Berry Phase and Anomalous Transport of the Composite Fermions at the Half-Filled Landau Level

Abstract

The fractional quantum Hall effect (FQHE) in two-dimensional electron system (2DES) is an exotic, superfluid-like matter with an emergent topological order. From the consideration of Aharonov-Bohm interaction of electrons and magnetic field, the ground state of a half-filled lowest Landau level is mathematically transformed to a Fermi sea of composite objects of electrons bound to two flux quanta, termed composite fermions (CFs). A strong support for the CF theories comes from experimental confirmation of the predicted Fermi surface at $\nu$ = 1/2 (where $\nu$ is the Landau level filling factor) from the detection of the Fermi wave vector in the semi-classical geometrical resonance experiments. Recent developments in the theory of CFs have led to a prediction of a $\pi$ Berry phase for the CF circling around the Fermi surface at half-filling. In this paper we provide the first experimental evidence for the detection of the Berry phase of CFs in the fractional quantum Hall effect. Our measurements of the Shubnikov-de Haas oscillations of CFs as a function carrier density at a fixed magnetic field provide a strong support for an existence of a $\pi$ Berry phase at $\nu$ = 1/2. We also discover that the conductivity of composite fermions at $\nu$ = 1/2 displays an anomalous linear density dependence, whose origin remains mysterious yet tantalizing.

arXiv commentaccepted to Nature Physics

References in corpus (18)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• The half-filled Landau level: the case for Dirac composite fermions
• Transition from an electron solid to the sequence of fractional quantum Hall states at very low Landau level filling factor
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• Composite fermi liquids in the lowest Landau level
• What Determines the Fermi Wave Vector of Composite Fermions?
• Composite Dirac liquids: parent states for symmetric surface topological order
• Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
• Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
• Composite fermions in a long-range random magnetic field: Quantum Hall effect versus Shubnikov-de Haas oscillations
• Thermoelectric transport signatures of Dirac composite fermions in the half-filled Landau level
• The $\nu =\frac{1}{2}$ Landau level: Half-full or half-empty?
• Effective Mass of the Four Flux Composite Fermion at $\nu =1/4$
• Resistance scaling for Composite Fermions in the presence of a density gradient

Cited by in corpus (16)

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• High quality electrostatically defined hall bars in monolayer graphene
• The Dirac Composite Fermion of the Fractional Quantum Hall Effect
• Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids
• Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• Geometric Resonance of Four-Flux Composite Fermions
• Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Competition of Pairing and Nematicity in the Two-Dimensional Electron Gas
• Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions
• Asymmetry of the Geometrical Resonances of Composite Fermions
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation
• Resistively loaded coplanar waveguide for microwave measurements of induced carriers
• Probing Quantum Geometric Phases via Scanning Tunneling Microscopy
• Emergence of Dirac Composite Fermions: Dipole Picture