Over the past few years, a surprisingly large number of strongly interacting electron phases have been experimentally discovered and reproduced in a variety of crystalline graphene systems with rhombohedral (ABC) stacking orders, including AB bilayer, ABC trilayer, ABCA tetralayer, ABCAB pentalayer, and even thicker systems. The long list of phases includes not only layer-antiferromagnetic states, large-Chern-number quantum anomalous Hall states, and quantum Hall ferroelectrics at charge neutrality, but also Stoner-like half and quarter metals, spin singlet and triplet superconductors, Wigner and Hall crystals, and orbital multiferroics near low-density van Hove singularities. When these systems are aligned with h-BN to form moiré superlattices, multiple fractional quantum anomalous Hall states have been clearly evidenced in transport experiments. Discovery and optimization of these novel phases show that RG is a superior platform with simple chemistry, rich physics, low disorder, and high tunability, advancing our understanding of the interplay between symmetry, topology, and interaction. This tutorial will provide a pedagogical introduction to the RG systems, their moiré heterostructures and unusual band structures, their experimental identification and device fabrication, and a variety of emergent correlated and topological phases in these systems. Multiscale modeling and transport/optical experiments of the RG systems will be discussed in depth with a focus on the discoveries and characteristics of these emergent phases. Open questions and challenges will also be discussed.
Topics
- Theories & modeling of RG: Stacking orders of graphene, first-principles band structures, effective models, Berry phase, first Chern number, Wigner–Seitz radius, Hartree-Fock theory, perturbative renormalization group, and exact diagonalization.
- Experimental techniques applied to RG: Raman spectroscopy, atomic force microscopy, near-field infrared microscopy, nano fabrication, moiré engineering, milli-Kelvin magneto transport, and penetration field capacitance measurement.
- Interacting electron phases in RG: Stoner phases, Wigner and Hall crystals, integer and fractional quantum anomalous Hall states, layer-antiferromagnets, RG-superconductors, quantum Hall ferroelectrics, and orbital multiferroics.
Who should attend?
Graduate students, postdocs, and other scientists interested in 2D materials, topological matter, correlated electrons, superconductivity, magnetism, quantum Hall effect, nano fabrication, etc. Particularly those interested in learning about the exciting new area of correlated and topological electrons in rhombohedral graphene (RG) systems.
Organizer
- Raymond Ashoori, Massachusetts Institute of Technology
Presenters
- Fan Zhang, The University of Texas at Dallas
- Long Ju, Massachusetts Institute of Technology