Band-Resolved Superconducting Gaps via the Thermal Hall Effect in CeRu2

The gist: Thermal Hall transport resolves ambiguity in multiband superconductors by assigning superconducting gaps to specific Fermi surface sheets through a low-field sign reversal in thermal Hall conductivity.

Why it matters

Standard bulk probes fail to assign pairing gaps to specific electron or hole Fermi surfaces because they measure a sum over all sheets weighted by their respective densities of states or velocities, which are insensitive to carrier sign The thermal Hall conductivity κxy remains finite in the mixed state and selectively tracks the entropy transport of thermally excited Bogoliubov quasiparticles (BQPs) without a competing phonon background Developing a robust κxy methodology is essential for disentangling multiple superconducting gaps and assigning them to specific Fermi surface sheets.

How it works

The study uses the cubic Laves-phase superconductor CeRu2 as an ideal platform because its compensated metal structure makes the thermal Hall response exceptionally sensitive to modest differences between gaps. The researchers fixed two distinct temperature-equivalent gap scales using zero-field specific heat, finding ∆e/kB ≈ 13 K and ∆h/kB ≈ 8 K. These gap magnitudes are then assigned to the electron and hole sheets based on a low-field sign reversal in κxy upon cooling from an electron-dominated normal state.

Key findings from transport and thermodynamics

The analysis combines zero-field specific heat, normal-state magnetotransport, and thermal Hall transport to uniquely assign superconducting gaps of comparable magnitude to their respective Fermi surface sheets.

** Zero-field specific heat fixes two distinct temperature-equivalent gap scales (8 K and 13 K, respectively). The normal-state mobility ratio µh/µe locks in their relative transport weights. The resulting low-field sign reversal of κxy places the larger gap on the heavy Ce 4f electron sheets and the smaller gap on the hole sheets. **

Decomposition of electronic channels

The electronic thermal conductivity below Tc is modeled as a sum of two independent s-wave Bardeen–Rickayzen–Tewordt (BRT) contributions corresponding to the electron and hole bands. The fractional hole-band weight (ch) is fixed by the normal-state mobility ratio µh/µe, which is found to be approximately 0.4. This decomposition allows for the complete constraint of the electronic channels κxx,e and κxx,h.

Mixed-state behavior and field dependence

The thermal Hall conductivity is linked to the zero-field BRT decomposition via band-dependent thermal Hall angles tan θi(H) = κxy,i/κxx,i. The field dependence of κxy/T shows a prominent low-field sign reversal below 1 T on cooling. At intermediate fields (1 T < µ0H < µ0Hc2), the quadratic-in-field recovery of κxy seen in Fig. 2(b) translates to a linear variation of the normalized response κxy/κ(n) with field. This intermediate-field regime reveals a crossover near 1 T from compensated two-carrier transport to an electron-dominated regime.

Lattice thermal conductivity modeling

The lattice thermal conductivity κph(T) is modeled using the Debye–Callaway model, incorporating the BRT-prescribed reduction in phonon-BQP scattering below Tc. The fitting of κph(T) to the residual lattice conductivity yields a boundary mean free path lb = (0.9±0.1) mm, comparable to the physical cross-sectional dimensions. This approach unifies parameter-free longitudinal BRT channels with band-dependent thermal Hall angles to isolate signed quasiparticle currents.

Conclusion and implications

The work demonstrates that combining thermal Hall transport with zero-field thermodynamics and magnetotransport uniquely assigns superconducting gaps of comparable magnitude to their respective Fermi surface sheets. This provides a general blueprint for assigning carrier bands to superconducting gaps and disentangling multiband quasiparticle dynamics across compensated, flatband, and heavy-fermion superconductors. The results confirm that the larger superconducting gap in CeRu2 resides on the electron band, while BQP excitations across the smaller hole gap govern the low-field sign reversal at low temperatures. The study successfully isolates signed quasiparticle currents by linking longitudinal transport to thermal Hall conductivity via band-dependent thermal Hall angles.

