1998/12/22 by Nicolas Macris, N. Macris, Philippe Martin +3 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Amplitude #Condensed matter physics #Electron #Enhanced Data Rates for GSM Evolution #Graphene research and applications #Hamiltonian (control theory) #Impurity #Landau quantization #Magnetic field #Mathematics #Physics #Planar #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Topological Materials and Phenomena #cond-mat.mes-hall #math-ph #math.MP
paper · pdf · doi:10.1088/0305-4470/32/10/015
20 pages, no figures, plain TEX, to appear in J. Phys. A
arxiv created 1998/12/22 · openalex publication_date 1999/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.