Nodal Superconductivity of UTe$_2$ Probed by Field-Angle-Resolved Specific Heat on a Crystal with $T_{\rm c}=2.1$ K

TL;DR

This study uses field-angle-resolved specific heat on a high-quality UTe$_2$ crystal ($T_c=2.1$ K) to probe the superconducting gap topology. The observed linear $C(B)$ for $B\parallel b$ and plane-dependent angular oscillations point to nodal excitations with $\bm{v}_{\rm F}$ along the $b$ axis, consistent with either a $B_{2u}$ point-node state in the strong-SOC limit or line nodes confined to flat regions of the $\beta$-sheet FS in a finite-SOC framework. By combining Doppler-shift considerations (Volovik effect) and realistic FS models, the work narrows down the gap symmetry to two main candidates and clarifies how field orientation influences quasiparticle spectra, offering crucial guidance toward resolving the pairing mechanism in UTe$_2$ and its spin-triplet superconductivity.

Abstract

Field-angle-resolved specific-heat measurements were performed on a clean single crystal of a spin-triplet superconductor UTe$_2$ with $T_{\rm c}=2.1$ K and a low residual electronic specific heat. At low temperatures, the specific heat exhibits a linear dependence on the magnetic field when the field is applied precisely along the $b$ axis, in stark contrast to its rapid increase at low fields for other orientations. This pronounced anisotropy suggests the presence of nodal quasiparticle excitations with the Fermi velocity predominantly aligned along the $b$ axis. Considering the characteristic field-angle dependences of both the specific heat and the upper critical field, these observations are broadly compatible with theoretical models that assume a superconducting gap structure featuring either point nodes consistent with $B_{\rm 2u}$ symmetry, allowed in the infinitely strong spin-orbit coupling scheme, or line nodes confined to flat regions of the quasi-two-dimensional Fermi surface, consistent with $^3B_{\rm 3u}$ symmetry in the finite spin-orbit classification scheme. These results yield crucial hints for resolving the pairing symmetry of UTe$_2$, paving the way for a deeper understanding of its spin-triplet superconductivity.

Figures (4)

• Figure 1: (Color online) (a) Temperature dependence of $C/T$ under magnetic fields applied along the $c$ axis. (b) Magnetic-field dependence of $C/T$ at 0.3 K for each field orientation. The inset shows the same data plotted as a function of $\sqrt{B}$.
• Figure 2: (Color online) Field-angle dependence of $C/T$ at 0.3 K under various magnetic fields rotated within the (a) $ac$, (b) $ab$, and (c) $bc$ planes. The numbers labeling each set of data indicate the magnetic-field strength in tesla. Open symbols represent data points mirrored with respect to the crystal symmetry axes.
• Figure 3: (Color online) (a) Field-angle dependence of $C/T$ in the superconducting state at various temperatures under a magnetic field of 0.5 T rotated within the $bc$ plane. (b)-(d) $C/T$ in the normal state at 2.3 K under a magnetic field of 2 T rotated within the (b) $ac$, (c) $ab$, and (d) $bc$ planes. Open symbols indicate data points mirrored with respect to the crystal symmetry axes.
• Figure 4: (Color online) (a) Top view of the 3D Fermi surfaces projected onto the $k_a$-$k_b$ plane. The thickness of the FS lines is roughly proportional to the warping along the $k_c$ axis. The red circles indicate the positions of the line nodes for ${^3}B_{\rm 3u}$. Point nodes are located at both circles and squares for $B_{\rm 2u}$. The sign of the order parameter is alternate along the $k_a$ direction. The original figure is drawn by Eaton et al. Eaton2024NC. (b) Calculated results of the ZDOS, $N(E=0)/N_0$ or $\gamma(B)$, as a function of $B$ for three field orientations. The inset shows the same data plotted as a function of $\sqrt{B}$. (c)-(e) The spatial profiles of the ZDOS centered at the vortex core in a unit cell for three field directions at $B=0.04$. Here, $B$ is expressed in the Eilenberger unit Tsutsumi2016PRB and $T=0.2T_\mathrm{c}$.