Twisted bilayer U(1) Dirac spin liquids

TL;DR

This paper investigates the effects of twisting two layers of Dirac quantum spin liquids on their stability and phase behavior, revealing that twisting softens interlayer instabilities and leads to a vortex lattice magnetic order.

Contribution

It introduces a novel analysis of twisted bilayer Dirac spin liquids using conformal mean field theory and perturbation methods, highlighting the impact of twist angle on phase stability.

Findings

Twisting reduces the instability caused by interlayer monopole tunneling.

Finite twist angles soften the interlayer interaction effects.

Magnetic vortices form in the ordered phase with tunable lattice constants.

Abstract

When two layers of two-dimensional materials are assembled with a relative twist, moir\'e 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 (QED$_3$) with an emergent $\mathrm{U}(1)$ 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 analyse 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 QED$_3$ 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 moir\'e 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.