Composite Fermions, Edge Currents and the Fractional Quantum Hall Effect

Abstract

We present a theory of composite fermion edge states and their transport properties in the fractional and integer quantum Hall regimes. We show that the effective electro-chemical potentials of composite fermions at the edges of a Hall bar differ, in general, from those of electrons. An expression for the difference is given. Composite fermion edge states of three different types are identified. Two of the three types have no analog in previous theories of the integer or fractional quantum Hall effect. The third type includes the usual integer edge states. The direction of propagation of the edge states agrees with experiment. The present theory yields the observed quantized Hall conductances at Landau level filling fractions p/(mp+-1), for m=0,2,4, p= 1,2,3,... It explains the results of experiments that involve conduction across smooth potential barriers and through adiabatic constrictions, and of experiments that involve selective population and detection of fractional edge channels. The relationship between the present work and Hartree theories of composite fermion edge structure is discussed.

19 pages + 6 figures. Self-unpacking uuencoded postscript. To appear in Physical Review B. Revised version has more details in the Appendix and a discussion of one more experiment in Section 6

References in corpus (5)

• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$
• Resonant Tunneling Between Quantum Hall Edge States
• The Structure of Fractional Edge States: A Composite Fermion Approach
• Composite Edge States in the $\nu =2/3$ Fractional Quantum Hall Regime
• Characterization of fractional-quantum-Hall-effect quasiparticles

Cited by in corpus (10)

• The Aharonov-Bohm Effect in the Fractional Quantum Hall Regime
• Nonlinear Dynamics of Composite Fermions in Nanostructures
• 2-Dimensional Electron Gas in a Linearly Varying Magnetic Field. ``Quantisation'' of the Electron and Current Density
• Magnetic field dependent equilibration of fractional quantum Hall edge modes
• Composite Fermion Edge States and Transport Through Nanostructures in the Fractional Quantum Hall Regime
• Ballistic Composite Fermions in Semiconductor Nanostructures
• Composite fermion edge states, fractional charge and current noise
• Temperature dependent equilibration of spin orthogonal quantum Hall edge modes
• Understanding the dynamics of fractional edge states with composite fermions
• Composite Fermion Theory, Edge Currents and the Fractional Quantum Hall Effect