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Register a new userAbsolute Poissons ratio and the bending rigidity exponent of a crystalline two-dimensional membrane
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We compute the absolute Poissons ratio $ u$ and the bending rigidity exponent $eta$ of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality $d = 2 + d_c$, $d_c gg 1$. We demonstrate that, in the regime of anomalous Hookes law, the absolute Poissons ratio approaches material independent value determined solely by the spatial dimensionality $d_c$: $ u = -1 +2/d_c-a/d_c^2+dots$ where $aapprox 1.76pm 0.02$. Also, we find the following expression for the exponent of the bending rigidity: $eta = 2/d_c+(73-68zeta(3))/(27 d_c^2)+dots$. These results cannot be captured by self-consistent screening approximation.
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We consider a one-dimensional elastic membrane, which is pushed by growing filaments. The filaments tend to grow by creating local protrusions in the membrane and this process has surface energy and bending energy costs. Although it is expected that with increasing surface tension and bending rigidity, it should become more difficult to create a protrusion, we find that for a fixed bending rigidity, as the surface tension increases, protrusions are more easily formed. This effect also gives rise to nontrivial dependence of membrane velocity on the surface tension, characterized by a dip and a peak. We explain this unusual phenomenon by studying in detail the interplay of the surface and the bending energy and show that this interplay is responsible for a qualitative shape change of the membrane, which gives rise to the above effect.
We present first-principles calculations of elastic properties of multilayered two-dimensional crystals such as graphene, h-BN and 2H-MoS2 which shows that their Poissons ratios along out-of-plane direction are negative, near zero and positive, respectively, spanning all possibilities for sign of the ratios. While the in-plane Poissons ratios are all positive regardless of their disparate electronic and structural properties, the characteristic interlayer interactions as well as layer stacking structures are shown to determine the sign of their out-of-plane ratios. Thorough investigation of elastic properties as a function of the number of layers for each system is also provided, highlighting their intertwined nature between elastic and electronic properties.
We develop the theory of anomalous elasticity in two-dimensional flexible materials with orthorhombic crystal symmetry. Remarkably, in the universal region, where characteristic length scales are larger than the rather small Ginzburg scale ${sim} 10, {rm nm}$, these materials possess an infinite set of flat phases which are connected by emergent continuous symmetry. This hidden symmetry leads to the formation of a stable line of fixed points corresponding to different phases. The same symmetry also enforces power law scaling with momentum of the anisotropic bending rigidity and Youngs modulus, controlled by a single universal exponent -- the very same along the whole line of fixed points. These anisotropic flat phases are uniquely labeled by the ratio of absolute Poissons ratios. We apply our theory to monolayer black phosphorus (phosphorene).
A two-dimensional quantum mechanical system consisting of a particle coupled to two magnetic impurities of different strengths, in a harmonic potential, is considered. Topological boundary conditions at impurity locations imply that the wave functions are linear combinations of two-dimensional harmonics. A number of low-lying states are computed numerically, and the qualitative features of the spectrum are analyzed.
As a basic mechanical parameter, Poissons ratio ({ u}) measures the mechanical responses of solids against external loads. In rare cases, materials have a negative Poissons ratio (NPR), and present an interesting auxetic effect. That is, when a material is stretched in one direction, it will expand in the perpendicular direction. To design modern nanoscale electromechanical devices with special functions, two dimensional (2D) auxetic materials are highly desirable. In this work, based on first principles calculations, we rediscover the previously proposed {delta}-phosphorene ({delta}-P) nanosheets [Jie Guan et al., Phys. Rev. Lett. 2014, 113, 046804] are good auxetic materials with a high NPR. The results show that the Youngs modulus and Poissons ratio of {delta}-P are all anisotropic. The NPR value along the grooved direction is up to -0.267, which is much higher than the recently reported 2D auxetic materials. The auxetic effect of {delta}-P originated from its puckered structure is robust and insensitive to the number of layers due to weak interlayer interactions. Moreover, {delta}-P possesses good flexibility because of its relatively small Youngs modulus and high critical crack strain. If {delta}-P can be synthesized, these extraordinary properties would endow it great potential in designing low dimensional electromechanical devices.
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