Field-resolved hierarchy of superconducting energy gaps in PdTe

The gist: Low-temperature point-contact spectroscopy resolves two characteristic superconducting energy scales in PdTe, both of which are suppressed toward the same superconducting transition temperature, but their magnetic-field evolution reveals two distinct characteristic fields near 4.5 and 7.5 kG, establishing a field-resolved hierarchy of superconducting responses that cannot be characterized by a single scale.

Investigation Methodology

The study investigated the superconducting state of PdTe using low-temperature soft point-contact spectroscopy in a sealed 3He immersion environment to resolve two characteristic energy scales near 0.5 and 1.1 meV. The technique utilized soft point-contact spectroscopy, which is a sensitive probe of superconducting gap structures and interfacial electronic properties. Electrical contacts were formed using a soft-contact technique where small silver grains were gently deposited onto the sample surface to minimize mechanical strain and preserve intrinsic electronic properties. Measurements were performed using a sealed 3He immersion cell mounted on and thermally anchored to the mixing chamber of a dry dilution refrigerator system. Both the sample and the electrical leads were fully immersed in liquid 3He, providing efficient thermalization and reducing local heating effects at the point-contact interface.

Spectroscopic Energy-Scale Hierarchy

The soft point-contact Andreev-reflection spectroscopy revealed two characteristic superconducting energy scales near 0.5 and 1.1 meV that are not adequately described by a single-gap BTK model. Both energy scales are progressively suppressed upon warming toward the same superconducting transition temperature Tc. In contrast, their magnetic-field evolution reveals two distinct characteristic fields near 4.5 and 7.5 kG. The lower scale is associated with the loss of the zero-resistance superconducting state. The higher-energy spectroscopic response persists to substantially larger fields. Independent field-dependent gap analysis yields suppression scales consistent with those identified from the zero-bias conductance.

Gap Modeling and Temperature Dependence

The differential conductance G measured at 330 mK exhibited a pronounced double-peak structure characteristic of point-contact Andreev-reflection (PCAR) spectra. The second derivative, d2G/dV2, highlighted two characteristic energy scales. When compared to single-gap s-, p-, and d-wave BTK models, the fully gapped s-wave model yielded the smallest residual sum of squares (RSS) among the single-gap models considered. To provide a better description, a two-gap s-wave model was employed, yielding gap values of ∆l = 1.1 meV and ∆s = 0.5 meV. The two extracted energy gaps decrease with increasing temperature and are suppressed when approaching Tc. The solid lines in the temperature dependence of the superconducting energy gaps represent the BCS-like temperature dependence, ∆i(T) = ∆i(0) tanh (1.74rTc/T - 1).

Magnetic-Field Robustness

The magnetic-field evolution of the PCAR response shows that the features are gradually weakened and broadened, rather than vanishing abruptly as the field increases. This gradual suppression indicates that the spectroscopic superconducting response evolves over more than a single characteristic field scale. The zero-bias conductance evolves toward the normal-state value and exhibits a slope-change region that terminates near 4.5 kG, together with a second characteristic feature near 7.5 kG. The phenomenological fits indicate that ∆s and ∆l vanish approximately at 5.1±0.2 kG and 7±0.5 kG, respectively. This correspondence suggests that suppression of the smaller energy scale is closely associated with the loss of the zero-resistance superconducting state, whereas the larger energy scale remains detectable to a higher characteristic field.

Comparison with Other Probes

A comparison between these spectroscopic energy gaps and those inferred from bulk specific-heat measurements is instructive. A two-gap analysis of the electronic specific heat yielded gap values of approximately 0.37 meV and 1.93 meV. The smaller gap is reasonably close to the present value of approximately 0.5 meV, whereas the higher-energy gap resolved here, approximately 1.1 meV, lies below the large gap inferred from specific heat. These differences may reflect the distinct weighting of Fermi-surface sheets and momentum-space regions by thermodynamic and point-contact probes. The larger spectroscopic energy scales obtained from PCAR compared with those inferred from earlier bulk magnetic and thermodynamic measurements [9] may be consistent with a surface-sensitive contribution to the measured spectra.

Conclusion

The central result is not only the presence of multiple spectroscopic energy scales, but their contrasting magnetic-field robustness. Although both scales are suppressed toward the same Tc, their field evolution separates into two characteristic suppression scales near 4.5 and 7.5 kG. This establishes a field-resolved hierarchy of superconducting responses that is not captured by a single superconducting energy or field scale. The distinct temperature and field evolution of the two spectroscopic components therefore reveals a hierarchy of superconducting energy scales that cannot be described by a single superconducting field scale. This behaviour is compatible with a multiband superconducting state and may also reflect anisotropic or surface-sensitive contributions to the measured response.

Future Directions

Further microscopic studies of the surface electronic structure and surface density of states will be needed to determine whether the higher-energy and higher-field spectroscopic features observed here are associated with surface superconductivity. The present soft point-contact spectroscopy provides an energy-resolved probe of the superconducting state and shows that the conductance spectra are more naturally described by two superconducting energy gaps. Further microscopic studies of the surface electronic structure and surface density of states will be needed to determine whether the higher-energy and higher-field spectroscopic features observed here are associated with surface superconductivity. The present soft point-contact spectroscopy provides an energy-resolved probe of the superconducting state and shows that the conductance spectra are more naturally described by two superconducting energy gaps. The distinct temperature and field evolution of the two spectroscopic components therefore reveals a hierarchy of superconducting energy scales that cannot be described by a single superconducting field scale. The results provide a spectroscopic framework for disentangling superconducting components with different magnetic-field robustness in PdTe.

Acknowledgements

This work was substantially revised following its presentation at the VI International Conference ”Condensed Matter & Low-Temperature Physics”. We thank M. W. Meisel and Y. G. Naidyuk for insightful discussions that helped improve the manuscript. This work was performed at the National High Magnetic Field Laboratory High B/T Facility on the campus of the University of Florida. The National High Magnetic Field Laboratory is supported by the National Science Foundation through Grants DMR-2128556 and the State of Florida. This work was partially supported by the National High Magnetic Field Laboratory through the NHMFL User Collaboration Grants Program (UCGP). Work at USC (D.D.

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