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Abstract Structural imperfections can be a promising testbed to engineer the symmetries and topological states of solid-state platforms. Here, we present direct evidence of hierarchical transitions of zero- (0D) and one-dimensional (1D) topological states in symmetry-enforced grain boundaries (GB) in 1T′–MoTe2. Using a scanning tunneling microscope tip press-and-pulse procedure, we construct two distinct types of GBs, which are differentiated by the underlying symmorphic and nonsymmorphic symmetries. The GBs with the nonsymmorphic rotation symmetry harbor first-order topological edge states protected by a nonsymmorphic band degeneracy. On the other hand, the edge state of the symmorphic GBs attains a band gap. More interestingly, the gapped edge state realizes a hierarchical topological phase, evidenced by the additional 0D boundary states at the GB ends. We anticipate our experiments will pioneer the material platform for the hierarchical realization of first-order and higher-order topology.

Abstract Two-dimensional (2D) ferroelectric materials have emerged as significant platforms for multi-functional three-dimensional (3D) integrated electronic devices. Among 2D ferroelectric materials, ferro-ionic CuInP2S6 has the potential to achieve the versatile advances in neuromorphic computing systems due to its phase tunability and ferro-ionic characteristics. As CuInP2S6 exhibits a ferroelectric phase with insulating properties at room temperature, the external temperature and electrical field should be required to activate the ferro-ionic conduction. Nevertheless, such external conditions inevitably facilitate stochastic ionic conduction, which completely limits the practical applications of 2D ferro-ionic materials. Herein, free-standing 2D ferroelectric heterostructure is mechanically manipulated for nano-confined conductive filaments growth in free-standing 2D ferro-ionic memristor. The ultra-high mechanical bending is selectively facilitated at the free-standing area to spatially activate the ferro-ionic conduction, which allows the deterministic local positioning of Cu+ ion transport. According to the local flexoelectric engineering, 5.76×102-fold increased maximum current is observed within vertical shear strain 720 nN, which is theoretically supported by the 3D flexoelectric simulation. In conclusion, we envision that our universal free-standing platform can provide the extendable geometric solution for ultra-efficient self-powered system and reliable neuromorphic device.

Asymmetric construction of alkyl C–C bonds with good stereocontrol of the two connecting carbons, particularly when using alkenes as feedstocks, is challenging. Here, the authors show a catalytic method to form multiple adjacent carbon stereocentres in a single operation.