Reentrant Superconductivity in Zeeman Fields

Abstract

We propose a theoretical model for a superconductor that exhibits the reentrant superconductivity in Zeeman fields. The Bogoliubov-de Gennes Hamiltonian includes three vectors in spin space: a $d$ vector of a spin-triplet superconducting state, a potential representing spin-orbit interactions, and a Zeeman field. When the three vectors are perpendicular to one another, the spin-orbit interaction suppresses superconductivity in weak Zeeman fields and enhances superconductivity in strong Zeeman fields. The instability (stability) of superconducting state is characterized by the appearance of odd-frequency (even-frequency) Cooper pairs.

Figures (2)

• Figure 1: The critical magnetic field $H_{c}$ is plotted as a function of temperature $T$. (a) All the three vectors are align in parallel, $\bm{d} \parallel \bm{\alpha} \parallel \bm{H}$. The arrow at the vertical axis indicates the Pauli limit $H_{\mathrm{P}}$. (b) The three vectors are perpendicular to one another, $\bm{d} \perp \bm{\alpha}$, $\bm{d}\perp \bm{H}$, and $\bm{\alpha} \perp \bm{H}$. At $H=0$, superconductivity is absent because of $\alpha > \mu_{\mathrm{B}} H_{\mathrm{P}}$. (c) The mixed states with $\alpha_x=0.75T_0$ exhibit the reentrant superconductivity. The two superconducting phases tend to separate from each other for large $\alpha_y$.
• Figure 2: The critical magnetic field $H_{c}$ is plotted as a function of temperature for a single-band spin-triplet superconductors with Rashba SOI. The pair potential is chosen as Eq. \ref{['eq:d2a']} in (a) and Eq. \ref{['eq:d2b']} in (b).