Abstract
Fractional Majorana defects are point-like objects that support robust non-local storage of quantum information and non-abelian unitary operations required in a topological quantum computer. Their presence relies on a symmetry of the underlying topological system rather than a non-abelian topological order. In this talk we explore two non-heterostructure theoretical possibilities. (i) Majorana bound states (MBS) can arise at disclinations and dislocations of a topological crystalline superconductor (TCS) as a result of lattice rotation and translation symmetry protected bulk topology. TCS is completely classified by a set of integral topological invariants, which form a Z2-index that counts the MBS number parity at a crystalline defect. (ii) Twist defects in a symmetry enhanced topological phase, such as a bilayer fractional quantum Hall state and the Zn Kitaev toric code, can carry fractional Majorana-like characteristics. Their non-abelian nature is exhibited by the non-trivial quantum dimension, multichannel fusion, and unitary projective braiding. They are however fundamentally different from quantum deconfined non-abelian anyons in a true topological phase and satisfy a modified set of spin and braiding statistics properties. Defect exchange phase is identified with multiple 2π rotation, and the braiding S and spin T matrices no longer represent modular transformations of a torus but congruent transformations of a branch cut decorated torus.
Coffee and tea will be served 20 minutes prior to the seminar.