Abstract
Effects of the electron-electron interaction on tunneling into a metal in a very strong magnetic field (ultra-quantum limit) are considered. It is shown that for short-range repulsive interactions, tunneling is dominated by the renormalization of the coupling constant leading eventually to the CDW instability. Near the gap, the conductance gT assumes a universal form. For the long-range interaction, there exists an intermediate energy EPL such that for Δ ≪ E ≤ EPL the conductance obeys a power-law scaling form, similar to that of a 1D Luttinger liquid. For smaller energies, scaling breaks down and gT is again dominated by the CDW-instability. It is also shown that the energy dependence of gT may be non-monotonic: whereas gT is always suppressed by the interaction at lower energies, at higher energies it may also be enhanced above its non-interacting value. Such an unusual behavior gets a natural explanation in terms of multiple scattering from the Friedel oscillation near the surface.
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