Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet

Abstract

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic (QHFM) phases with broken spin or valley symmetry. Visualizing atomic-scale electronic wave functions with scanning tunneling spectroscopy (STS), we resolved microscopic signatures of valley ordering in QHFM phases and spectral features of fractional quantum Hall phases of graphene. At charge neutrality, we observed a field-tuned continuous quantum phase transition from a valley-polarized state to an intervalley coherent state, with a Kekulé distortion of its electronic density. Mapping the valley texture extracted from STS measurements of the Kekulé phase, we could visualize valley skyrmion excitations localized near charged defects. Our techniques can be applied to examine valley-ordered phases and their topological excitations in a wide range of materials.

Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride

“…21,33 . However, more recently, scanning tunneling spectroscopy (STS) meaurements have in fact detected a transition from the CDW states to a KD state at neutrality 34,35 , and therefore these experiments have a great potential to detect the corresponding transition in the fractionally filled case that we predict here.…”

“…One of our key predictions is the presence of a Canted Kekule (CaKD) Laughlin-like state, in which the occupied spinors point in different directions in the valley Bloch sphere, in contrast to the Kekule state (KD) realized at the integer filling corresponding to neutrality, where the spinors point into a common direction in the Bloch sphere (this state has been detected in very recent experiments 34,35 ). Another important prediction is the existence of a transition around B ∼ 1.6T from a singletlike CDW phase to a Laughlin-like CDW state.…”

“…Another interesting avenue for experimentally probing these phases, that has been developed very recently, is the use of scanning tunneling spectroscopy(STS) to detect and distinguish valley-symmetry broken phases and their transitions 34,35 . These studies have so far been restricted to the case of the integer quantum Hall ferromagnets at neutrality.…”

“…This is why we have termed this state a "CaKD" (Canted Kekule Distortion) to emphasize this difference from the KD state at neutrality where the two occupied spinors have a common orientation in the valley Bloch sphere and thus a valley ferromagnetic-like character. Recent tunneling experiments have demonstrated clear and tantalizing evidence for the presence of these states 34,35 .…”

“…The quantum Hall regime in Graphene offers a fantastic arena to investigate the interplay of broken symmetry, topology and fractionalization , that continues to flourish thanks to a combination of high quality samples, enlarged degeneracy from its valley degree of freedom, and its exposed nature that allows new ways to measure and control the states of interest. For example, recent experiments have developed remarkable techniques to generate and detect long-range transmission of collective excitations in broken-symmetry integer and fractional quantum Hall states 7,21,22,[28][29][30][31][32][33][34] , and recent scanning tunneling microscopy has provided detailed evidence of valence-bond quantum Hall Kekule-type states 34,35 .…”