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 moir{\'e} structure can be mathematically described in terms of a diffeomorphism in a continuum formulation. We stress that twisting is just one example of moir{\'e} 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 moir{\'e} pattern (rotated by\ 90 degrees\ 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 {\textquotedblleft}moir{\'e} energy scales,{\textquotedblright} 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 {\textquotedblleft}moir{\'e} gravity{\textquotedblright} with low emergent energy scales. Motivated by these analogies, we present an explicit toy construction of moir{\'e} 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.

}, doi = {10.1103/PhysRevResearch.4.L022027}, url = {https://link.aps.org/doi/10.1103/PhysRevResearch.4.L022027}, author = {Parhizkar, Alireza and Galitski, Victor} } @article { WOS:000652838200010, title = {Chiral Anomaly in Interacting Condensed Matter Systems}, journal = {Phys. Rev. Lett.}, volume = {126}, number = {18}, year = {2021}, month = {MAY 7}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {The chiral anomaly is a fundamental quantum mechanical phenomenon which is of great importance to both particle physics and condensed matter physics alike. In the context of QED, it manifests as the breaking of chiral symmetry in the presence of electromagnetic fields. It is also known that anomalous chiral symmetry breaking can occur through interactions alone, as is the case for interacting one-dimensional systems. In this Letter, we investigate the interplay between these two modes of anomalous chiral symmetry breaking in the context of interacting Weyl semimetals. Using Fujikawa{\textquoteright}s path integral method, we show that the chiral charge continuity equation is modified by the presence of interactions which can be viewed as including the effect of the electric and magnetic fields generated by the interacting quantum matter. This can be understood further using dimensional reduction and a Luttinger liquid description of the lowest Landau level. These effects manifest themselves in the nonlinear response of the system. In particular, we find an interaction-dependent density response due to a change in the magnetic field as well as a contribution to the nonequilibrium and inhomogeneous anomalous Hall response while preserving its equilibrium value.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.126.185303}, author = {Rylands, Colin and Parhizkar, Alireza and Burkov, Anton A. and Galitski, Victor} }