Bifurcations and dynamics of nonlinear excitations in twisted-bilayer optical lattices

In nonlinear systems, the introduction of moiré lattice potentials significantly modifies the energy spectrum, giving rise to novel physical phenomena, such as the formation of flat bands and thus the rich local nonlinear structures. Furthermore, it is found that a deep moiré lattice leads to the degeneracy of Bloch eigenvalues. In this paper, we establish a fundamental relationship between the degeneracy of the Bloch eigenvalues and the spatial configurations of the solitons in a twisted-bilayer moiré lattice, revealing two primary bifurcation phenomena: (i) Solitons bifurcating from Bloch eigenstates. The norms of these solitons traverse narrow energy bands, revealing the existence of embedded solitons in the narrow bands. Detailed analysis is provided for solitons bifurcating from the edges of the first 5 Bloch bands. (ii) Vortex dipole states bifurcating from dipole solitons at a critical chemical potential. The bifurcated states inherit the instability of the original soliton. These results expand our understanding of nonlinear excitations in twisted-bilayer moiré lattice and highlight the critical role of Bloch band structures in shaping soliton patterns.