Probing the intermediate state of type-I superconductor SnAs using Muon Spin Spectroscopy

TL;DR

This study uses μSR (ZF and TF) and first-principles calculations to resolve the superconducting nature of SnAs, a topological semimetal candidate. It unambiguously establishes conventional type-I superconductivity with preserved time-reversal symmetry and a weak electron-phonon coupling leading to an isotropic $s$-wave gap, consistent with $T_C$ near 3.7 K. TF-μSR maps a complete Meissner–intermediate–normal phase diagram, while ZF-μSR finds no TRS breaking, reinforcing a single Sn valence state. Ab initio results show SOC-driven band features and a modest λ_e-ph that align with experimental Tc, suggesting SnAs sits at the intersection of topology and superconductivity and is a potential platform for topological superconductivity studies.

Abstract

Superconductivity with non-trivial band topology provides a novel platform for exploring topological superconductivity and its quantum applications. A detailed microscopic understanding of the superconducting ground state in such materials is crucial. Here, we report the results of a muon spin rotation/relaxation study ($μ$SR) of the topologically non-trivial superconductor SnAs, which exhibits superconductivity below 3.74(1) \si{K}. Zero-field (ZF) $μ$SR data reveal that this system is a time-reversal invariant superconductor, and systematic transverse-field (TF) $μ$SR measurements unveil the type-I nature of the SnAs superconductor. We have established the superconducting phase diagram to understand the intermediate state of type-I superconductors. Moreover, ab \textit{initio} band structure and phonon calculations are performed, which correlate with the experimental characterization.

Figures (11)

• Figure 1: (a) Microscopic image and (b) Laue diffraction pattern for SnAs single crystal. (c) Crystal structure of the SnAs unit cell. Grey and maroon balls denote the As and the Sn atoms, respectively. (d) The first Brillouin zone with relevant high-symmetry directions is shown using red arrows. (e,f) The bulk band structure and electronic DOS, with and without the SOC contribution. Inset of (e) shows the zoomed view of the band degeneracy at the $\Gamma$ point. (g) Rietveld refinement of the powder XRD spectrum. Inset: XRD pattern for the SnAs single crystal. (h) Temperature-dependent magnetization indicates $T_C$ at 3.74(1) K. The inset shows the M-H loop at 1.8 K. (i) Critical field versus the normalized temperature is fitted with the GL equation, giving an $H_C$ of 187.5(5) Oe. Inset: Magnetization data at low applied field at various temperatures below $T_C$. (j) Electronic specific heat fitted with the s-wave model. Inset displays the Debye fitting for the normal state $C/T$ versus $T^2$ data.
• Figure 2: The ZF-$\mu$SR spectra above and below $T_C$ fitted with an exponentially damped Gaussian KT function. The inset shows the electronic and nuclear relaxation rates, which exhibit negligible changes across the superconducting transition.
• Figure 3: The $\mu$SR asymmetry spectra in TF configuration for (a) 0.05 K, (c) 2.1 K, and (e) 2.8 K at a magnetic field of 75 Oe, fitted using Eq. \ref{['Eq:TF']}. The field distribution of the local field obtained from the MaxEnt transformation of the corresponding $\mu$SR spectra, denoting (b) Meissner, (d) intermediate, and (f) normal states.
• Figure 4: The internal field distribution P(B), at 0.05 K under varying magnetic fields up to 300 Oe.
• Figure 5: The temperature-dependent field distribution of the internal field at constant magnetic fields between 25 Oe and 150 Oe. (a-d) In a particular field between 25 Oe to 100 Oe, the 3D plots show the transition from the Meissner state to the intermediate state, followed by the normal state, as the temperature increases. (e,f) At 125 Oe and 150 Oe, there is a transition from the intermediate state to the normal state.