Superconductivity-induced improper orders

TL;DR

This paper proposes a novel mechanism linking superconductivity to improper odd-parity orders via nonsymmorphic symmetries, explaining phenomena in heavy fermion superconductors and broadening understanding of ferroic orders.

Contribution

It introduces a new coupling mechanism between superconducting and odd-parity orders using nonsymmorphic symmetries, expanding the theoretical framework of improper orders.

Findings

Bilinear superconducting order couples to odd-parity orders.

Nonsymmorphic symmetries generate nonintuitive order couplings.

Explains phenomenology of CeRh₂As₂ superconductor.

Abstract

The study of improper phases in the context of multiferroic materials has a long history, but superconductivity has yet to be connected to the network of ferroic orders. In this work, we highlight an overlooked mechanism that couples superconducting order parameters to odd-parity orders in the charge or spin sectors such that the latter emerge as improper orders. For that, we explore a novel perspective of nonsymmorphic symmetries based on extended symmetry groups in real space. We highlight how nonsymmorphic symmetries can generate rather nonintuitive couplings between order parameters. In particular, we find that a bilinear in the superconducting order parameter can couple linearly to odd-parity orders in centrosymmetric systems. Our findings can account for the unusual phenomenology of CeRh$_2$As$_2$, a recently discovered heavy fermion superconductor, and open the door for exploring nonsymmorphic symmetries in the broader context of improper orders with potential applications to functional materials.