Fig. 2: Dispersion relation of the holey twistsonic medium with different gap separations hg and twist angles.

Specifically, we vary the gap from hg = 0.8a0 to hg = 0.5a0 (four columns) and twist the bilayer according to a m = 1 (θ = 21.78∘), b m = 2 (θ = 13.17∘), and c m = 3 (θ = 9.43∘). The plate thickness is fixed at h1 = h2 = h = 2a0. Red circles mark the regions of the field plots in Fig. 4.