Fig. 1: Moiré configuration in linear dissipative conduction.

a, b present the schematic band structures of a typical linear and nonlinear 1D SSH models without geometric frustrations, possessing the same intracell and intercell hopping. Notably, the introduction of nonlinearity in (b) could artificially flatten the existing bands without additional implementations to create geometric-dependent flat bands with intrinsic geometric interference like Lieb, Kagome, and Dice lattices. c plots the alternating spatial-dependent thermal conductivities in a conductive monolayer to supplement the missing efforts caused by nonlinearity. The global four-site unit cell serves as the minimal model for repeating the conductivity distribution within a single layer, whereas the left-upper local region highlights a single site exhibiting a centrosymmetric distribution with respect to its local origin \({{{\rm{O}}}}^{{\prime} }\). \(r\) and \(\theta\) represent the spatial coordinates of an arbitrary point in the global reference frame of a single four-site unit cell. d denotes the new spatial characteristic and base wavevectors after stacking the two monolayers. Significant changes occur in conductivity distributions under the linear superposition of original conductive interactions. e showcases two types of effective wavenumbers at different twisted angles, including \(\left|{{{\bf{k}}}}_{{{\rm{moire}}}}\right|\) for presenting the global periodic function of the entire superlattice, and \(\left|{{{\bf{k}}}}_{{\mathrm{mod}}}\right|\) for modulating the interior profile of moiré pattern in each unit cell of the superlattice. The right-inset presents the effective wavenumbers \(\left|{{{\bf{k}}}}_{{{\rm{ref}}}}\right|\) without considering the differences of directional wavevectors after wave supersessions.