Sign-Reversible Anomalous Transport

• Sign-reversible anomalous transport is a nonequilibrium phenomenon where tuning external parameters inverts responses such as current or Hall conductivity.
• It arises from the interplay of competing mechanisms including magnetic phase crossover, Berry-curvature engineering, and disorder effects.
• Experimental validations in materials like Cr₇₋δTe₈ and hydrogenated PdCoO₂ demonstrate controlled reversals, paving the way for programmable quantum devices.

Sign-reversible anomalous transport encompasses a broad class of nonequilibrium phenomena in condensed matter, quantum, and classical systems, in which the direction (sign) of a transport response—such as current, voltage, magnetoresistance, or Hall conductivity—can be reversed by tuning an external parameter such as temperature, field, gating, symmetry, or disorder. This nontrivial sign reversal typically arises from the interplay of multiple competing microscopic mechanisms, symmetry breaking, or topological effects, often far from equilibrium. Recent research has elucidated a wide range of distinct mechanisms leading to sign-reversible anomalous transport, including fluctuation-induced scalar chirality, competing scattering channels, Berry-curvature engineering, correlated disorder, and symmetry-controlled band topology.

1. Mechanistic Origins of Sign-Reversible Anomalous Transport

Several fundamentally different microscopic mechanisms drive sign-reversible anomalous transport:

• Magnetic phase competition and scalar spin chirality In centrosymmetric magnets such as Cr$_{7-\delta}$Te$_8$, sign-reversal of the anomalous Hall effect (AHE) is driven by a reorganization of the magnetic state involving long-range ferromagnetic (FM) and short-range (SR) fluctuating orders. The scalar spin chirality $$\chi_{ijk} = \mathbf{S}_i \cdot (\mathbf{S}_j \times \mathbf{S}_k)$$, which arises from noncollinear local spin textures around atomic vacancies, can enhance the topological Hall effect (THE) and provide emergent gauge fields for itinerant electrons. The balance and temperature evolution of these competing mechanisms control the sign and magnitude of the total Hall signal, with clear reversal at specific transitions (Chen et al., 2024).
• Competing scattering processes and chemical manipulation In thin-film PdCoO$_2$ reduced by hydrogenation, AHE sign reversal results from the crossover between skew-scattering and (side-jump, intrinsic) Berry-curvature contributions to the Hall conductivity, as variation in carrier scattering and electronic structure modulate the relative strengths and even the sign of these terms. This enables chemical programmability of the Hall sign post-synthesis (Rimal et al., 2021).
• Correlated disorder in Dirac systems In 2D massive Dirac materials, statistical anti-correlation between charge and mass-type (magnetic) disorder can reverse the effective Dirac mass seen by charge carriers, changing the sign of the AHE even though the bare magnetization remains fixed. This sign flip occurs at a critical correlation coefficient, with the boundary precisely determined by the ratio $m/\epsilon$ (Dirac mass to Fermi energy) (Keser et al., 2019).
• Symmetry and topology (Berry curvature engineering) In 2D and 3D altermagnetic materials, sign-reversible anomalous Hall and Nernst effects are induced by breaking specific crystalline symmetries (e.g., sublattice-exchange, $C_{4z}T$) via uniaxial strain or inversion of lattice chirality. The sign of the integrated Berry curvature—and hence the Hall response—is locked to the symmetry-breaking field or structural handedness (Li et al., 4 Jan 2026, Xie et al., 18 Aug 2025).
• Dynamical symmetry breaking and nonlinearity In driven systems (e.g., periodic ratchets, quantum dots, classical wave-particle entities), breaking temporal or spatial symmetries and engineering parameter regimes with multiple periodic orbits can lead to absolute negative mobility (ANM)—current opposite to an applied bias—which is robustly sign-reversible by tuning system parameters such as drive amplitude, field, or damping (Mulhern, 2013, Wiśniewski et al., 2022, Valani, 2021, Zhang et al., 2024).
• Band-structure engineering and valley degrees of freedom In valley-half semiconductors like VSi$_2$N$_4$, the use of strain, external field, or electron correlations can selectively invert the Berry curvature at individual valleys, leading to quantized sign reversals in valley Hall conductivity and associated transport plateaux (Zhou et al., 2021).

2. Experimental Realizations and Observed Sign Reversals

Sign-reversible anomalous transport has been validated experimentally in a growing list of quantum materials, classical analogs, and synthetic engineered systems.

Cr$_{7-\delta}$Te$_8$ (layered ferromagnetic chalcogenide):

• Exhibits an AHE sign change near $T_{sr} \sim 280\,$K, coinciding with an anomalous magnetic susceptibility feature evidenced by AC $\chi' (T)$.
• The THE remains positive and robust ($$\rho_{xy}^{T,\,\text{peak}} \approx 1\,\mu\Omega\cdot\text{cm}$$ at $T\lesssim 100$ K) up to room temperature, indicating a fluctuation-driven mechanism independent of skyrmion formation.
• Key implication: Tunable, decoupled control of Hall sign and THE for memory and logic devices (Chen et al., 2024).

Hydrogenated PdCoO$_2$ thin films:

• Hydrogenation leads to atomically-mixed PdCo alloy with strong perpendicular FM order ($T_C \sim 650$ K).
• The Hall resistivity $R_s$ changes sign twice with annealing time or temperature, with the OHE invariant.
• The sign-reversal is attributed to a nontrivial balance shift between skew-scattering and intrinsic/side-jump Hall conductivity channels, strongly modulated by disorder and electronic environment (Rimal et al., 2021).

