Two-dimensional (2D) materials have emerged as promising candidates for various optoelectronic applications based on their diverse electronic properties, ranging from insulating to superconducting. However, cooperative phenomena such as ferroelectricity in the 2D limit have not been well explored. Here, we report room-temperature ferroelectricity in 2D CuInP2S6 (CIPS) with a transition temperature of ∼320 K. Switchable polarization is observed in thin CIPS of ∼4 nm. To demonstrate the potential of this 2D ferroelectric material, we prepare a van der Waals (vdW) ferroelectric diode formed by CIPS/Si heterostructure, which shows good memory behaviour with on/off ratio of ∼100. The addition of ferroelectricity to the 2D family opens up possibilities for numerous novel applications, including sensors, actuators, non-volatile memory devices, and various vdW heterostructures based on 2D ferroelectricity.

No abstract

The effect of surface energies, strains, and stresses on the size-dependent elastic state of embedded inhomogeneities are investigated. At nanolength scales, due to the increasing surface-to-volume ratio, surface effects become important and induce a size dependency in the otherwise size-independent classical elasticity solutions. In this letter, closed-form expressions are derived for the elastic state of eigenstrained spherical inhomogeneities with surface effects using a variational formulation. Our results indicate that surface elasticity can significantly alter the fundamental nature of stress state at nanometer length scales. Additional applications of our work on nanostructures such as quantum dots, composites, etc. are implied.

The complete Ref [1] is also included in the discussion of this erratum. The central conclusions of our work (e.g. enhanced size-dependent piezoelectricity in nanostructures due to flexoelectricity) remain the same. In fact, corrected theoretical results in the case of BaTiO 3 in piezoelectric phase compare better with atomistics than the original publication [1]. We provide here the corrected equations and for completeness, the revised figures as well.

The classical formulation of Eshelby (Proc. Royal Society, A241, p. 376, 1957) for embedded inclusions is revisited and modified by incorporating the previously excluded surface/interface stresses, tension and energies. The latter effects come into prominence at inclusion sizes in the nanometer range. Unlike the classical result, our modified formulation renders the elastic state of an embedded inclusion size-dependent making possible the extension of Eshelby’s original formalism to nano-inclusions. We present closed-form expressions of the modified Eshelby’s tensor for spherical and cylindrical inclusions. Eshelby’s original conjecture that only inclusions of the ellipsoid family admit uniform elastic state under uniform stress-free transformation strains must be modified in the context of coupled surface/interface-bulk elasticity. We reach an interesting conclusion in that only inclusions with a constant curvature admit a uniform elastic state, thus restricting this remarkable property only to spherical and cylindrical inclusions. As an immediate consequence of the derivation of modified size-dependent Eshelby tensor for nano-inclusions, we also formulate the overall size-dependent bulk modulus of a composite containing such inclusions. Further applications are illustrated for size-dependent stress concentrations on voids and opto-electronic properties of embedded quantum dots.