KTH/Nordita/SU seminar in Theoretical Physics

Fractional quantum Hall trial wave functions

by Joost Slingerland (Dublin Institute for Advanced Studies)



Trial wave functions like the famous Laughlin wave function have played an essential role in the early stages of examination of all observed conductance plateaus of the fractional quantum Hall effect. After a short introduction to the general principles involved in constructing such wave functions I will focus on a particular hierarchy of trial wave functions which may explain most of the observed conductance plateaus in the second Landau level. These wave functions can be viewed as descendants of the quantum Hall state at filling fraction 5/2, which has recently come under close experimental investigation, because it is expected to allow for quasiparticle excitations with exchange behaviour described by a non-Abelian representation of the braid group (non-Abelian anyons). The newly proposed hierarchy inherits this feature. Experimental and numerical signatures of the new states will be discussed and compared to those of competing states. I will also include some comments on the possible consequences for topologically fault tolerant quantum computation based on fractional quantum Hall anyons.