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Synthesis

Single crystals of CeRu2 were grown by the Czochralski method in a tetra-arc furnace equipped with a watercooled copper hearth under a high-purity argon atmosphere. A 3.7 g stoichiometric charge of elemental Ce and Ru (1:2 molar ratio) was melted and flipped 11 times prior to growth to ensure compositional homogeneity. The single crystal boule was pulled at 4.2 mm h−1 with a clockwise hearth rotation of 9.8 rpm and a counterclockwise seed rotation of 2.2 rpm. Samples for magnetometry and transport were sectioned from the as-grown boule using a wire saw. Across crystals from the growth, the residual resistivity ratio RRR = ρxx(300 K)/ρ0—where ρ0 is the low-temperature normal-state residual resistivity extrapolated to 0 K from above Tc—ranges from 5–8. Bulk magnetization and susceptibility measurements were first performed on a cylindrical disk (Tc = 5.8 K) of diameter 2 mm and thickness 0.44 mm. To eliminate sample-to-sample variations between bulk and transport probes, this same disk was subsequently sectioned into a rectangular bar of dimensions 2 mm ×1 mm ×0.15 mm for electrical and thermal transport measurements. Thermal conductivity and thermal Hall measurements were conducted using a home-built steady-state one-heater, three-thermometer probe. A longitudinal heat current JQ was generated via a resistive chip heater driven by a Stanford Research Systems CS580 voltage-controlled current source, and the resulting longitudinal (∆Tx) and transverse (∆Ty) temperature gradients were measured using calibrated Lakeshore Cernox 1050 resistance temperature detectors (RTDs). Each thermometer was excited with a 100 nA AC current at 133.77 Hz sourced by a Keithley 6221, and the differential voltages were read out using Zurich Instruments MFLI lock-in amplifiers. To account for geometric contact misalignment, the measured longitudinal and transverse thermal (electrical) resistivities were field-symmetrized and antisymmetrized, respectively, using positive and negative magnetic field sweeps. The thermal (electrical) conductivity tensor components were then obtained by matrix inversion. To ensure a uniform vortex state and avoid flux-trapping history effects between field polarities, the sample was thermally cycled above Tc and zero-field cooled (ZFC) prior to acquiring each positive and negative field sweep. Similarly, fixed-field temperature sweeps were recorded under ZFC conditions by cooling the sample in zero field to base temperature before applying the target magnetic field and warming through Tc.

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Compensated two-band magnetotransport

To determine the normal-state carrier density and band mobilities of CeRu2, we simultaneously fit the fielddependent magnetoresistance ∆ρxx/ρxx(0) and Hall resistivity ρxy(H) across multiple temperatures from 10 K to 50 K. Motivated by band-structure calculations and de Haas–van Alphen measurements establishing CeRu2 as a compensated metal <ref:2610.

1. Bold header: Precise Superconducting Gap Assignment in Multiband Systems

This capability allows AI to definitively assign superconducting gaps of comparable magnitude to their respective Fermi-surface sheets by combining thermal Hall transport with zero-field thermodynamics and magnetotransport, resolving the ambiguity that standard bulk probes cannot address.

2. Bold header: Carrier Band Identification via Thermal Hall Sign Reversal

The system can detect a specific physical phenomenon: a prominent low-field sign reversal of κxy upon cooling from an electron-dominated normal state unambiguously places the larger gap on the heavy, Ce 4f-derived electron sheets and the smaller gap on the hole sheets.

3. Bold header: Parameter-Free Two-Band Decomposition

The AI can perform parameter-free decomposition of thermal conductivity, using the fractional hole weight (0.4) is fixed by the normal-state mobility ratio µh/µe to accurately model the electronic channels: κxx,e(T) + κxx,h(T) = (1 − ch)Re(T) + chRh(T).

4. Bold header: Mixed-State Transport Modeling

The system can predict the quadratic-in-field recovery of κxy/T toward the normal state in the mixed state based on microscopic theory, specifically by applying the linear Caroli–Cyrot recovery of κxy/κ(n) xy with field [Fig. 3(c)] for intermediate fields.

5. Bold header: Microscopic Vortex Lattice Dynamics Prediction

The AI can model how the field-induced suppression of each gap using the Ginzburg–Landau scaling ∆i(H, T) = ∆i(T)p1 − H/Hc2, enabling accurate predictions of the rapid recovery of κxx(H) at intermediate fields across the mixed state.