Imaging Quantum Hall Wavefunctions With A Scanning Tunneling Microscope: From Spontaneous Symmetry Breaking To Interacting Domain Boundary Modes

Abstract

Quantum materials provide a rich platform for realizing emergent phenomena, where interactions between electrons lead to properties that are strikingly different from those of individual electrons. Confining electrons to two dimensions and subjecting them to large magnetic fields enhances the effects of Coulomb interactions, which can manifest as a spontaneous lifting of spin, valley or other degeneracies in these quantum Hall systems. Experiments on a number of materials have primarily relied on global measurement techniques to explore this phase space, but locally imaging these broken-symmetry states has remained a challenge. With the use

of a scanning tunneling microscope (STM), we directly visualize quantum Hall wavefunctions on the surface of a bismuth crystal, which enables us to probe the spatial signatures of spontaneous valley ordering. We identify the emergence of a nematic electronic phase, which breaks the rotational symmetry of the underlying crystal lattice, and a ferroelectric phase that carries an in-plane electric dipole

moment. Furthermore, we use the STM to investigate one-dimensional channels that form at the boundary between different valley-polarized quantum Hall states. We find markedly different regimes where these channels are either metallic or insulating, depending on constraints imposed on electron-electron interactions by the valley flavor. These experiments set the stage visualizing fractional quasiparticles in quantum Hall systems, and more generally for using local imaging techniques in future explorations of novel interaction-driven phenomena.