Twisted bilayer U(1) Dirac spin liquids

When two layers of two-dimensional materials are assembled with a relative twist, moire patterns arise, inducing a tremendous wealth of exotic phenomena. In this work, we consider twisting two triangular lattices hosting Dirac quantum spin liquids. A single decoupled layer is described by compact quantum electrodynamics in 2+1 dimensions (QED3) with an emergent U(1) gauge field, which is assumed to flow to a strongly interacting fixed point in the IR with conformal symmetry. We use recent results for the quantum numbers of monopole operators, which tunnel 2 pi fluxes of the compact gauge field. It is found that, in the bilayer system, interlayer monopole tunneling is a symmetry-allowed relevant perturbation which induces an (ordering) instability. We show using perturbation theory that upon twisting the two layers the system remains unstable under the interlayer interaction, but any finite twist angle softens this instability compared to the untwisted case. To analyze the resulting phase induced by the (twisted) interlayer tunneling, we use conformal mean-field theory, which reduces the interacting bilayer system to two copies of QED3 coupled to background fields which are to be determined self-consistently. In the weak-coupling regime, where the interlayer coupling is weak compared to the energy scale set by the moire lattice constant, we solve the self-consistency equations perturbatively. In the limit of strongly coupled layers, a local scaling approximation is used, and we find that the magnetically ordered state exhibits a lattice of magnetic vortices, with the lattice constant tunable through the twisting angle.

Automated summary

This study investigates the exotic phenomena arising from the relative twist of two layers of two-dimensional materials, particularly in a system with triangular lattices hosting Dirac quantum spin liquids. By using perturbation theory and self-consistency methods, it is found that the twisting angle can regulate the system's instability and the lattice constant of the magnetically ordered state.