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

TL;DR

This paper investigates the behavior of Fermi liquids in high magnetic fields, revealing a new universality class characterized by unique correlation functions and phase transition behaviors depending on electron interactions.

Contribution

The study introduces a novel universality class of Fermi liquids in high magnetic fields, analyzing phase transitions and correlation functions using parquet equations.

Findings

Phase transition to density-wave state at finite temperature with repulsive interactions.

No phase transition occurs with attractive interactions.

Correlation functions exhibit new forms not seen in conventional 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.