2D massive Dirac metals:

• The anomalous Hall effect reverses sign as correlated (anti-correlated) charge-mass disorder changes the effective Dirac mass $m_{\text{eff}}$ across zero at $\beta_{\text{crit}} = -\arctan(m/\epsilon)$.
• This mechanism explains experimental observations where AHE sign flips without inversion of the macroscopic magnetization (Keser et al., 2019).

Topological and symmetry-controlled platforms:

• 3D chiral altermagnetic MOFs (e.g., K[Co(HCOO)$_3$]) display AHE and magneto-optical effects whose sign is strictly locked to lattice chirality—switchable by enantiomer inversion with no change in magnetic order (Xie et al., 18 Aug 2025).
• In 2D altermagnets, the direction of Hall and Nernst responses can be reversed by rotating the axis of applied strain, demonstrating full electrical programmability of anomalous transport (Li et al., 4 Jan 2026).

3. Theoretical Frameworks for Sign Reversal

Several theoretical constructs underpin the analysis and prediction of sign-reversible anomalous transport:

• Transport Decomposition:

Hall resistivity is decomposed as $\rho_{xy} = R_0\mu_0H + R_A M + \rho_{xy}^T$, separating ordinary, anomalous (Berry-curvature and scattering contributions), and topological components (Chen et al., 2024).

• Energy-Dependent Scattering:

In multiband semiconductors, energy-dependent lifetimes $\tau(E)$ due to electron-phonon or inter-band scattering can reverse the sign of the Seebeck coefficient and suppress the conductivity upon doping past a critical band-edge, leading to anomalous thermoelectric response (Fedorova et al., 2021).

• Symmetry Constraints:

Crystal and magnetic group symmetries rigorously determine when anomalous Hall (or Nernst) responses vanish, and how they re-emerge with sign reversals upon breaking particular combination of operations (e.g., $C_{4z}T$ in AMs) (Li et al., 4 Jan 2026, Xie et al., 18 Aug 2025).

• Berry-Curvature Engineering:

Berry curvature, as a geometric property of Bloch bands, incorporates the effect of band topology, magnetic texture, and symmetry. Tuning the distribution or integrated sum via band structure or symmetry manipulation inverts the sign of Hall and related anomalous transports (Xie et al., 18 Aug 2025, Zhou et al., 2021).

4. Parameter Control and Phase Diagrams

Sign reversal typically occurs at well-defined phase boundaries controlled by tuning of temperature, field, strain, chemical potential, disorder, or chemical composition:

System	Control Parameter	Sign-Reversal Mechanism	Reversal Condition / Value
Cr$_{7-\delta}$Te$_8$	Temperature ($T$)	SR/LR magnetic crossover, chirality	$T_{sr} \approx 280\,\text{K}$
PdCoO$_2$ (hydrogenated)	Annealing time, dose, $T_A$	Skew vs. intrinsic/side-jump AHE	$t_A \approx 10–15$ h, $T_A \approx 300^\circ\text{C}$
2D Dirac metal (disorder)	Correlation parameter ($\beta$)	Effective mass inversion	$\beta_{\text{crit}} = -\arctan(m/\epsilon)$
Chiral AM MOF	Lattice chirality (enantiomer Cₗ/Cᵣ)	Berry curvature inversion	Mirror transformation
2D Altermagnet (Cr$_2$O$_2$)	Strain axis, magnitude	Breaking $C_{4z}T$ sublattice symmetry	Rotation of strain axis or $\Delta$
VSi$_2$N$_4$ (valley SC)	Biaxial strain, $E_z$, $U$	Valley mass sign flip	$\epsilon_{\text{strain}} = 1.4\%$

Sign reversals are often abrupt (e.g., at critical transition points) and manifest as sharp changes or plateaux in the corresponding transport coefficient.

5. Anomalous Transport Beyond Linear Response

Nonlinear and time-dependent driving can produce sign-reversible or sign-selectable transport even without intrinsic magnetic or topological order.

• Absolute negative mobility (ANM):

In periodically driven, time-reversal-symmetry–broken systems, directed or even uphill current is realized in a finite window of control parameters (e.g., static bias, inhomogeneity), with the direction of current switching upon small parameter variations. This effect is robust both to deterministic and certain classes of stochastic driving (Mulhern, 2013, Wiśniewski et al., 2022, Valani, 2021).

• Quantum dot models:

Sign reversals in thermodiffusion, charge, and heat currents are controllably realized by tuning the energy of the dot level ($\epsilon_d$) through a "reversible" energy $\epsilon_\text{rev}$, with all sign-reversal boundaries strictly determined by the Landauer–rate-formulas for steady-state currents (Zhang et al., 2024).

6. Implications, Applications, and Future Directions

Sign-reversible anomalous transport represents a paradigm for dynamical, programmable control and switching in quantum devices, with implications including:

• Electrically or thermally switchable Hall memories and spin filters leveraging abrupt sign reversals (Chen et al., 2024, Li et al., 4 Jan 2026).
• Chirality-encoded information storage and readout via topologically protected hinge modes or Berry curvature sign (Xie et al., 18 Aug 2025).
• Active strain-gated electronics with mechanically or piezoelectrically tunable Hall and Nernst responses (Li et al., 4 Jan 2026).
• High-performance thermoelectric materials with ambipolar response and dual-peak power factors from band-structure engineered anomalies (Fedorova et al., 2021).
• Valleytronic architectures employing strain- or field-tunable quantized transport states (Zhou et al., 2021).
• Reconfigurable oxide and oxide–heterostructure spintronics via post-growth chemical processing (Rimal et al., 2021).

The continued integration of symmetry analysis, transport decomposition, and numerical or first-principles modeling is expected to broaden the catalog of sign-reversible anomalous transport phenomena, especially in multifunctional and low-dimensional quantum materials.