Abstract
We study the excitations that emerge upon doping the translationally invariant correlated insulating states in magic-angle twisted bilayer graphene at various integer filling factors . We identify parameter regimes where these are excitations associated with skyrmion textures in the spin or pseudospin degrees of freedom, and explore both short-distance pairing effects and the formation of long-range ordered skyrmion crystals. We perform a comprehensive analysis of the pseudospin skyrmions that emerge upon doping insulators at even , delineating the regime in parameter space where these are the lowest-energy charged excitations by means of self-consistent Hartree-Fock calculations on the interacting Bistritzer-MacDonald model. We explicitly demonstrate the purely electron-mediated pairing of skyrmions, a key ingredient behind a recent proposal of skyrmion superconductivity. Building upon this, we construct hopping models to extract the effective masses of paired skyrmions, and discuss our findings and their implications for skyrmion superconductivity in relation to experiments, focusing on the dome-shaped dependence of the transition temperature on the twist angle. We also investigate the properties of spin skyrmions about the quantized anomalous Hall insulator at . In both cases, we demonstrate the formation of robust spin or pseudospin skyrmion crystals upon doping to a finite density away from integer filling.
- Received 20 January 2022
- Revised 13 June 2022
- Accepted 29 June 2022
DOI:https://doi.org/10.1103/PhysRevX.12.031020
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
Twisted bilayer graphene (TBG)—two sheets of graphene stacked and twisted—has attracted lots of attention because of its plethora of exotic electronic behaviors. Under ideal circumstances, electrons in TBG behave approximately like free electrons in a magnetic field. When there are an integer number of electrons per unit cell of the bilayer’s emergent “superlattice,” the electrons form a correlated insulator similar to the quantum Hall ferromagnet. A striking property of quantum Hall ferromagnets is that extra charges injected into the system do not enter as single electrons but as complex spin and pseudospin textures called skyrmions. In this study, we show through numerical simulations that similar excitations can also appear when adding charges to the correlated insulators in TBG, despite the complicated band structure and the absence of a magnetic field.
Following a recent theoretical prediction, we further demonstrate that two such skyrmions can attract to form a bound pair, even though electrons repel via the Coulomb interaction. This is significant because skyrmion pairs can act as tightly bound Cooper pairs and condense to create a superconductor, a fascinating phase of matter seemingly antithetical to insulators. Through extensive numerical analysis, we study the properties of the paired skyrmions and the corresponding skyrmion superconductor and extract important considerations regarding the relevance of this exotic pairing mechanism to the observed superconducting phases in experiments.
Our work paves the way for more detailed studies of skyrmion superconductivity not only in twisted bilayer graphene but also in other moiré heterostructures that exhibit strong correlations and topological physics.
