Building Fractional Topological Insulators

          @misc{ pirsa_PIRSA:11090070,
            doi = {10.48660/11090070},
            url = {https://pirsa.org/11090070},
            author = {Burnell, Fiona},
            keywords = {Condensed Matter},
            language = {en},
            title = {Building Fractional Topological Insulators},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {sep},
            note = {PIRSA:11090070 see, \url{https://pirsa.org}}
          }
          

Abstract

Time-reversal invariant band insulators can be separated into two categories: `ordinary' insulators and `topological' insulators. Topological band insulators have low-energy edge modes that cannot be gapped without violating time-reversal symmetry, while ordinary insulators do not. A natural question is whether more exotic time-reversal invariant insulators (insulators not connected adiabatically to band insulators) can also exhibit time-reversal protected edge modes. In 2 dimensions, one example of this is the fractional spin Hall insulator (essentially a spin-up and spin-down copy of a fractional quantum Hall insulator, with opposite effective magnetic fields for each spin). I will discuss another family of strongly interacting insulators, which exist in both 2 and 3 dimensions, that can have time-reversal protected edge modes. This gives a new set of examples of `fractional' topological insulators.