While quantum spin liquids as fractionalized phases of matter are typically discussed in the context of insulators, it is an interesting question to ask if one can also construct metallic phases that share some of these features, for example with quasiparticles which are not adiabatically connected to non-interacting electrons with charge e and spin-1/2, thereby lying outside the Fermi liquid paradigm.

One scenario in which such non-Fermi liquid states can be constructed are Kondo lattices, where one couples an electronic band of intolerant charge carriers to a second band with localized magnetic moments. If the latter exhibit a quantum spin liquid, it can be argued that for weak Kondo couplings, the system realizes a fractionalized Fermi liquid (FL*).

In [1], we have investigated a Kitaev-Kondo lattice, where the local moments form an exactly solvable Z2 quantum spin liquid state, which allows for exact controlled results in the weak-coupling limit. Using mean-field theory and analytic arguments, we mapped out the phase diagram of the system, finding that the transition between the FL* phase and an ordinary ("heavy") Fermi liquid at large Kondo coupling is masked by triplet superconducting states (SC). The pairing in these states is mediated by excitations of the Z2 spin liquid, and the superconductor inherits symmetry properties of the spin liquid.

Recently, we have studied an effective electronic theory for the FL* phase with effective electron-electron interactions mediated by the spin liquid [2]. Using functional renormalization group methods, we found that these electron-electron interactions give rise to a pairing instability within the FL* phase which leads to an exotic fractionalized superconductor (SC*) that features both charge-2e excitations as well as fractionalized quasiparticles.