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Electrodynamics of Thin Sheets of Twisted Material

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We construct a minimal theory describing the optical activity of a thin sheet of a twisted material, the simplest example of which is twisted bilayer graphene. We introduce the notion of "twisted electrical conductivity" which parametrizes the parity-odd response of a thin film to a perpendicularly falling electromagnetic wave with wavelength larger than the thickness of the sheet, and relate the chiral response to this kinetic coefficient. We show that the low-frequency Faraday rotation angle has different behaviors in different phases: \omega^2 for insulators and \omega^0 for superconductors. In both cases the frequency dependence of the Faraday rotation angle can be obtained from a simple power counting in an effective field theory. In the metallic state, the twisted conductivity is proportional to the "magnetic helicity" (scalar product of the velocity and the magnetic moment) of the quasiparticle, averaged around the Fermi surface. Many aspects of the theory are general and applicable to strongly correlated phases.

Reference: Dung X. Nguyen and DTS, arXiv:2008.02812.