Polar metals characterized by the simultaneous coexistence of ferroelectric distortions and metallicity have attracted tremendous attention. Developing such materials at low dimensions remains challenging since both conducting electrons and reduced d
imensions are supposed to quench ferroelectricity. Here, based on first-principles calculations, we report the discovery of ferroelectric behavior in two-dimensional (2D) metallic materials with electrostatic doping, even though ferroelectricity is unconventional at the atomic scale. We reveal that PbTe monolayer is intrinsic ferroelectrics with pronounced out-of-plane electric polarization originated from its non-centrosymmetric buckled structure. The ferroelectric distortions can be preserved with carriers doping in the ferroelectric monolayer, which thus enables the doped PbTe monolayer to act as a 2D polar metal. With an effective Hamiltonian extracted from the parametrized energy space, we found that the elastic-polar mode interaction is of great importance for the existence of robust polar instability in the doped system. The application of this doping strategy is not specific to the present crystal, but is rather general to other 2D ferroelectrics to bring about the fascinating metallic ferroelectric properties. Our findings thus change conventional acknowledge in 2D materials and will facilitate the development of multifunctional material in low dimensions.
In this paper, we propose a novel tensor graph convolutional neural network (TGCNN) to conduct convolution on factorizable graphs, for which here two types of problems are focused, one is sequential dynamic graphs and the other is cross-attribute gra
phs. Especially, we propose a graph preserving layer to memorize salient nodes of those factorized subgraphs, i.e. cross graph convolution and graph pooling. For cross graph convolution, a parameterized Kronecker sum operation is proposed to generate a conjunctive adjacency matrix characterizing the relationship between every pair of nodes across two subgraphs. Taking this operation, then general graph convolution may be efficiently performed followed by the composition of small matrices, which thus reduces high memory and computational burden. Encapsuling sequence graphs into a recursive learning, the dynamics of graphs can be efficiently encoded as well as the spatial layout of graphs. To validate the proposed TGCNN, experiments are conducted on skeleton action datasets as well as matrix completion dataset. The experiment results demonstrate that our method can achieve more competitive performance with the state-of-the-art methods.
Symmetric positive definite (SPD) matrices (e.g., covariances, graph Laplacians, etc.) are widely used to model the relationship of spatial or temporal domain. Nevertheless, SPD matrices are theoretically embedded on Riemannian manifolds. In this pap
er, we propose an end-to-end deep manifold-to-manifold transforming network (DMT-Net) which can make SPD matrices flow from one Riemannian manifold to another more discriminative one. To learn discriminative SPD features characterizing both spatial and temporal dependencies, we specifically develop three novel layers on manifolds: (i) the local SPD convolutional layer, (ii) the non-linear SPD activation layer, and (iii) the Riemannian-preserved recursive layer. The SPD property is preserved through all layers without any requirement of singular value decomposition (SVD), which is often used in the existing methods with expensive computation cost. Furthermore, a diagonalizing SPD layer is designed to efficiently calculate the final metric for the classification task. To evaluate our proposed method, we conduct extensive experiments on the task of action recognition, where input signals are popularly modeled as SPD matrices. The experimental results demonstrate that our DMT-Net is much more competitive over state-of-the-art.
