Quadrupolar spin liquid, octupolar Kondo coupling and odd-frequency superconductivity in an exactly solvable model

Abstract

We propose an exactly solvable model on the honeycomb lattice in which j eff = 3 2 local moments interact via bond-dependent quadrupole-quadrupole interactions. The model is solved using a Majorana fermion representation for multipole operators. When time reversal symmetry is explicitly broken, we obtain a gapped spin liquid characterized by three chiral edge states. We also investigate another solvable model in which the time-reversal-invariant spin liquid is coupled to conduction electrons in a superconductor. In the presence of a Kondo coupling that involves the octupole moment of the localized spins, the itinerant electrons hybridize with the emergent Majorana fermions in the spin liquid. This leads to spontaneous time reversal symmetry breaking and generates oddfrequency pairing. Our results suggest that j eff = 3 2 systems with strong quadrupole-quadrupole interactions may provide a route towards non-Abelian quantum spin liquids and unconventional superconductivity.