Superconductivity with High Upper Critical Field in the Cubic Centrosymmetric η-Carbide Nb4Rh2C1-δ

Abstract

The upper critical field is a fundamental measure of the strength of superconductivity in a material. It is also a cornerstone for the realization of superconducting magnet applications. The critical field arises because of the Cooper pair breaking at a limiting field, which is due to the Pauli paramagnetism of the electrons. The maximal possible magnetic field strength for this effect is commonly known as the Pauli paramagnetic limit given as μ₀ H _Pauli ≈ 1.86[T/K]·T _c for a weak-coupling Bardeen-Schrieffer-Cooper (BCS) superconductor. The violation of this limit is only rarely observed. Exceptions include some low-temperature heavy Fermion and some strongly anisotropic superconductors. Here, we report on the superconductivity at 9.75 K in the centrosymmetric, cubic η-carbide-type compound Nb₄Rh₂C_1-δ, with a normalized specific heat jump of ΔC/γT _c = 1.64. We find that this material has a remarkably high upper critical field of μ₀ H _c2(0) = 28.5 T, which is exceeding by far its weak-coupling BCS Pauli paramagnetic limit of μ₀ H _Pauli = 18.1 T. Determination of the origin and consequences of this effect will represent a significant new direction in the study of critical fields in superconductors.

Figure 1

Crystal structure of Nb₄Rh₂C_1−δ. (a–c) Different crystal directions. (d) Rietveld refinement and PXRD data. (e) Measured [110]* electron diffraction pattern of Nb₄Rh₂C_1−δ superimposed to the theoretical one. (f) The lower figure is a section of a larger experimental [110] oriented HRTEM-image. Upper-left corner: FFT of the complete HRTEM-image. The lower-right corner is a HAADF simulation.

Figure 2

Superconducting properties of Nb₄Rh₂C_1−δ. (a) ZFC magnetization M(H) in a temperature range between T = 1.8 and 9 K for external fields between μ₀H = 0 T and 50 mT. Inset: Lower-critical field H_c1(T); orange line is a fit using the empirical formula: H_c1(T) = H_c1(0) [1 – (T/T_c)²]. (b) Field-dependent resistivity in the vicinity of the superconducting transition in fields between μ₀H = 0 and 17 T. (c) Field dependent specific heat in fields between μ₀H = 0 and 9 T. Inset: Entropy-conserving construction of the zero-field measurement.

Figure 3

Upper critical fields H_c2 of Nb₄Rh₂C_1−δ. Data points from specific heat measurements and using the 10%, 50%, and 90% criteria from the resistivity are shown. The data was fitted using eq 7. For comparison, the critical fields of optimal NbTi and Nb₃Sn alloys are depicted after ref (42).

Figure 4

Electronic structure of Nb₄Rh₂C_1−δ calculated with GGA. (a) Overview and (b) detail of the band structure and density of states. Green shading indicates the range 0 ≤ δ ≤ 0.3.