Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States

Abstract

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, {\it i. e.} as FQH states of the quasi-particles or quasi-holes 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 {\em any} hierarchical Jain FQH states has the scaling behavior $G\sim V^{\alpha }$ with the universal exponent $\alpha =1/\nu$, where $\nu$ 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.

arXiv comment10 pages, 50 references, no figures; formerly known as "Composite Fermions: The Next Generation(s)" (title changed by the PRB thought police). This version has more references and a discussion of the stability of the new states. Published version. One erroneous reference is corrected

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Cited by in corpus (29)

• Non-Abelian Anyons and Topological Quantum Computation
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Quantum Hall system in Tao-Thouless limit
• Chern-Simons-Matter Theory
• Non-Abelian states with negative flux: a new series of quantum Hall states
• Supersymmetric Chern-Simons Theory in Presence of a Boundary
• Microscopic origin of the next generation fractional quantum Hall effect
• Harmonic Superspace Gaugeon Formalism for the ABJM Theory
• Fractional Quantum Hall Effect in the Second Landau Level: the Importance of Inter-Composite-Fermion Interaction
• Scaling flow diagram in the fractional quantum Hall regime of GaAs/AlGaAs heterostructures
• Possible Reentrance of the Fractional Quantum Hall Effect in the Lowest Landau Level
• The BV Formalization of Chern-Simons Theory on Deformed Superspace
• Spin phase diagram of the nu_e=4/11 composite fermion liquid
• Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect
• A general approach to quantum Hall hierarchies
• The Hierarchy of Incompressible Fractional Quantum Hall States
• Transition from Free to Interacting Composite Fermions away from $\nu$=1/3
• On the self-similarity in quantum Hall systems
• Non-anticommutative ABJ Theory
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• States of interacting composite fermions at Landau level fillig $\nu =2+3/8$
• Chern-Simons theory of multi-component quantum Hall systems
• Novel Families of Fractional Quantum Hall States : A Berry Phase Approach
• Composite Fermion Wavefunctions Derived by Conformal Field Theory
• Second Generation of Composite Fermions and the Self-Similarity of the Fractional Quantum Hall Effect
• Self-Dual Vortices in the Fractional Quantum Hall System
• Fractional quantum Hall states in charge-imbalanced bilayer systems
• Charge and Statistics of Quasiholes in Pfaffian States of Composite Fermion Excitations