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The study of $\mathrm{ZrT}{\mathrm{e}}_{5}$ crystals is revived because of the recent theoretical prediction of topological phase in bulk $\mathrm{ZrT}{\mathrm{e}}_{5}$. However, the current conclusions for the topological character of bulk $\mathrm{ZrT}{\mathrm{e}}_{5}$ are quite contradictory. To resolve this puzzle, we here identify the Berry phase on both $b$- and $c$ planes of high-quality $\mathrm{ZrT}{\mathrm{e}}_{5}$ crystals by the Shubnikov--de-Hass (SdH) oscillation under tilted magnetic field at 2 K. The angle-dependent SdH oscillation frequency, both on $b$- and $c$ planes of $\mathrm{ZrT}{\mathrm{e}}_{5}$, demonstrates the two-dimensional feature. However, phase analysis of SdH verifies that a nontrivial \ensuremath{\pi}-Berry phase is observed in the $c$-plane SdH oscillation, but not in the $b$-plane one. Compared to bulk Fermi surface predicted by the first-principle calculation, the two-dimensional-like behavior of SdH oscillation measured at $b$ plane comes from the bulk electron. Based on these analyses, it is suggested that bulk $\mathrm{ZrT}{\mathrm{e}}_{5}$ at low temperature (\ensuremath{\sim}2 K) belongs to a weak topological insulator, rather than Dirac semimetal or strong topological insulator as reported previously.

We report a postgrowth aging mechanism of ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$(111) films with scanning tunneling microscopy in combination with density functional theory calculation. It is found that a monolayered structure with a squared lattice symmetry gradually aggregates from the surface steps. Theoretical calculations indicate that the van der Waals (vdW) gap not only acts as a natural reservoir for self-intercalated Bi and Te atoms, but also provides them easy diffusion pathways. Once hopping out of the gap, these defective atoms prefer to develop into a two-dimensional BiTe superstructure on the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$(111) surface driven by positive energy gain. Considering the common nature of weak bonding between vdW layers, we expect such unusual diffusion and aggregation of the intercalated atoms may be of general importance for most kinds of vdW layered materials.

Surface reactivity is important in modifying the physical and chemical properties of surface-sensitive materials, such as the topological insulators. Even though many studies addressing the reactivity of topological insulators towards external gases have been reported, it is still under heavy debate whether and how the topological insulators react with ${\mathrm{H}}_{2}\mathrm{O}$. Here, we employ scanning tunneling microscopy to directly probe the surface reaction of $\mathrm{B}{\mathrm{i}}_{2}\mathrm{T}{\mathrm{e}}_{3}$ towards ${\mathrm{H}}_{2}\mathrm{O}$. Surprisingly, it is found that only the top quintuple layer is reactive to ${\mathrm{H}}_{2}\mathrm{O}$, resulting in a hydrated Bi bilayer as well as some Bi islands, which passivate the surface and prevent subsequent reaction. A reaction mechanism is proposed with ${\mathrm{H}}_{2}\mathrm{Te}$ and hydrated Bi as the products. Unexpectedly, our study indicates that the reaction with water is intrinsic and not dependent on any surface defects. Since water inevitably exists, these findings provide key information when considering the reactions of $\mathrm{B}{\mathrm{i}}_{2}\mathrm{T}{\mathrm{e}}_{3}$ with residual gases or atmosphere.

We report an atomic-scale characterization of ${\mathrm{ZrTe}}_{5}$ by using scanning tunneling microscopy. We observe a bulk band gap of $\ensuremath{\sim}80\text{ }\text{ }\mathrm{meV}$ with topological edge states at the step edge and, thus, demonstrate that ${\mathrm{ZrTe}}_{5}$ is a two-dimensional topological insulator. We also find that an applied magnetic field induces an energetic splitting of the topological edge states, which can be attributed to a strong link between the topological edge states and bulk topology. The relatively large band gap makes ${\mathrm{ZrTe}}_{5}$ a potential candidate for future fundamental studies and device applications.

We study theoretically the propagation of lower-order Lamb waves in one-dimensional composite thin plates. The dispersion curves of Lamb modes propagating parallel to the surfaces of the thin plates in the periodic direction are calculated based on the plane wave expansion method. The existence of band gaps for low-order Lamb wave modes is demonstrated in the systems made of alternating strips of tungsten materials and silicon resin. The finite element method is employed to calculate the transmitted power spectra, which is in good agreement with the results by plane wave exposition. A crucial parameter, i.e., the ratio of the plate thickness $(L)$ to the lattice spacing $(D)$, is discussed in detail for the influence of formation of band gaps.