Probing spontaneous symmetry-breaking in graphene quantum Hall wavefunctions with a Scanning Tunneling Microscope

Abstract

In quantum materials, electrons confined in two dimensions (2D) under high magnetic fields reside in discrete energy levels known as Landau levels. Enhanced Coulomb repulsion in Landau levels beget a myriad of exotic phases with spontaneous broken-symmetry which favor ordering of the electron’s flavors, such as valley or spin, also known as quantum Hall ferromagnetism (QHFM). These systems are typically studied with bulk measurements unable to probe the microscopic order of electrons. Graphene’s zeroth Landau level (ZLL) with four-fold valley-spin degeneracy is a model for studying these phases, and yet after more than a decade of experiments the nature of its broken-symmetry states is still not understood. In this work, we used a scanning tunneling microscope (STM) to image the electronic wavefunction of the ZLL in ultra-clean graphene devices. Specifically, we discovered that near charge-neutrality the ZLL is in a coherent superposition of the two valleys, and detected a topological defect in the electron excitation spectrum. Moreover, we investigate lifting of the orbital degeneracy of the ZLL by charged impurities and compare it to perturbative models. By preparing non-invasive STM probes, we quantify the energy landscape of the fractional quantum Hall states, and detect first and second-order transitions in the valley phase diagram of the ZLL. These results set a benchmark for imaging other interacting 2D systems that harbor broken-symmetry states, including non-Abelian anyons in bilayer graphene or the broken-symmetry states recently discovered in moire materials.