AUTHOR=Nica Emilian M. , Ran Sheng , Jiao Lin , Si Qimiao 

TITLE=Multiple superconducting phases in heavy-fermion metals

JOURNAL=Frontiers in Electronic Materials

VOLUME=2

YEAR=2022

URL=https://www.frontiersin.org/journals/electronic-materials/articles/10.3389/femat.2022.944873

DOI=10.3389/femat.2022.944873

ISSN=2673-9895

ABSTRACT=<p>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 UTe<sub>2</sub>, CeRh<sub>2</sub>As<sub>2</sub>, and CeCu<sub>2</sub>Si<sub>2</sub>, 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.</p>