Fermion Chern-Simons theory of hierarchical fractional quantum Hall states

Ana López, Eduardo Fradkin

Research output: Contribution to journalArticlepeer-review


We present an effective Chern-Simons 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 ∼ Vα 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.

Original languageEnglish (US)
Article number155322
Pages (from-to)155322-1-155322-10
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number15
StatePublished - Apr 2004

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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