Ferroelectric quantum Hall phase revealed by visualizing Landau level wavefunction interference

TL;DR

This paper visualizes Landau level wavefunctions in bismuth to directly observe a ferroelectric quantum Hall state caused by valley polarization and interference effects, revealing new insights into symmetry breaking in multi-valley systems.

Contribution

It introduces a direct imaging method to identify valley ordering and broken symmetry phases in bismuth surface states under high magnetic fields.

Findings

Degeneracy of surface state pockets is fully lifted at high magnetic field.

Wavefunction interference signatures reveal valley polarization and ferroelectric order.

Confirmation of theoretical predictions about interaction-driven valley occupation.

Abstract

Novel broken symmetry states can spontaneously form due to Coulomb interactions in electronic systems with multiple internal degrees of freedom. Multi-valley materials offer an especially rich setting for the emergence of such states, which have potential electronic and optical applications. To date, identification of these broken symmetry phases has mostly relied on the examination of macroscopic transport or optical properties. Here we demonstrate a powerful direct approach by visualizing the wave functions of bismuth surface states with a scanning tunneling microscope. Strong spin-orbit coupling on the surface of bismuth leads to six degenerate teardrop-shaped hole pockets. Our spectroscopic measurements reveal that this degeneracy is fully lifted at high magnetic field as a result of exchange interactions, and we are able to determine the nature of valley ordering by imaging the broken symmetry Landau level (LL) wave functions. The remarkable spatial features of singly degenerate LL wave functions near isolated defects contain unique signatures of interference between spin-textured valleys, which identify the electronic ground state as a quantum Hall ferroelectric. Our observations confirm the recent prediction that interactions in strongly anisotropic valley systems favor the occupation of a single valley, giving rise to emergent ferroelectricity in the surface state of bismuth.