Spontaneous Twirls and Structural Frustration in Moir\'e Materials

Structural twirls form spontaneously in the domain wall networks of some moir'e materials. We show that in heterobilayers, neighboring twirl chiralities tend to anti-align, forming staggered patterns that are well described by antiferromagnetic lattice ${\varphi }^4$ theories. In moir'e systems with triangular domains, this leads to frustration in the chirality configuration of the structural twirls and to hysteresis with respect to variation of the average twist angle and possibly other control parameters.