Fermion ChernSimons theory of hierarchical fractional quantum Hall states
Abstract
We present an effective ChernSimons theory for the bulk fully polarized fractional quantum Hall (FQH) hierarchical states constructed as daughters of general states of the Jain series, i.e., as FQH states of the quasiparticles or quasiholes of Jain states. We discuss the stability of these new states and present two reasonable stability criteria. We discuss the theory of their edge states which follows naturally from this bulk theory. We construct the operators that create elementary excitations, and discuss the scaling behavior of the tunneling conductance in different situations. Under the assumption that the edge states of these fully polarized hierarchical states are unreconstructed and unresolved, we find that the differential conductance G for tunneling of electrons from a Fermi liquid into any hierarchical Jain FQH states has the scaling behavior G∼V^{α} with the universal exponent α=1/ν, where ν is the filling fraction of the hierarchical state. Finally, we explore alternative ways of constructing FQH states with the same filling fractions as partially polarized states, and conclude that this is not possible within our approach.
 Publication:

Physical Review B
 Pub Date:
 April 2004
 DOI:
 10.1103/PhysRevB.69.155322
 arXiv:
 arXiv:condmat/0310128
 Bibcode:
 2004PhRvB..69o5322L
 Keywords:

 73.43.Cd;
 71.10.Pm;
 Theory and modeling;
 Fermions in reduced dimensions;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 10 pages, 50 references, no figures