Majorana fermions have potential application in topological quantum computation. Potential hosts for Majorana fermions include certain quantum spin liquids, and some of them are, thanks to certain symmetries, exactly soluble. In this thesis we review and study some exactly-soluble quantum spin liquids which host Majorana excitations. We first review the definition and exact solution of the Kitaev model. We also discuss the possibility for a novel type of spin transport which can take place in regions that have zero spin polarization. We then move on to discuss some possible material realizations and experimental signatures of the Kitaev model. We then present two spin 3/2 models which host quantum spin liquid phases with Majorana excitations. The first model is defined on a square lattice, which is exactly solvable thanks to a theorem by Lieb. We find that it hosts either fermions or Majorana particles at its corners under suitable choice of coupling constants. The second model is defined on the Kagome lattice. We find that it can host two types of edge states, and given certain coupling constants, they can localize at one corner of a finite Kagome lattice with flat edges.
|Date of Award||6 Jan 2023|
- The University of Manchester
|Supervisor||Niels Walet (Supervisor)|