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A double moiré superlattice can be realized by stacking three layers of atomically thin two-dimensional materials with designer interlayer twisting or lattice mismatches. In this novel structure, atomic reconstruction of constituent layers could introduce significant modifications to the lattice symmetry and electronic structure at small twist angles. Here, we employ conductive atomic force microscopy (cAFM) to investigate symmetry breaking and local electrical properties in twisted trilayer graphene. We observe clear double moiré superlattices with two distinct moire periods all over the sample. At neighboring domains of the large moiré, the current exhibit either two- or six-fold rotational symmetry, indicating delicate symmetry breaking beyond the rigid model. Moreover, an anomalous current appears at the 'A-A' stacking site of the larger moiré, contradictory to previous observations on twisted bilayer graphene. Both behaviors can be understood by atomic reconstruction, and we also show that the cAFM signal of twisted graphene samples is dominated by the tip-graphene contact resistance that maps the local work function of twisted graphene and the metallic tip qualitatively. Our results unveil cAFM is an effective probe for visualizing atomic reconstruction and symmetry breaking in novel moiré superlattices, which could provide new insights for exploring and manipulating more exotic quantum states based on twisted van der Waals heterostructures.

Exploring phase transition behaviors and constructing phase diagrams are of importance for theoretically and experimentally studying ferroelectric physics and materials. Because of the rapid development of computers and artificial intelligence, especially machine learning methods combined with other computational methods such as first principle calculation, it is possible to predict and choose appropriate materials that meet the target requirements from a large number of material data, which greatly saves the cost of experiments. In this work, we use neural network method and phenomenological theoretical calculations to accurately predict the phase structures that may appear in the phase diagrams of different orientated Pb(Zr0.52Ti0.48)O3 ferroelectric films, and establish the temperature-strain phase diagrams of (001), (110) and (111) oriented thin film, and calculate the polarization and dielectric properties of different oriented films at room temperature. By analyzing the changes of prediction accuracy and loss with the number of iterations, it is found that the deep neural network method has the advantages of high accuracy and speed in the construction of the film temperature-strain phase diagram and the prediction of the types of phases. Through the analysis of the room temperature polarization and dielectric properties, it is found that the (111)-oriented PbZr0.52Ti0.48O3 film has the largest out-of-plane polarization and the smallest out-of-plane dielectric coefficient, and they are insensitive to misfit strain. This work provides guidelines for designing micro-nano devices that require the stable dielectric coefficient and polarization performance in the special working environment and operation.

The generalized 2-D problem of a half-infinite interfacial electrode layer between two arbitrary piezoelectric half-spaces is studied. Based on the Stroh formalism, exact expressions for the Green’s functions of a line force, a line charge and a line electric dipole applied at an arbitrary point near the electrode edge, were prsented, respectively. The corresponding solution for the intensity factors of fields were also obtained in an explicit form. These results can be used as the foundational solutions in boundary element method (BEM) to solve more complicated fracture problems of piezoelectric composites.

The generalized two-dimensional problem of a dielectric rigid line inclusion, at the interface between two dissimilar piezoelectric media subjected to piecewise uniform loads at infinity, is studied by means of the Stroh theory. The problem was reduced to a Hilbert problem, and then closed-form expressions were obtained, respectively, for the complex potentials in piezoelectric media, the electric field inside the inclusion and the tip fields near the inclusion. It is shown that in the media, all field variables near the inclusion-tip show square root singularity and oscillatory singularity, the intensity of which is dependent on the material constants and the strains at infinity. In addition, it is found that the electric field inside the inclusion is singular and oscillatory too, when approaching the inclusion-tips from inside the inclusion.

The generalized 2D problem in piezoelectric media with collinear cracks is addressed based on Stroh's formulation and the exact electric boundary conditions on the crack faces. Exact solutions are obtained, respectively, for two special cases: one is that a piezoelectric solid withN collinear cracks is subjected to uniform loads at infinity, and the other is that a piezoelectric solid containing a single crack is subjected to a line load at an arbitrary point. It is shown when uniform loads are applied at infinity or on the crack faces that, the stress intensity factors are the same as those of isotropic materials, while the intensity factor of electric displacement is dependent on the material constants and the applied mechanical loads, but not on the applied electric loads. Moreover, it is found that the electric field inside any crack is not equal to zero, which is related to the material properties and applied mechanical-electric loads.