Theoretical Study of Impurity Effects on Superconductivity in UTe2

TL;DR

This work addresses the unresolved pairing symmetry in UTe$_{2}$ by analyzing impurity effects on the superconducting transition temperature $T_c$ using a six-orbital $f$-$d$-$p$ model within the self-consistent Born approximation (SCBA). It treats magnetic and nonmagnetic impurities across different impurity configurations, solving the linearized gap equations with impurity corrections via $I^{N}$ and $I^{S}$ to map $T_c(n)$ for candidate pairings ($A_g$, $A_u$, $B_{2u}$, $B_{3u}$). The main findings show that U-site impurities dominantly suppress $T_c$, Te-site impurities have little effect, and nonmagnetic impurities preserve $T_c$ for the anisotropic $s$-wave state (Anderson's theorem) while triplet states follow the Abrikosov-Gor'kov (AG) suppression; magnetic impurities induce stronger suppression in the singlet case. The results indicate two experimentally viable scenarios—spin-triplet pairing or spin-singlet pairing with magnetic impurities—and underscore the importance of determining the magnetic nature of impurities to identify the actual pairing symmetry in $ ext{UTe}_2 $.

Abstract

This study investigates the impurity effects on UTe2 within the self-consistent Born approximation using the six-orbital f-d-p model which contains two uranium and tellurium atoms in the minimum unit cell. We analyze the dependence of superconducting transition temperature (Tc) on impurity concentration for various pairing symmetries proposed by experiments and theories. It clarifies that the decrease of Tc significantly depends on which atom sites the impurities reside. Particulalry, the analysis shows that the impurity at U-site has dominant effect on the change of Tc. Then, either the singlet state in the case of magnetic impurities or the triplet states in both non-magnetic and magnetic impurities are consistent with experiments. Thus, this indicates that elucidating the magnetic properties of impurities (i.e. magnetic or non-magnetic) is crucial for identifying the pairing symmetry of UTe2.

Figures (5)

• Figure 1: Typical cases of impurity configurations with $c_{AB}= 0.0, 0.5, 1.0$. When $c_{AB}=0.0$, the probability of having two impurity sites within a unit cell is neglected.
• Figure 2: Feynman diagram of the BCS gap equation including the processes of impurity scattering. The first term on the right-hand side represents the original effective pairing interaction, while the second corresponds to the impurity effects within SCBA.
• Figure 3: Change in $T_{c}$ as a function of the impurity concentration $n$ regarding (A) nonmagnetic and (B) magnetic impurities. For each superconducting symmetry, we considered three types of defects $[(\mathrm{i})$ U-U, $(\mathrm{ii})$ U-Te, and $(\mathrm{iii})$Te-Te$]$, with $c_{AB}=0,1$ (nonmagnetic impurities) and $c_{AB}=0$ (magnetic impurities).
• Figure 4: Superconducting gap structures $\lvert \Delta_{a}(\bm{k})\rvert$ for each pairing symmetry. (a) Gap structure for an anisotropic $s$-wave state with nonmagnetic impurities at $n=0.5\%$ and $c_{ab}=0$. (b) Gap structure for an anisotropic $s$-wave state with magnetic impurities at $n=0.5\%$ and $c_{ab}=0$. (c) Gap structure for $A_u$ state with nonmagnetic impurities at $n=0.5\%$ and $c_{ab}=0$.
• Figure 5: Change in $T_{c}$ as a function of damping $\gamma$ when both nonmagnetic- and magnetic- impurities are introduced. We calculate $(\mathrm{i})$ U-U with $c_{AB}$ = 0.0. The size of the symbols represents to the impurity concentration ($0 \le n \le 0.5\%$).