Nonunitary superconductivity in complex quantum materials

Abstract

We revisit the concept of nonunitary superconductivity and generalize it to address complex quantum materials. Starting with a brief review of the notion of nonunitary superconductivity, we discuss its spectral signatures in simple models with only the spin as an internal degree of freedom. In complex materials with multiple internal degrees of freedom, there are many more possibilities for the development of nonunitary order parameters. We provide examples focusing on d-electron systems with two orbitals, applicable to a variety of materials. We discuss the consequences for the superconducting spectra, highlighting that gap openings of band crossings at finite energies can be attributed to a nonunitary order parameter if this is associated with a finite superconducting fitness matrix. We speculate that nonunitary superconductivity in complex quantum materials is in fact very common and can be associated with multiple cases of recently reported time-reversal symmetry breaking superconductors.

Sensitivity of superconducting states to the impurity location in layered materials

“…Later, the same concept was shown to be useful in the context of electronic structure engineering for the optimization of the superconducting critical temperature [41]. More recently, this concept was proved to be related to a variety of unusual properties and responses in unconventional superconductors: the presence of odd-frequency correlations [42]; anomalous Hall effect in chiral superconductors [43]; opening of highenergy gaps in nonunitary superconductors [44]; abnormal evolution of the critical temperature under strain [45]; the presence of gap nodes in superconductors associated with local pairing interactions [46]; photon-induced supercurrents in anapole superconductors [47]; and Bogoliubov Fermi surfaces in even-parity time-reversal symmetry-breaking superconductors [48].…”

Impurity-induced excitations in a topological two-dimensional ferromagnet/superconductor van der Waals moiré heterostructure

“…It is worth noting that, since the scattering potential induced by the previous impurities is nonmagnetic, the emergence of in-gap modes stems from the nontrivial nature of the superconducting gap in the moiré system [43]. In particular, nonmagnetic impurities in conventional s-wave superconductors are well known to not give rise to in-gap states as given by Anderson's theorem [82][83][84][85]. In contrast, topological superconductors with nonzero Chern number feature in-gap modes in the presence of nonmagnetic impurities, rendering artificial topological superconductors vulnerable to disorder [86][87][88][89].…”

Nonequilibrium Green’s function approach to multi-band Cooper-pair transport: linear magnetoresistance effect due to nonunitary superconductivity

“…In such materials, quantum effects emerge at macroscopic scales as a result of reduced dimensionality, interactions, band structure specifics or a combination of these factors. The recent flurry of results on topological insulators [3], Weyl semimetals [4], transition metal dichalcogenides (TMDs) [5], topological and unconventional superconductors [6][7][8][9][10][11][12][13] is a case in point. A common thread that links these groups of materials is their multi-band electronic structure associated with internal degrees of freedom (DOF).…”

“…Such superconductors can often be identified as nonunitary superconductors and are currently the subjects of intense experimental and theoretical effort in a broader context of quantum materials (see e.g. [17][18][19][20][21][22] and reviews [8,9,13]). From the perspective of a transport study, it is convenient to define unitary and nonunitary superconducting states, using the matrix condensate Green's function F. 1 The state is then called unitary if FF † is proportional to a unit matrix, otherwise it is called nonunitary.…”

“…Beyond the single-orbital picture, one encounters a bigger family of the candidate nonunitary order parameters (see e.g. [9,13,22]), so the ability to access and characterize them becomes instrumental. Experimentally, the states with broken TRS can be detected by using the muon spin relaxation technique [9].…”