain, and temperature dependence relative to the underlying order parameter (Ye et al., 2022, Lazrak et al., 21 Aug 2025).

5. Representative material platforms

The phenomenon is realized across several classes of quantum materials and device geometries. The table collects representative cases in which the internal source of symmetry breaking and the dominant nonreciprocal channel are explicitly identified.

Platform	Internal symmetry breaking	Representative signature
MnBi$V_{xx}^{2\omega}$1Te$V_{xx}^{2\omega}$2/Pt bilayer	Surface inversion breaking plus antiferromagnetism	$V_{xx}^{2\omega}$3, onset below $V_{xx}^{2\omega}$4 K, magnon-mediated asymmetric scattering (Ye et al., 2022)
(Ge,Mn)Te	Ferroelectric polarization, ferromagnetism, Rashba SOC	$V_{xx}^{2\omega}$5, five orders larger than GeTe (Yoshimi et al., 2022)
NdRu$V_{xx}^{2\omega}$6Al$V_{xx}^{2\omega}$7	Zero-magnetization antiferromagnetic toroidal dipole order	Spontaneous zero-field nonreciprocity with domain-dependent sign and $V_{xx}^{2\omega}$8 (Sudo et al., 8 Nov 2025)
EuO/SrTiO$V_{xx}^{2\omega}$9 interface	Ferromagnetic Rashba 2DEG	Spontaneous nonlinear MR and gate-tuned anomalous Hall sign reversal (Lazrak et al., 21 Aug 2025)
$V_{xy}^{2\omega}$0	Inversion-breaking ionic displacements in a layered quantum well	Zero-bias cross-plane photocurrent with $V_{xy}^{2\omega}$1 mV and shift-current origin (Zhang et al., 15 Dec 2025)

These examples show that spontaneous nonreciprocity is not tied to a single microscopic motif. It can be surface-driven in a centrosymmetric antiferromagnet, bulk multiferroic in a Rashba semiconductor, toroidal in a compensated metal, interface-stabilized in an oxide 2DEG, or quantum-geometric in a layered optoelectronic crystal (Ye et al., 2022, Yoshimi et al., 2022, Sudo et al., 8 Nov 2025, Lazrak et al., 21 Aug 2025, Zhang et al., 15 Dec 2025).

They also suggest a practical design rule. Large responses recur when four ingredients coexist: a broken inversion center or polar axis, broken time reversal or an equivalent internal odd-parity order, a directional spin–charge or wavefunction–geometry coupling, and an efficient asymmetric channel such as magnon scattering, Berry-curvature reshaping, toroidal exchange, or shift-vector-dominated interband transitions (Yoshimi et al., 2022, Zhang et al., 15 Dec 2025).

6. Related nonreciprocal regimes and open directions

The same organizing principles extend into superconducting, optical, active-matter, and hydrodynamic systems. In gyrotropic superconducting hybrids composed of a normal metal with spin Hall effect proximitized by a ferromagnetic insulator, broken inversion through a polar axis and internal time-reversal breaking generate spontaneous equilibrium supercurrents and a superconducting diode effect without any external magnetic field (Kokkeler et al., 2023). In sodium vapor, a spontaneous parametric four-wave-mixing process becomes nonreciprocal by unidirectional coupling to an auxiliary quantum vacuum field, yielding optical isolation with bandwidth larger than 100 GHz for isolation ratio $V_{xy}^{2\omega}$2 dB (Li et al., 2024).

Beyond condensed-matter charge transport, the notion of spontaneous nonreciprocity has been generalized to systems in which broken symmetry is distributed in space rather than localized at a point. In artificial collecting lymphatics, densely distributed leaflets act as continuous broken symmetries that rectify spatiotemporal contraction waves into robust forward flow; in a single-species Vicsek model with a vision cone, spontaneous symmetry breaking converts microscopic single-species nonreciprocity into an emergent macroscopic non-Hermitian two-species structure that stabilizes traveling bands and even a traveling-line condensation (Winn et al., 29 Mar 2026, Guo et al., 1 Apr 2026). Linear open systems can also become nonreciprocal through parity-broken balanced gain and loss in the bulk, but only when inelastic scattering generates a finite scattering length; in that sense, dissipation itself can be the enabling symmetry-breaking environment (Bag et al., 2024).

Open problems remain largely comparative rather than definitional. One is the quantitative separation of scattering-driven and band-structure-driven contributions in a single material, which Co$V_{xy}^{2\omega}$3Zn$V_{xy}^{2\omega}$4Mn$V_{xy}^{2\omega}$5 shows is possible but not yet routine (Nakamura et al., 2024). Another is the role of domains, which can either average the response to zero or convert it into a powerful domain-imaging observable, as seen in NdRu$V_{xy}^{2\omega}$6Al$V_{xy}^{2\omega}$7 (Sudo et al., 8 Nov 2025). A further issue is how microscopic local asymmetries—surfaces, interfaces, impurities, or soft lattice distortions—renormalize into bulk second-order tensors, especially when the system is metallic and strongly correlated (Isobe et al., 2022, Oh et al., 2023).

A plausible implication is that spontaneous nonreciprocal transport should be viewed less as a narrow transport anomaly and more as a unifying response class of symmetry-broken nonequilibrium matter. Whether the carriers are Dirac electrons, Rashba holes, superconducting condensates, excitons, photons, or active particles, the phenomenon repeatedly reduces to the same core principle: once internal order fixes a handedness or polar direction and couples it to transport, the system acquires a preferred sign of motion.