Magnetic surface levels

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Abstract
As is well known, the energy spectrum of conduction electrons in a metal in a magnetic field is split into the Landau levels. These levels give rise to several phenomena whose essence is in the oscillatory dependence of some property of the metal characteristics on the strength of the magnetic field, in the range of strong and medium fields. Of these the most famous are the de Haas-van Alphen effect, and the Shubnikov-de Haas effect. Electronic transitions between the Landau levels give rise to the cyclotron resonance. In a surface layer of a metal placed in a weak magnetic field another system of levels appears for electrons moving along shallow arcs, with their ends resting upon the surface of the metal. These levels originate from the quantized periodic motion of electrons along such ‘skipping’ trajectories due to a specular reflection at the metal surface. The spectrum of the system of magnetic surface levels manifests itself in an oscillatory dependence of the surface impedance on a weak magnetic field. The oscillations are due to a resonant absorption of microwave radiation in transitions of electrons between the magnetic levels occurring at discrete values of the magnetic field. This new quantum effect discovered in several metals in both the normal and superconducting states should, in principle, be common to all the conductors. Studies of the effect are being extended rapidly, and one foresees a discovery of some new phenomena due to the surface bound states of charged quasiparticles, arising in a conductor when exposed to a weak magnetic field.