Strained Bilayer Graphene, Emergent Energy Scales, and Moire Gravity

Abstract

Twisted bilayer graphene is a rich condensed matter system, which allows one to tune energy scales and electronic correlations. The low-energy physics of the resulting moiré structure can be mathematically described in terms of a diffeomorphism in a continuum formulation. We point out that twisting is just one example of moiré diffeomorphisms. Another particularly simple and experimentally relevant transformation is a homogeneous isomorphic strain of one of the layers, which gives rise to a nearly identical moiré pattern (rotated by $90^{\circ }$ relative to the twisted structure) and potentially flat bands. We further observe that low-energy physics of the strained bilayer graphene takes the form of a theory of fermions tunneling between two curved space-times. Conformal transformation of the metrics results in emergent "moiré energy scales," which can be tuned to be much lower than those in the native theory. This observation generalizes to an arbitrary space-time dimension with or without an underlying lattice or periodicity and suggests a family of toy models of "moiré gravity" with low emergent energy scales. Motivated by these analogies, we present an explicit toy construction of moiré gravity, where the effective cosmological constant can be made arbitrarily small. We speculate about possible relevance of this scenario to the fundamental vacuum catastrophe in cosmology.

4.5 pages, 3 figures; the new version includes a picture and a more detailed description of the curved bilayer

References in corpus (5)

• The electronic properties of graphene
• Graphene as an electronic membrane
• Lectures on the Cosmological Constant Problem
• Strained bilayer graphene: Band structure topology and Landau level spectrum
• General continuum model for twisted bilayer graphene and arbitrary smooth deformations

Cited by in corpus (13)

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• A Generic Topological Criterion for Flat Bands in Two Dimensions
• Gravity from symmetry breaking phase transition
• On the path integral approach to quantum anomalies in interacting models
• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration
• A generalized framework for straintronics in 2D quantum materials using group theory
• Localizing Transitions via Interaction-Induced Flat Bands
• Interference effects in polarization controlled Rayleigh scattering in twisted bilayer graphene
• A Lorentz-violating low-energy model for the bilayer Graphene
• Epitaxial two-dimensional membranes under intrinsic and extrinsic strains
• Geometric Delocalization in Two Dimensions
• Strain-induced stacking transition in bilayer graphene