Abstract
A remarkable recent experiment has observed Mott insulator and proximate superconductor phases in twisted bilayer graphene when electrons partly fill a nearly flat miniband that arises a “magic” twist angle. However, the nature of the Mott insulator, the origin of superconductivity, and an effective low-energy model remain to be determined. We propose a Mott insulator with intervalley coherence that spontaneously breaks valley symmetry and describe a mechanism that selects this order over the competing magnetically ordered states favored by the Hund’s coupling. We also identify symmetry-related features of the nearly flat band that are key to understanding the strong correlation physics and constrain any tight-binding description. First, although the charge density is concentrated on the triangular-lattice sites of the moiré pattern, the Wannier states of the tight-binding model must be centered on different sites which form a honeycomb lattice. Next, spatially localizing electrons derived from the nearly flat band necessarily breaks valley and other symmetries within any mean-field treatment, which is suggestive of a valley-ordered Mott state, and also dictates that additional symmetry breaking is present to remove symmetry-enforced band contacts. Tight-binding models describing the nearly flat miniband are derived, which highlight the importance of further neighbor hopping and interactions. We discuss consequences of this picture for superconducting states obtained on doping the valley-ordered Mott insulator. We show how important features of the experimental phenomenology may be explained and suggest a number of further experiments for the future. We also describe a model for correlated states in trilayer graphene heterostructures and contrast it with the bilayer case.
- Received 4 June 2018
- Revised 13 August 2018
DOI:https://doi.org/10.1103/PhysRevX.8.031089
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
In the last few months, researchers have discovered that twisted bilayer graphene—two sheets of graphene layered at a slight angle to one another—can behave as either a superconductor or a type of insulator. An exciting aspect of this realization is that the behavior is selectable: By simply changing an applied voltage, it is possible to go from insulator to superconductor and back. Here, we provide fundamental aspects of a theory describing how these systems work.
In particular, we look at three elements related to this dual nature of twisted bilayer graphene. First, we point out key properties of the electronic band structure that make this problem unique and place surprising constraints on how these systems are modeled. Second, we calculate Wannier functions—orthogonal functions commonly used to describe molecular orbitals in a crystal—as a first step toward incorporating the effects of electron correlation effects. Finally, we provide a simple theory of the insulating and superconducting phases that relies on an unusual form of broken symmetry ordering, and we discuss the observed phenomenology in this light.
Our work reveals important topological aspects to the band structure and raises fascinating challenges for future theories to incorporate both the topology and the strong Coulomb interactions. We also make a number of proposals for future experiments that will illuminate the physics of this system.