Hall-coefficient sign reversal: carriers, mobility and evidence

Scope

A Hall-coefficient sign reversal is a change in the sign of the transverse response under a declared wiring and field convention. It is distinct from a change in Hall magnitude, a peak, or an inferred Hall number. Electron and hole contributions can exchange transport weight without either Fermi-surface pocket disappearing. Neither a sign change nor a Hall anomaly by itself proves superconductivity, a Lifshitz transition or a particular pairing mechanism. R1 R2 R3 R5

Here $E_y=R_HJ_xB_z$ defines the sign. The elementary single-band Drude values are $R_H=-1/(n_e e)$ for electrons and $R_H=1/(n_h e)$ for holes, with $e>0$. These density interpretations require restrictive assumptions. Even a single crystalline band can have a complicated Hall response because Fermi-surface curvature and a momentum-dependent mean free path affect the weak-field conductivity. A temperature-dependent Hall coefficient is therefore not sufficient evidence for multiple bands. R7

Mathematical assumptions

For independent isotropic electron and hole Drude channels with positive mobilities and $\mu_i B\ll1$, $R_H=(n_h\mu_h^2-n_e\mu_e^2)/[e(n_h\mu_h+n_e\mu_e)^2]$. The sign changes when the mobility-squared weights cross. Fixed carrier densities can therefore produce a reversal as the mobility ratio varies. At zero field $\sigma_0=e(n_h\mu_h+n_e\mu_e)$; even simultaneous values of $\sigma_0$ and weak-field $R_H$ do not uniquely determine four density/mobility parameters. Independent tensor-inversion checks illustrate this degeneracy without fitting a material. R4 R7

Beyond weak field, add conductivity tensors and invert the sum. In the same classical model, when both $\mu_iB\gg1$ and $n_h\ne n_e$, the asymptotic slope is $\rho_{yx}/B\to1/[e(n_h-n_e)]$. Exact compensation is a different limit: for $n_h=n_e=n$, $\rho_{yx}/B=(\mu_h-\mu_e)/[en(\mu_h+\mu_e)]$ at all fields in this model. A large laboratory field alone establishes neither of these asymptotic conditions. Quantum effects, coupled scattering and reconstructed bands may require a different model. R4 R7

Ordinary and anomalous contributions must also be distinguished. A schematic $\rho_{yx}=R_0B+\rho_{yx}^{A}$ is not a universal fit, and an anomalous term need not be proportional to magnetization with a constant coefficient. Intrinsic Berry curvature, skew scattering and side jump are distinct mechanisms. Field antisymmetrization, $[\rho_{yx}(B)-\rho_{yx}(-B)]/2$, removes even longitudinal contact leakage but retains an odd anomalous Hall contribution. It does not isolate ordinary Hall transport by itself. R6

Experimental criteria

Tsukada and Ono studied epitaxial La2−xSrxCuO4 films on SrTiO3 with residual tensile strain. Their room-temperature Hall coefficient changes from positive to negative between x=0.28 and x=0.32. The heavily overdoped samples used field sweeps to ±6 T. This is a sample-series result at 300 K, not a universal cuprate doping boundary. The x=0.32 film lacks zero resistance but has a reported resistive onset, which the authors discuss in relation to possible oxygen inhomogeneity. Describing it simply as having no superconducting evidence would erase that distinction. R1

Brouet's Ba(Fe0.65Ru0.35)2As2 study reports a temperature-dependent Hall sign together with electron and hole pockets. The checked primary abstract supports that limited statement; complete transport methods and a precise reversal temperature remain unreviewed here. Mun's Co- and Cu-substituted BaFe2As2 crystals provide a separate comparison: thermopower and Hall changes occur at comparable added-electron counts, but the Cu comparison does not show the corresponding resistive superconductivity. These Hall anomalies are not a superconductivity criterion or a universal sign-change threshold. R2 R3

Mun's experiment measured composition by wavelength-dispersive spectroscopy and applied the Hall field along the crystal c axis, reversing field polarity to reduce contact offsets. Its 25 K comparison is a measurement temperature, not a transition temperature. Sample exfoliation can alter geometric factors, so normalized trends and absolute Hall magnitudes carry different uncertainties. Co/Cu substitution fraction and inferred added-electron count are also different horizontal axes. R3

Iida's strained Ba(Fe1−xCox)2As2 films used MgO and CaF2 substrates and Hall measurements at 9 T. Their effective Hall number $n_H=V/(4e|R_H|)$, with unit-cell volume $V$, is positive by construction and expressed per Fe. It discards the Hall sign and is not a direct count of all mobile carriers in a multiband metal. The reported phase-diagram alignment concerns the studied strained films and selected bulk comparisons. The superconducting temperature uses a resistive onset criterion, rather than silently substituting zero resistance or magnetic shielding. R4

Badoux's YBa2Cu3Oy experiment distinguishes a charge-order reconstruction endpoint near p=0.16 from a pseudogap endpoint near p=0.19. The Hall-number interpretation changes from approximately 1+p toward p; this is not evidence for a mandatory Hall-sign reversal at the latter point. Pulsed fields reached 88 T, with a 50 K, 80 T cross-sample comparison. The author manuscript establishes normal-state access down to at least 40 K and explicitly leaves the lower-temperature p=0.16 behavior unresolved. Its vortex-melting field is not automatically the upper critical field. R5

Limits and disputes

Normal-state extraction needs more than a high-field label. Retain temperature, current, field direction, hysteresis branch and the independently justified superconducting boundary; vortex motion and magnetic contributions can contaminate a transverse signal. Yang's field-induced superconductivity study is a boundary example, not a source of an ordinary-Hall reversal field. Its superconducting phase-diagram scales must not be relabeled as Hall or anomalous-Hall thresholds. R5 R6 R8

Complete scientific acceptance remains open. Most experimental checks here cover selected author-manuscript methods, results and figures, not complete final articles or raw-data reproduction. Brouet remains abstract-scoped; Ong's full geometric derivation and the anomalous-Hall review remain incompletely read. Apparent numeric typographical inconsistencies in the Mun and Iida author versions require final-version comparison; those uncertain composition values are not adopted. The independent Drude checks establish model algebra, not a unique interpretation of any experimental Hall curve. R1 R2 R3 R4 R5 R6 R7

Discovery implications

Treat a sign change as a prompt to test competing transport explanations. Combine field-dependent longitudinal and transverse resistivity, magnetoresistance, magnetic characterization and independent Fermi-surface information. Compare constrained models and retain geometry, strain, oxygen content and uncertainty. A mobility crossover, reconstructed Fermi surface and anomalous contribution can produce different predictions beyond a single Hall slope; a defensible conclusion specifies which alternatives the measurements actually exclude. R1 R2 R4 R5 R7

Related topics

Parallel conduction channels, Nonlinear Hall effect, and Field-induced superconductivity.

Material cases

Values describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.