Multiple superconducting phases in heavy-fermion metals

TL;DR

This paper reviews heavy-fermion superconductors with multiple phases, emphasizing orbital-selective pairing, quantum criticality, and recent experimental and theoretical insights into materials like UTe2, CeRh2As2, and CeCu2Si2.

Contribution

It introduces the concept of orbital-selective pairing functions and discusses their role in multiple superconducting phases in heavy-fermion metals, integrating recent experimental and theoretical findings.

Findings

Multiple superconducting phases observed under magnetic field or pressure.

Orbital-selective pairing functions are crucial for understanding unconventional superconductivity.

Quantum criticality influences the emergence of multiple superconducting states.

Abstract

Symmetry breaking beyond a global U(1) phase is the key signature of unconventional superconductors. As prototypical strongly correlated materials, heavy-fermion metals provide ideal platforms for realizing unconventional superconductivity. In this article, we review heavy-fermion superconductivity, with a focus on those materials with multiple superconducting phases. In this context, we highlight the role of orbital-selective (matrix) pairing functions, which are defined as matrices in the space of effective orbital degrees of freedom such as electronic orbitals and sublattices as well as equivalent descriptions in terms of intra- and inter-band pairing components in the band basis. The role of quantum criticality and the associated strange-metal physics in the development of unconventional superconductivity is emphasized throughout. We discuss in some detail the recent experimental observations and theoretical perspectives in the illustrative cases of UTe2, CeRh2As2, and CeCu2Si2, where applied magnetic fields or pressure induce a variety of superconducting phases. We close by providing a brief overview of overarching issues and implications for possible future directions.