Patrick Ledwith
MIT/Harvard University
Nonlocal Moments and Dirac Trions in the Concentrated Chern Bands of Twisted Bilayer Graphene
Location: 1080 Physics Research Building
Faculty Host: Nandini Trivedi
Abstract: Twisted bilayer graphene (TBG) has elements in common with two paradigmatic examples of strongly correlated physics: quantum Hall physics and Hubbard physics. On one hand, TBG hosts flat topological Landau-level-like bands which exhibit quantum anomalous Hall effects. On the other hand, these bands have concentrated charge density and show signs of extensive entropy. The combination of these features leads to a question: can decoupled moments emerge in an isolated topological band, despite the lack of exponentially localized Wannier states? We answer this question affirmatively by proposing a minimal model for these bands in TBG that combines topology and charge concentration at the AA sites, leading to analytic wavefunctions that closely approximate those of the BM model with realistic parameters. Importantly, charge concentration also leads to Berry curvature concentration at Γ, generating a small parameter s that yields analytic tractability. The model hosts nearly decoupled flavor moments without any extra degrees of freedom. These moments are non-local due to topology-enforced power-law tails, yet have parametrically small overlap. We further develop a diagrammatic expansion in which the self energy can be computed exactly to leading order in s^2 in the fluctuating moment regime. At charge neutrality, we find a "Mott semimetal", with large flavor entropy and a Mott gap everywhere in the BZ except for the vicinity of the Γ point. Away from neutrality, the Mott semimetal gaps out in a spectrally imbalanced manner, with one Mott band having zero spectral weight at the Γ point. We show that the missing spectral weight corresponds to a trion excitation, which can be thought of as a hole combined with a density wave. Remarkably, despite being composed of heavy particles away from the Γ point, the trion can have an arbitrarily small mass. We find that the charge carriers in the normal state of the TBG superconductor are almost entirely trionic near ν=−2.
Bio: Patrick Ledwith is a MIT Pappalardo fellow in Physics with broad interest in the theory of quantum many-body systems. He did his PhD at Harvard with Ashvin Vishwanath where he worked on strongly interacting electrons in topological bands and their realization in moiré systems. Previously, while an undergraduate at MIT, he worked with Leonid Levitov on long-lived excitations in two-dimensional Fermi liquids and their impact on hydrodynamic transport.