Fermi surfaces of composite fermions
arXiv:2001.06524 · doi:10.1007/s10909-020-02389-3
Abstract
The fractional quantum Hall (FQH) effect was discovered in two-dimensional electron systems subject to a large perpendicular magnetic field nearly four decades ago. It helped launch the field of topological phases, and in addition, because of the quenching of the kinetic energy, gave new meaning to the phrase "correlated matter". Most FQH phases are gapped like insulators and superconductors; however, a small subset with even denominator fractional fillings nu of the Landau level, typified by nu = 1/2, are found to be gapless, with a Fermi surface akin to metals. We discuss our results, obtained numerically using the infinite Density Matrix Renormalization Group (iDMRG) scheme, on the effect of non-isotropic distortions with discrete N-fold rotational symmetry of the Fermi surface at zero magnetic field on the Fermi surface of the correlated nu = 1/2 state. We find that while the response for N = 2 (elliptical) distortions is significant (and in agreement with experimental observations with no adjustable parameters), it decreases very rapidly as N is increased. Other anomalies, like resilience to breaking the Fermi surface into disjoint pieces, are also found. This highlights the difference between Fermi surfaces formed from the kinetic energy, and those formed of purely potential energy terms in the Hamiltonian.
arXiv commentReview of arXiv:1701.07832, arXiv:1704.06265 and arXiv:1706.09470 with some new results. Conference proceedings for "Quantum Fluids and Solids 2019", Edmonton, AB, August 2019
References in corpus (26)
- The density-matrix renormalization group
- Topological crystalline insulator states in Pb(1-x)Sn(x)Se
- Matrix product states represent ground states faithfully
- Is the Composite Fermion a Dirac Particle?
- Exact results for interacting electrons in high Landau levels
- Geometrical Description of the Fractional Quantum Hall Effect
- Condensation of `composite bosons' in a rotating BEC
- Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
- Realizing Fractional Chern Insulators with Dipolar Spins
- Reaching Fractional Quantum Hall States with Optical Flux Lattices
- Infinite density matrix renormalization group for multicomponent quantum Hall systems
- The half-filled Landau level: the case for Dirac composite fermions
- Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth
- Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect
- Berry phase and model wavefunction in the half-filled Landau Level
- Giant Anisotropy of Spin-Orbit Splitting at the Bismuth Surface
- Fermi Contour Anisotropy of GaAs Electron-Flux Composite Fermions in Parallel Magnetic Fields
- Hole-flux Composite Fermion Commensurability Oscillations
- Transference of Fermi Contour Anisotropy to Composite Fermions
- Quantum Hall ferroelectrics and nematics in multivalley systems
- Numerical study of anisotropy in a composite Fermi liquid
- Composite fermions in bands with N-fold rotational symmetry
- Connection between Fermi contours of zero-field electrons and composite fermions in two-dimensional systems
- Signatures of an annular Fermi sea
- Interaction-dependent anisotropy of fractional quantum Hall states
- Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions