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arxiv: 1907.01920 · v1 · pith:LQWD2QI6new · submitted 2019-07-02 · ❄️ cond-mat.supr-con · cond-mat.str-el

Enhanced T_c and multiband superconductivity in the fully-gapped ReBe₂₂ superconductor

T. Shang , A. Amon , D. Kasinathan , W. Xie , M. Bobnar , Y. Chen , A. Wang , M. Shi
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M. Medarde H. Q. Yuan T. Shiroka
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Pith reviewed 2026-05-25 10:55 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el
keywords superconductivityReBe22muon spin rotationmultigap superconductivityfully gappedtime-reversal symmetryelectron-phonon couplingupper critical field
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The pith

ReBe22 is a fully gapped multiband superconductor with Tc raised to 9.4 K by higher Fermi-level density of states and stronger electron-phonon coupling.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines why ReBe22 superconducts at 9.4 K, far above pure beryllium's 0.026 K. Macroscopic measurements establish bulk superconductivity, while transverse-field muon-spin rotation and specific-heat data are used to extract the superfluid density. These data are interpreted as evidence for a fully gapped state that nevertheless requires two isotropic gaps, the larger one carrying 90 percent weight and exceeding the weak-coupling BCS value. Zero-field muon measurements show no spontaneous fields, confirming time-reversal symmetry is preserved. Band-structure results link the elevated Tc to a sharply increased density of states at the Fermi level together with enhanced electron-phonon coupling.

Core claim

ReBe22 displays bulk superconductivity below 9.4 K. Its superfluid density, obtained from transverse-field μSR and electronic specific heat, is described by a two-gap model with the dominant gap Δ0^l = 1.78 kB Tc. The material remains fully gapped, shows no spontaneous magnetization below Tc, and owes its high transition temperature to an increased density of states at the Fermi level combined with stronger electron-phonon coupling.

What carries the argument

Two-gap isotropic model fitted simultaneously to the temperature dependence of the superfluid density and the field dependence of the specific-heat coefficient.

If this is right

  • The larger gap exceeds the weak-coupling BCS limit while the smaller gap is well below it, indicating multigap character inside an almost elemental compound.
  • Absence of spontaneous fields below Tc shows time-reversal symmetry remains intact.
  • The dramatic rise in density of states at the Fermi level plus increased electron-phonon coupling together account for the order-of-magnitude jump in Tc relative to pure Be.
  • Field-dependent specific heat and the temperature dependence of the upper critical field both corroborate the multigap picture.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar Re-based intermetallics may host multigap states when dilution or alloying raises the density of states without introducing nodes.
  • The two-gap fit could be tested by directional tunneling or angle-resolved photoemission if single crystals become available.
  • If the multigap feature survives in cleaner samples, ReBe22 would serve as a reference for studying how elemental-like lattices can still support multiple Fermi-surface sheets with distinct pairing strengths.

Load-bearing premise

The observed temperature and field dependences can be decomposed into two isotropic gaps rather than arising from a single anisotropic gap or extrinsic effects.

What would settle it

A linear term in the low-temperature penetration depth or specific heat that survives after subtraction of impurity contributions would contradict the fully gapped claim.

Figures

Figures reproduced from arXiv: 1907.01920 by A. Amon, A. Wang, D. Kasinathan, H. Q. Yuan, M. Bobnar, M. Medarde, M. Shi, T. Shang, T. Shiroka, W. Xie, Y. Chen.

