Reentrant Superconductivity from Competing Spin-Triplet Instabilities

Abstract

Reentrant superconductivity in strong magnetic fields challenges the conventional expectation that magnetic fields necessarily suppress superconductivity. We show that reentrant superconductivity arises generically from the competition between spinful and spin-polarized superconducting instabilities. Using a minimal Ginzburg-Landau theory with two coupled spin-triplet order parameters, we demonstrate that a magnetic field can reorganize the hierarchy of superconducting instabilities, yielding a characteristic reentrant instability curve independent of microscopic details.

Figures (2)

• Figure 1: Representative critical-field curves $H_{c2}(T)$ obtained from the linear instability condition $\lambda_-(T,H)=0$ [Eq. (\ref{['eigenvalues']})]. Here, $T_c(0)$ and $H_{c2}(0)$ denote the zero-field transition temperature and the zero-temperature upper critical field, respectively, evaluated at $\varepsilon = 0$. The solid line represents the superconducting instability line, along which the dominant spin structure of the instability changes. (a) $\varepsilon/\gamma=0$ (a symmetry-degenerate limit), where the instability is rapidly reorganized toward the spin-polarized channel. (b) $\varepsilon/\gamma=0.1$, where the internal Josephson coupling enhances the spinful instability at low fields, producing a reentrant structure. Because our analysis is restricted to linearized superconducting instabilities, it does not determine a phase boundary between the spinful and spin-polarized states. See also Fig. \ref{['normalized-Xi']}.
• Figure 2: Variation of $\Xi/(2 |\Delta_1||\Delta_2)=\sin \phi_{12}$ on the critical field curves $H_{c2}(T)$. The graph shows that the magnetic field immediately favors the spin-polarized instability when (a) $\varepsilon/\gamma=0$, whereas spinful instability persists when (b) $\varepsilon/\gamma=0.1$. This persistence caused by $\varepsilon$ is crucial for the reentrant behavior.