Strained bilayer graphene, emergent energy scales, and moiré gravity
Abstract
Twisted bilayer graphene is a rich condensed matter system, which allows one to tune energy scales and electronic correlations. The lowenergy physics of the resulting moiré structure can be mathematically described in terms of a diffeomorphism in a continuum formulation. We stress 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^{∘} relative to the twisted structure) and potentially flat bands. We further observe that lowenergy physics of the strained bilayer graphene takes the form of a theory of fermions tunneling between two curved spacetimes. 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 spacetime 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.
 Publication:

Physical Review Research
 Pub Date:
 May 2022
 DOI:
 10.1103/PhysRevResearch.4.L022027
 arXiv:
 arXiv:2108.04252
 Bibcode:
 2022PhRvR...4b2027P
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Other Condensed Matter;
 General Relativity and Quantum Cosmology;
 Physics  Classical Physics;
 Quantum Physics
 EPrint:
 4.5 pages, 3 figures