Figure 1
Figure 1. Figure 1: Crystal structure of ReBe22. (a) ReBe16 units: the Be atoms (grey) around Re (red) occupy the vertices of a truncated tetrahedron (i.e., a Friauf polyhedron), highlighted by red connection lines. Four additional Be atoms cap the hexagonal faces. (b) The distorted Be13 icosahedra consist exclusively of Be atoms. (c) Arrangement of the ReBe16 and Be13 polyhedra in the unit cell. For clarity, only one coordin… view at source ↗
Figure 2
Figure 2. Figure 2: Temperature dependence of the electrical resistivity of ReBe22. The solid line through the data is a fit to equation (1). The inset shows the data in the low￾temperature region, highlighting the superconducting transition. The temperature dependence of the electrical resistivity ρ(T) of ReBe22 was measured in zero magnetic field from 300 K down to 2 K. As shown in figure 2, the resistivity exhibits metalli… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Temperature dependence of the magnetic susceptibility of ReBe22. Data were collected in a 1-mT applied field using both ZFC- and FC protocols. (b) Estimated lower critical field µ0Hc1 as a function of temperature. Lines are fits to the phenomenological model µ0Hc1(T ) = µ0Hc1(0)[1 − (T /Tc) α] β . The inset shows the field-dependent magnetization M(H) recorded at various temperatures up to Tc. For each… view at source ↗
Figure 4
Figure 4. Figure 4: Temperature dependence of the heat capacity measured in zero field between 2 and 300 K. The solid line represents a fit to a combined Debye and Einstein model, with the dashed- and the dash-dotted lines referring to the two components. the inset of figure 3(b), the M(H) curves, recorded using a ZFC-protocol, exhibit the typical response expected for a type-II superconductor. The resulting µ0Hc1 vs. tempera… view at source ↗
Figure 5
Figure 5. Figure 5: Normalized electronic specific heat Ce/γnT of ReBe22 as a function of T /Tc, measured using 4He- (circles) and 3He cooling (squares). Inset: low-T region of Ce/γnT . The solid- and the dash-dotted lines represent the electronic specific heat calculated by considering a fully-gapped s-wave model with two- and one gap, respectively. The low-T specific-heat data were further analyzed, since they can offer val… view at source ↗
Figure 6
Figure 6. Figure 6: (a) Specific heat of ReBe22 as a function of T 2 , measured under increasing magnetic fields (up to 0.6 T). (b) Normalized specific-heat coefficient γH/γn vs. the reduced magnetic field value H/Hc2(0). γH is estimated by extrapolating the data in (a) to zero temperature. The dash-dotted line indicates a linear dependence as predicted for an s-wave gap structure, the solid line represents the dependence exp… view at source ↗
Figure 7
Figure 7. Figure 7: (a) Upper critical field µ0Hc2 vs. reduced transition temperature Tc/Tc(0) for ReBe22. The Tc values were determined from temperature-dependent electrical resistivity ρ(T, H) (b) and specific-heat C(T, H)/T data (c) at various applied fields, and from field-dependent magnetization M(H, T ) (d) at different temperatures. For the ρ(T, H) measurements, Tc was defined as the onset of zero resistivity. Three di… view at source ↗
Figure 8
Figure 8. Figure 8: TF-µSR time spectra collected at 1.5 K (a) and 10 K (b) in an applied field of 40 mT, with the respective Fourier transforms being shown in (c) and (d). Solid lines are fits to equation (8) using three oscillations. The dashed vertical line indicates the applied magnetic field. Note the clear diamagnetic shift below Tc in panel (c). µSR measurements in an applied transverse field (TF) were carried out to … view at source ↗
Figure 9
Figure 9. Figure 9: Superfluid density vs. temperature, as determined from TF-µSR measurements in an applied magnetic field of 40 mT (a) and 120 mT (b). The insets show the temperature dependence of the muon-spin relaxation rate σ(T ). While three components are required to describe the TF-40 mT data, only two components are necessary in the TF-120 mT case. Lines represent fits to a fully-gapped s-wave model with either two- … view at source ↗
Figure 10
Figure 10. Figure 10: (a) Representative ZF-µSR spectra for ReBe22 in the superconducting (1.5 K) and the normal state (15 K). Additional LF-µSR data collected at 1.5 K in a 10-mT applied field. Solid lines are fits to equation (15). Temperature dependence of the Lorentzian- ΛZF (b), and Gaussian σZF (c) relaxation rates. None of them shows clear anomalies across Tc, marked by a dashed line. The solid line in (c) represents a … view at source ↗
Figure 11
Figure 11. Figure 11: Calculated density of states of ReBe22 scaled to formula units (f.u.). Total and partial (Be and Re) density of states (a). Orbital-resolved density of states for the Be- (b) and Re atoms (c). 3.8. Electronic band structure To shed more light on the underlying electronic properties of ReBe22, we performed electronic band-structure calculations based on DFT, including spin-orbit coupling [PITH_FULL_IMAGE:… view at source ↗
Figure 12
Figure 12. Figure 12: Calculated electronic band structure of ReBe22, within ±2 eV from the Fermi energy level, neglecting the spin-orbit coupling (here too small due to the low Re content) [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Uemura plot of the superconducting transition temperature Tc against the effective Fermi temperature TF for different kinds of superconductors. The shaded region, with 1/100 < Tc/TF < 1/10, indicates the band of unconventional superconductors, such as heavy fermions, organic, fullerenes, pnictides, cuprates, etc. The dotted and dashed lines correspond to Tc = TF and Tc = TB (TB is the Bose-Einstein conden… view at source ↗
read the original abstract

In search of the origin of superconductivity in diluted rhenium superconductors and their significantly enhanced $T_c$ compared to pure Be (0.026 K), we investigated the intermetallic ReBe$_{22}$ compound, mostly by means of muon-spin rotation/relaxation ($\mu$SR). At a macroscopic level, its bulk superconductivity (with $T_c=9.4$ K) was studied via electrical resistivity, magnetization, and heat-capacity measurements. The superfluid density, as determined from transverse-field $\mu$SR and electronic specific-heat measurements, suggest that ReBe$_{22}$ is a fully-gapped superconductor with some multigap features. The larger gap value, $\Delta_0^l=1.78$ k$_\mathrm{B}T_c$, with a weight of almost 90\%, is slightly higher than that expected from the BCS theory in the weak-coupling case. The multigap feature, rather unusal for an almost elemental superconductor, is further supported by the field-dependent specific-heat coefficient, the temperature dependence of the upper critical field, as well as by electronic band-structure calculations. The absence of spontaneous magnetic fields below $T_c$, as determined from zero-field $\mu$SR measurements, indicates a preserved time-reversal symmetry in the superconducting state of ReBe$_{22}$. In general, we find that a dramatic increase in the density of states at the Fermi level and an increase in the electron-phonon coupling strength, both contribute to the highly enhanced $T_c$ value of ReBe$_{22}$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript reports bulk superconductivity in ReBe22 with Tc=9.4 K (far above pure Be), characterized by resistivity, magnetization, and heat capacity. Transverse-field μSR and electronic specific-heat data are interpreted as indicating a fully gapped state with multigap features, the dominant gap being Δ0^l=1.78 kB Tc at ~90% weight. Zero-field μSR shows preserved time-reversal symmetry. Enhanced Tc is attributed to increased Fermi-level DOS and electron-phonon coupling, corroborated by band-structure calculations.

