On edge states in semi-infinite quantum Hall systems
- 1 January 1999
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 32 (10) , 1985-1996
- https://doi.org/10.1088/0305-4470/32/10/015
Abstract
We consider an electron in two dimensions submitted to a magnetic field and to the potential of impurities. We show that when the electron is confined to a half-space by a planar wall described by a smooth increasing potential, the total Hamiltonian necessarily has a continuous spectrum in some intervals in between the Landau levels provided that both the amplitude and spatial variation of the impurity potential are sufficiently weak. The spatial decay of the impurity potential is not needed. In particular, this proves the occurrence of edge states in semi-infinite quantum Hall systems.Keywords
All Related Versions
This publication has 10 references indexed in Scilit:
- The nature of the spectrum for a Landau Hamiltonian with delta impuritiesJournal of Statistical Physics, 1997
- Microlocalization, Percolation, and Anderson Localization for the Magnetic Schrödinger Operator with a Random PotentialJournal of Functional Analysis, 1997
- Observation of Chiral Luttinger Behavior in Electron Tunneling into Fractional Quantum Hall EdgesPhysical Review Letters, 1996
- Can a Local Repulsive Potential Trap an Electron?Physical Review Letters, 1996
- Landau Hamiltonians with random potentials: Localization and the density of statesCommunications in Mathematical Physics, 1996
- Localization in single Landau bandsJournal of Mathematical Physics, 1996
- Gauge invariance and current algebra in nonrelativistic many-body theoryReviews of Modern Physics, 1993
- Universality in quantum Hall systemsNuclear Physics B, 1991
- Gapless boundary excitations in the quantum Hall states and in the chiral spin statesPhysical Review B, 1991
- Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potentialPhysical Review B, 1982