Composite-fermion pairing at half and quarter filled lowest Landau level

Abstract

The Halperin-Lee-Read Fermi sea of composite fermions (CFs) at half-filled lowest Landau level is the realization of a fascinating non-Fermi liquid metallic phase. Remarkably, experiments have found that as the width of the quantum well is increased, this state makes a transition into a fractional quantum Hall (FQH) state, the origin of which has remained an important puzzle since its discovery more than three decades ago. We perform detailed and accurate quantitative calculations using a systematic variational framework for the pairing of CFs that closely mimics the BCS theory of superconductivity. We find: (i) as the quantum-well width is increased, the single-component CF Fermi sea occupying the lowest symmetric subband of the quantum well undergoes an instability into a single-component p-wave paired state of CFs; (ii) the theoretical phase diagram in the quantum-well width - electron density plane is in excellent agreement with experiments; (iii) a sufficient amount of asymmetry in the charge distribution of the quantum well destroys the FQH effect, as observed experimentally; and (iv) the two-component 331 state is energetically less favorable than the single component paired state. Evidence for FQH effect has been seen in wide quantum wells also at quarter-filled lowest Landau level; here our calculations indicate an f-wave paired state of CFs. We further investigate bosons in the lowest Landau level at filling factor equal to one and show that a p-wave pairing instability of CFs, which are bosons carrying a single flux quantum, in agreement with exact diagonalization studies. The general consistency of the composite-fermion BCS approach with experiments lends support to the notion of CF pairing as the mechanism of FQH effects at even-denominator filling factors. Various experimental implications are mentioned.

25 pages, 10 figures

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• Microscopic Model for Fractional Quantum Hall Nematics
• Topological phase transition between composite-fermion and Pfaffian daughter states near ν = 1/2 FQHS
• Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Developing fractional quantum Hall states at even-denominator fillings 1/6 and 1/8
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Exploring the nature of the emergent gauge field in composite-fermion metals: A large-scale microscopic study
• Topological pairing of composite fermions via criticality
• Edge reconstruction of compressible Quantum Hall fluid in the filling fraction range 1/3 to 2/3
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Dipole representation of composite fermions in graphene quantum Hall systems
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor