Superconducting States and Intertwined Orders in Metallic Altermagnets

TL;DR

This paper explores the complex superconducting phases and intertwined orders in metallic altermagnets, revealing how fluctuations influence the emergence of nematic and topological superconductivity in these novel magnetic materials.

Contribution

It introduces a mean-field theory framework for multicomponent superconductivity in altermagnets, highlighting the role of fluctuations in stabilizing diverse superconducting phases.

Findings

Multiple superconducting phase transitions due to different gap function condensations.

Fluctuations can promote nematic or chiral superconducting states.

Intertwined orders suggest pathways to realize nematic and topological superconductivity.

Abstract

Altermagnets are a newly identified class of magnets with nodal spin-split band structures, providing a fertile platform for studying unconventional superconductivity and intertwined orders. Here we investigate multicomponent superconductivity and fluctuation-induced intertwined orders in an interacting $d$-wave metallic altermagnet that is invariant under a combination of a fourfold rotation $C_4$ and time-reversal symmetry $T$. Within mean-field theory, the superconducting ground-state manifold is described in terms of two equal-spin two-component $p$-wave gap functions $(\Delta_A^x,\Delta_B^y)$ and $(\Delta_A^y,\Delta_B^x)$, where $A$ and $B$ refer to the two spin-polarized Fermi surfaces related by $C_4T$ symmetry. Because these two sets of gap functions condense at different temperatures, a rich phase diagram with multiple superconducting phase transitions emerges. Distinct fluctuations of sub-leading normal-state instabilities that compete with altermagnetism lift the degeneracy of the multicomponent pairing state in different ways. While nematic fluctuations enhance competition between distinct superconducting components and stabilize nematic superconducting phases, spin current-loop fluctuations promote coexistence and select a pair of chiral states. Our results uncover the pairing structure and elucidate how intertwined sub-leading fluctuations shape superconducting order in altermagnetic metals, suggesting a route toward realizing nematic and topological superconductivity.