Nonrelativistic-Ising superconductivity in p-wave magnets

TL;DR

The paper addresses Ising-type superconductivity in non-relativistic spin-split p-wave magnets (pwM), showing that large exchange-driven spin splitting yields a 50:50 mixing of spin singlet and $p$-wave triplet Cooper pairs. A minimal effective model with momentum-dependent spin splitting $\xi_{\mathrm{nr}}(\mathbf{k}) = 2 k_0 k_x/m$ and an exchange field leads to an intrinsic $s+p$ pairing with $\mathbf{d}_{\bm{k}} \propto f^t_{\bm{k}}$ (with $f^t_{\bm{k}}\sim k_x$) that cannot be treated as independent from the singlet channel, and Tc is set by the combined interaction $g_s+g_t$. Under an in-plane field, a non-unitary $s+p+ip'$ state is induced via a field-generated $p'$-wave component, governed by coupled self-consistency equations and a canting angle $\theta$; this field-tunable mixing signals rich phenomenology including topological/nodal transitions. The work also highlights possible field-induced re-entrant superconductivity via impurity-spin reorientation, made more feasible by the large non-relativistic spin splitting. Overall, the results extend Ising superconductivity to NR-IS pwMs, predicting large in-plane critical fields and unconventional parity-mixed pairing with potential topological features.

Abstract

We discuss a possibility of superconductivity in the p-wave magnets. These are recently discovered materials that have zero net magnetization by symmetry and finite non-relativistic spin splitting of electron bands, like in altermagnets. Similarly, the spin polarizations is collinear in the momentum space. Yet, as opposed to altermagnets, the magnetization is noncollinear in the real space, and the spin splitting obeys time-reversal symmetry in the momentum space. As a result, if such material harbors superconductivity (due to phonons, or any other mechanism), the only supported superconducting symmetry is Ising superconductivity, an exotic symmetry where any Cooper pair is a 50:50 mix of singlet and triplet. This unusual behavior is also in stark contrast to regular antiferromagnet, which can support Cooper pairs of any parity, and altermagnets, which can only support nonunitary triplet pairs. The presence of large triplet component and enhanced resilience against pair breaking is inherent to the p-wave magnets and as such is unconventional as it does not materialize in conventional spin-orbit coupling induced Ising superconductors.

Figures (2)

• Figure 1: (a) The p-wave spin-split bands with the momentum space spins (top panel) oriented perpendicular to the direct space (bottom panel) noncollinear magnetic order. (b) The dispersion relations of the two spin split bands $E_{\bm{k}}^{\uparrow,\downarrow}$, Eq. \ref{['eq:EkUD']} at $k_y=0$ as a function of $k_x$. (c) At a fixed Fermi energy, $E_F$ the two oppositely spin polarized Fermi surfaces are disjoint at sufficiently large separation, $2k_0$.
• Figure 2: The dispersion relations of the two spin split bands are not modified by the exchange field, $\bm{H} = H \hat{x}$ at $k_y=0$ in the lowest order in $H$, but spins cant into the field direction. The states at the two branches with opposite momenta are related by the $\mathcal{T}[C_{2\perp}||E]$ symmetry. At large enough $E_F$ the two branches remain disjoint at finite exchange field as in Fig. \ref{['fig:dispersion']}.