Metals in high magnetic field: a new universality class of Fermi liquids

Abstract

Parquet equations, describing the competition between superconducting and density-wave instabilities, are solved for a three-dimensional isotropic metal in a high magnetic field when only the lowest Landau level is filled. In the case of a repulsive interaction between electrons, a phase transition to the density-wave state is found at finite temperature. In the opposite case of attractive interaction, no phase transition is found. With decreasing temperature $T$, the effective vertex of interaction between electrons renormalizes toward a one-dimensional limit in a self-similar way with the characteristic length (transverse to the magnetic field) decreasing as ${\ln }^{-1/6}({\omega }_c/T)$ (${\omega }_c$ is a cutoff). Correlation functions have new forms, previously unknown for conventional one-dimensional or three-dimensional Fermi-liquids.

13 pages + 4 figures (included)

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