SU(3) Quantum Hall Ferromagnetism in SnTe

TL;DR

This paper predicts a nematic phase with broken $C_3$ symmetry in SnTe's (111) surface under magnetic fields, driven by Coulomb interactions and affected by Zeeman fields, revealing complex Landau level behaviors.

Contribution

It introduces the prediction of a nematic phase in SnTe's surface states under magnetic fields, highlighting the interplay of Coulomb interactions, intervalley scattering, and Zeeman effects.

Findings

Nematic phase occurs at specific Landau level fillings.

Phase boundary is influenced by Coulomb interactions and intervalley scattering.

Zeeman field modifies Landau level degeneracy and phase diagram.

Abstract

The (111) surface of SnTe hosts one isotropic $\bar{\Gamma}$-centered and three degenerate anisotropic $\bar{M}$- centered Dirac surface states. We predict that a nematic phase with spontaneously broken $C_3$ symmetry will occur in the presence of an external magnetic field when the $N=0$ $\bar{M}$ Landau levels are $1/3$ or $2/3$ filled. The nematic state phase boundary is controlled by a competition between intravalley Coulomb interactions that favor a valley-polarized state, and weaker intervalley scattering processes that increase in relative strength with magnetic field. An in-plane Zeeman field alters the phase diagram by lifting the three-fold $\bar{M}$ Landau level degeneracy, yielding a ground state energy with $2\pi/3$ periodicity as a function of Zeeman-field orientation angle.