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Transition metal dichalcogenide (TMD) twisted homobilayers have been established as an ideal platform for studying strong correlation phenomena, as exemplified by the recent discovery of fractional Chern insulator (FCI) states in twisted MoTe21–4 and Chern insulators (CI)5 and unconventional superconductivity6,7 in twisted WSe2. In these systems, nontrivial topology in the strongly layer-hybridized regime can arise from a spatial patterning of interlayer tunneling amplitudes and layer-dependent potentials that yields a lattice of layer skyrmions. Here we report the direct observation of skyrmion textures in the layer degree of freedom of Rhombohedralstacked (R-stacked) twisted WSe2 homobilayers. This observation is based on scanning tunneling spectroscopy that separately resolves the G-valley and K-valley moiré electronic states. We show that G-valley states are subjected to a moiré potential with an amplitude of ~ 120 meV. At ~150 meV above the G-valley, the K-valley states are subjected to a weaker moiré potential of ~30 meV. Most significantly, we reveal opposite layer polarization of the K-valley at the MX and XM sites within the moiré unit cell, confirming the theoretically predicted skyrmion layer-texture. The dI/dV mappings allow the parameters that enter the continuum model for the description of moiré bands in twisted TMD bilayers to be determined experimentally, further establishing a direct correlation between the shape of LDOS profile in real space and topology of topmost moiré band. 

Quasicrystals are characterized by atomic arrangements possessing long-range order without periodicity. Van der Waals (vdW) bilayers provide a unique opportunity to controllably vary atomic alignment between two layers from a periodic moir´e crystal to an aperiodic quasicrystal. Here, we reveal a remarkable consequence of the unique atomic arrangement in a dodecagonal WSe2 quasicrystal: the K and Q valleys in separate layers are brought arbitrarily close in momentum space via higher-order Umklapp scatterings. A modest perpendicular electric field is sufficient to induce strong interlayer K − Q hybridization, manifested as a new hybrid excitonic doublet. Concurrently, we observe the disappearance of the trion resonance and attribute it to quasicrystal potential driven localization. Our findings highlight the remarkable attribute of incommensurate systems to bring any pair of momenta into close proximity, thereby introducing a novel aspect to valley engineering.