Significance. If the two-gap interpretation is robust, the result is significant for documenting multiband superconductivity in an intermetallic compound near the elemental limit, which is uncommon, and for linking the gap structure and enhanced Tc to DOS and coupling changes. The use of complementary probes (μSR, specific heat, transport) provides a solid experimental foundation for the material characterization.

major comments (1)
  1. [Abstract and superfluid-density/specific-heat modeling sections] The central multigap claim rests on decomposing the T-dependence of superfluid density (from TF-μSR) and the field dependence of the specific-heat coefficient into two isotropic gaps without reported comparison to a single anisotropic gap (e.g., angular variation within s-wave). If the latter reproduces the data comparably, the multigap interpretation and its connection to enhanced Tc would not be required. Explicit model comparison and robustness checks against sample inhomogeneity are needed in the superfluid-density and specific-heat analysis sections.
minor comments (1)
  1. [Abstract] The abstract contains the typo 'unusal' (should be 'unusual').

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive major comment. We address the point below and will revise the manuscript to incorporate the requested analysis.

read point-by-point responses

  1. Referee: [Abstract and superfluid-density/specific-heat modeling sections] The central multigap claim rests on decomposing the T-dependence of superfluid density (from TF-μSR) and the field dependence of the specific-heat coefficient into two isotropic gaps without reported comparison to a single anisotropic gap (e.g., angular variation within s-wave). If the latter reproduces the data comparably, the multigap interpretation and its connection to enhanced Tc would not be required. Explicit model comparison and robustness checks against sample inhomogeneity are needed in the superfluid-density and specific-heat analysis sections.

    Authors: We agree that an explicit comparison between the two-isotropic-gap model and single-gap anisotropic s-wave models (with angular variation) is necessary to substantiate the multigap interpretation. In the revised manuscript we will add such model comparisons for both the superfluid density (from TF-μSR) and the electronic specific-heat data. We will demonstrate that the anisotropic single-gap models yield systematically poorer fits, particularly failing to capture the low-temperature curvature of the superfluid density and the field dependence of the specific-heat coefficient. In addition, we will include robustness checks against sample inhomogeneity by (i) simulating the effect of a distribution of gap values or Tc values on the observables and (ii) verifying consistency of the extracted parameters across independent data sets (different samples or measurement techniques). These additions will be placed in the superfluid-density and specific-heat analysis sections; the abstract will remain unchanged as it already qualifies the multigap feature as “some multigap features.” revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental fits and band calculations remain independent

full rationale

The paper's central claims rest on direct experimental inputs (TF-μSR relaxation rates yielding superfluid density, specific-heat jumps and field dependence) fitted to standard isotropic-gap models, plus separate electronic band-structure calculations. No equation or claim reduces by construction to its own inputs, no fitted parameter is relabeled as a prediction, and no load-bearing step depends on a self-citation chain. The multigap suggestion is presented as a modeling choice supported by multiple observables rather than a self-definitional or uniqueness-imported result. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard BCS gap-fitting procedures and the assumption that μSR depolarization rates map directly to superfluid density; no new particles or forces are introduced, but two gap magnitudes are fitted parameters.

free parameters (2)
  • larger gap magnitude = 1.78 k_B T_c
    Extracted by fitting the temperature dependence of superfluid density and electronic specific heat; quoted as 1.78 kBTc with ~90% spectral weight.
  • smaller gap magnitude and relative weight
    Required to reproduce the low-temperature curvature of the superfluid density; not numerically quoted in abstract.
axioms (2)
  • domain assumption Isotropic s-wave gaps on multiple bands can be distinguished from anisotropic single-gap behavior by the temperature and field dependence of specific heat and μSR relaxation rates.
    Invoked when the abstract states that the data 'suggest' multigap features.
  • domain assumption Zero-field μSR asymmetry remains constant below Tc if and only if time-reversal symmetry is preserved.
    Used to conclude preserved TRS from the absence of spontaneous fields.

pith-pipeline@v0.9.0 · 5866 in / 1650 out tokens · 38225 ms · 2026-05-25T10:55:34.164546+00:00 · methodology

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