Spin Susceptibility, Upper Critical Field and Disorder Effect in $j=\frac{3}{2}$ Superconductors with Singlet-Quintet Mixing

TL;DR

This paper theoretically investigates the properties of singlet-quintet mixed superconducting states in $j=3/2$ materials, focusing on spin susceptibility, upper critical field, and disorder effects, providing insights for future experiments.

Contribution

It derives key physical quantities for singlet-quintet mixed states and demonstrates their stability against weak non-magnetic disorder, highlighting the role of spin-orbit coupling.

Findings

Zero-temperature spin susceptibility remains zero with centrosymmetric SOC.

Singlet-quintet mixing can enhance the upper critical field.

Strong mixing stabilizes the quintet component despite disorder.

Abstract

Recently, a new pairing state with the mixing between s-wave singlet channel and isotropic d-wave quintet channel induced by centrosymmetric spin-orbit coupling has been theoretically proposed in the superconducting materials with $j=\frac{3}{2}$ electrons. In this work, we derive the expressions of the zero-temperature spin susceptibility, the upper critical field close to the zero-field critical temperature $T_c$ and the critical temperature with weak random non-magnetic disorders for the singlet-quintet mixed state based on the Luttinger model. Our study revealed the following features of the singlet-quintet mixing. (1) The zero-temperature spin susceptibility remains zero for the singlet-quintet mixed state if only the centrosymmetric spin-orbit coupling is taken into account, and will deviate from zero when the non-centrosymmetric spin-orbit coupling is introduced. (2) The singlet-quintet mixing can help enhance the upper critical field roughly because it can increase $T_c$. (3) Although the quintet channel is generally suppressed by the non-magnetic disorder scattering, we find the strong mixing between singlet and quintet channels can help to stabilize the quintet channel. As a result, we still find a sizable quintet component mixed into the singlet channel in the presence of weak random non-magnetic disorders. Our work provides the guidance for future experiments on spin susceptibility and upper critical field of the singlet-quintet mixed superconducting states, and illustrates the stability of the singlet-quintet mixing against the weak random non-magnetic disorder.