Majorana edge and corner states in square and kagome quantum spin-32 liquids

Quantum spin liquids hosting Majorana excitations have recently experienced renewed interest for potential applications to topological quantum computation. Performing logical operations with reduced poisoning requires to localize such quasiparticles at specific point of a device, with energies that are well defined and inside the bulk energy gap. These are two defining features of second-order topological insulators (SOTIs). Here, we show two spin-3/2 models that support quantum spin liquid phases characterized by Majorana excitations. One of them, defined on a square lattice, is analytically solvable thanks to a theorem by Lieb and behaves as a known SOTI. We show that, depending on the values of spin couplings, it is possible to localize either fermions or Majorana particles at its corners. The second model, defined on a kagome lattice, exhibits coexisting topologies, which reflect in a complex pattern of edge states. For certain choices of spin couplings, edge states can localize at one of the corners of a finite kagome lattice with flat edges.