Moiré superlattices in van der Waals heterostructures provide a tunable platform to study emergent properties that are absent in the natural crystal form. Twisted bilayer transition metal dichalcogenides (TB-TMDs) can host moiré flat bands over a wide range of twist angles. For twist angle close to 60°, it was predicted that TB-TMDs undergo a lattice reconstruction which causes the formation of ultra-flat bands. Here, by using scanning tunneling microscopy and spectroscopy, we show the emergence of multiple ultra-flat bands in twisted bilayer WSe2 when the twist angle is within 3° of 60°. The ultra-flat bands are manifested as narrow tunneling conductance peaks with estimated bandwidth less than 10 meV, which is only a fraction of the estimated on-site Coulomb repulsion energy. The number of these ultra-flat bands and spatial distribution of the wavefunctions match well with the theoretical predictions, strongly evidencing that the observed ultra-flat bands are induced by lattice reconstruction. Our work provides a foundation for further study of the exotic correlated phases in TB-TMDs.
Moiré heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moiré bands in heterobilayer TMDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling ν ¼ 2 (two holes per moiré unit cell) and a valley-polarized quantum anomalous Hall state at filling ν ¼ 1 were observed in AB stacked moiré MoTe 2 =WSe 2 heterobilayers. However, how the topologically nontrivial states emerge is not known. In this Letter, we propose that the pseudomagnetic fields induced by lattice relaxation in moiré MoTe 2 =WSe 2 heterobilayers could naturally give rise to moiré bands with finite Chern numbers. We show that a timereversal invariant quantum valley Hall insulator is formed at full filling ν ¼ 2, when two moiré bands with opposite Chern numbers are filled. At half filling ν ¼ 1, the Coulomb interaction lifts the valley degeneracy and results in a valley-polarized quantum anomalous Hall state, as observed in the experiment. Our theory identifies a new way to achieve topologically nontrivial states in heterobilayer TMD materials.
Overhead cranes with double-pendulum effect seem more practical than those with single-pendulum effect. However, in this case, it is difficult to find an applicable controller for such systems. Hence, a linearized and decoupled double-pendulum overhead crane dynamic model is derived by adopting a disturbance observer and modal analysis technique. The S-shaped trajectory is planned by solving algebraic equations, and the stability of the system is confirmed by the Routh–Hurwitz stability theory. Experimental results and simulations demonstrate the effectiveness of the proposed method. It could be realized to operate the crane accurately without sensor systems for measuring load sways by using the proposed method.
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