Abstract
We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to nonlocal interlayer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wave vectors. We find that at all nonzero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal-symmetric and spatially nonuniform order. This order, which we dub the “incommensurate Kekulé spiral” (IKS) order, spontaneously breaks both the emergent valley-charge conservation and moiré translation symmetries but preserves a modified translation symmetry —which simultaneously shifts the spatial coordinates and rotates the angle which characterizes the spontaneous intervalley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order.
- Received 30 June 2021
- Accepted 8 November 2021
DOI:https://doi.org/10.1103/PhysRevX.11.041063
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
Two layers of graphene stacked slightly askew to a specific “magic” angle can host exotic electronic behaviors. A unified theoretical understanding of the insulating states that can emerge is hampered by the fact that experiments see a diverse collection of behaviors under different conditions, depending on the particular sample. We propose that when the system is sufficiently strained (inevitably true of all real samples to some degree), a new type of insulator emerges that can help explain the multitude of experimental findings.
In twisted bilayer graphene, the two off-kilter honeycomb lattices of carbon atoms produce an interference pattern known as a moiré pattern. Insulating behavior is sometimes observed when each moiré cell is filled with an integer number of extra or missing electrons. Through numerical simulations, we discover that physically reasonable values of strain trigger a periodic distortion of the electron density driven by electron interactions, which further modulates at the moiré scale with a generally incommensurate wavelength. The distortion resembles a spatially rotating Kekulé pattern, familiar from benzene, in which the electron density increases and decreases on alternating bonds around each hexagonal plaquette, and so we dub this state the incommensurate Kekulé spiral.
By considering a large space of external perturbations such as strain and substrate alignment, and exploring each integer filling, we show that this novel state plays a role in explaining the various insulators observed in experiment. Clarifying the insulating phase diagram of twisted bilayer graphene is also an important step in understanding its superconducting behavior.
