Ferroelectric quantum Hall phase revealed by visualizing Landau level wavefunction interference

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.

arXiv commentAccepted to Nature Physics, available through Advance Online Publication

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Cited by in corpus (13)

• Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet
• Resolving the Topological Classification of Bismuth with Topological Defects
• Reversible Gas Sensing by Ferroelectric Switch and 2D Molecule Multiferroics in In2Se3 Monolayer
• A modular ultra-high vacuum millikelvin scanning tunneling microscope
• Valley interference and spin exchange at the atomic scale in silicon
• Interacting multi-channel topological boundary modes in a quantum Hall valley system
• Quantum Hall Valley Nematics
• Valley-Polarized quantum Hall phase in a strain-controlled Dirac system
• Visualization of spin-polarized electronic states by imaging-type spin-resolved photoemission microscopy
• Local Probes for Quantum Hall Ferroelectrics and Nematics
• Moiré superlattices of antimonene on a Bi(111) substrate with van Hove singularity and Rashba-type spin polarization
• Valley polarization of Landau levels driven by residual strain in the ZrSiS surface band
• Spontaneous Breaking of the SU(3) Flavor Symmetry in a Quantum Hall Valley Nematic