Theoretical Study of Impurity Effects on Superconductivity in UTe2

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.

💡 Research Summary

This paper presents a comprehensive theoretical investigation of how impurities affect superconductivity in the heavy‑fermion compound UTe₂. Using a six‑orbital f‑d‑p tight‑binding model that explicitly includes two uranium (U) atoms and four tellurium (Te) atoms per primitive cell, the authors study the suppression of the superconducting transition temperature (Tc) as a function of impurity concentration, impurity site (U‑site versus Te‑site), and impurity magnetic character (magnetic versus non‑magnetic). The impurity scattering is treated within the self‑consistent Born approximation (SCBA), which allows for a fully self‑consistent calculation of the normal self‑energy Σ and the effective scattering matrix I_N.

Key methodological points:

1. The Hamiltonian H₀(k) reproduces the realistic band structure of UTe₂, including strong spin‑orbit coupling, and yields quasiparticle energies ξₐ(k) and the unitary transformation matrices Uₗₙₐₘ(k).
2. Impurity potentials are introduced on‑site as uₗ^{s₁s₂}(r) = vₗ(r)δ_{s₁s₂} + wₗ(r)(S·σ)_{s₁s₂}, where vₗ is the non‑magnetic part and wₗ the magnetic part. Both U‑site (f‑orbital) and Te‑site (p‑orbital) impurities are considered; d‑orbital contributions at the U‑site are neglected for simplicity.
3. The probability that two impurity types (A and B) occupy the same unit cell is encoded in a correlation coefficient c_{AB}. Three configurations are examined: (i) both impurities on U‑sites (U‑U), (ii) one on U and one on Te (U‑Te), and (iii) both on Te (Te‑Te). c_{AB}=1 corresponds to perfect correlation (always co‑located), while c_{AB}=0 corresponds to independent placement.
4. The normal self‑energy Σ is obtained from Σ = Σ_{k′,a₃,a₄,s₃,s₄} I_{N}^{a₁s₁a₄s₄,a₂s₂a₃s₃}(k,k′) G^{a₃s₃,a₄s₄}(k′), and the Green’s function is updated self‑consistently. The effective scattering rate I_N acquires momentum dependence through the unitary matrices U, even though the bare orbital‑space scattering I_{AB} is momentum‑independent.
5. The linearized BCS gap equation, λΔ = T∑_{k′,a′,s₃,s₄}