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Theory of tunable flux lattices in the homobilayer moiré of twisted and uniformly strained transition metal dichalcogenides

The spatial texture of internal degree of freedom of electrons has profound effects on the properties of materials. Such texture in real space can manifest as an emergent magnetic field (or Berry curvature), which is expected to induce interesting valley/spin-related transport phenomena. Moiré pattern, which emerges as a spatial variation at the interface of 2D atomic crystals, provides a natural platform for investigating such real space Berry curvature effects. Here we study moiré structures formed in homobilayer transition metal dichalcogenides (TMDs) due to twisting, various uniform strain profiles, and their combinations, where electrons can reside in either layer with the layer index serving as an internal degree of freedom. The layer pseudo-spin exhibits vortex/antivortex textures in the moiré supercell, leading to a giant geometric magnetic field and a scalar potential. Within a geometric picture, the moiré magnetic field is found as the cross product of the gradients of the out-of-plane pseudo-spin and the in-plane pseudo-spin orientation respectively. We discover dual roles of uniform strain: Besides being a cause of the moire atomic texture in the homobilayer, it also contributes a pseudo-gauge potential that modifies the local phase of interlayer coupling. Consequently, strain can be employed to tune the in-plane pseudo-spin texture, while interlayer bias tunes the out-of-plane pseudo-spin, and we show how the moiré magnetic field's spatial profile, intensity, and flux per supercell can be engineered. Through the geometric scalar correction, the landscape of the scalar potential can also be engineered along with the moiré magnetic field, forming distinct effective lattice structures. These properties render TMD moiré structures promising to build tunable flux lattices for transport and topological material applications.