We report systematic optical studies of WS2 and WSe2 monolayers and multilayers. The efficiency of second harmonic generation shows a dramatic even-odd oscillation with the number of layers, consistent with the presence (absence) of inversion symmetry in even-layer (odd-layer). Photoluminescence (PL) measurements show the crossover from an indirect band gap semiconductor at multilayers to a direct-gap one at monolayers. A hot luminescence peak (B) is observed at ~0.4 eV above the prominent band edge peak (A) in all samples. The magnitude of A-B splitting is independent of the number of layers and coincides with the spin-valley coupling strength in monolayers. Ab initio calculations show that this thickness independent splitting pattern is a direct consequence of the giant spin-valley coupling which fully suppresses interlayer hopping at valence band edge near K points because of the sign change of the spin-valley coupling from layer to layer in the 2H stacking order.
Periodic stripe patterns are ubiquitous in living organisms, yet the underlying developmental processes are complex and difficult to disentangle. We describe a synthetic genetic circuit that couples cell density and motility. This system enabled programmed Escherichia coli cells to form periodic stripes of high and low cell densities sequentially and autonomously. Theoretical and experimental analyses reveal that the spatial structure arises from a recurrent aggregation process at the front of the continuously expanding cell population. The number of stripes formed could be tuned by modulating the basal expression of a single gene. The results establish motility control as a simple route to establishing recurrent structures without requiring an extrinsic pacemaker.
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