Topological invariant and domain connectivity in moir\'e materials

Recently, a moir\'e material has been proposed in which multiple domains of different topological phases appear in the moir\'e unit cell due to a large moir\'e modulation. Topological properties of such moir\'e materials may differ from that of the original untwisted layered material. In this paper, we study how the topological properties are determined in moir\'e materials with multiple topological domains. We show a correspondence between the topological invariant of moir\'e materials at the Fermi level and the topology of the domain structure in real space. We also find a bulk-edge correspondence that is compatible with a continuous change of the truncation condition, which is specific to moir\'e materials. We demonstrate these correspondences in the twisted Bernevig-Hughes-Zhang model by tuning its moir\'e periodic mass term. These results give a feasible method to evaluate a topological invariant for all occupied bands of a moir\'e material, and contribute to the design of topological moir\'e materials and devices.Comment: 12 pages, 12 figure

Electronic topological transition of 2D boron by the ion exchange reaction

We systematically investigated electronic evolutions of non-symmorphic borophene with chemical environments that were realized by the ion exchange method. Electronic structures can be characterized by the topological $Z_2$ invariant. Spectroscopic experiments and DFT calculations unveiled that a sheet of hydrogenated borophene (borophane) is the Dirac nodal loop semimetal ($Z_2=-1$), while a layered crystal of YCrB$_4$ is an insulator ($Z_2=1$). The results demonstrate the electronic topological transition by replacement of the counter atoms on the non-symmorphic borophene layer

Prediction of a Cyclic Hydrogenated Boron Molecule as a Promising Building Block for Borophane

We have extensively searched for a cyclic hydrogenated boron molecule that has a three-center two-electron bond at the center. Using first-principles calculations, we discovered a stable molecule of 2:4:6:8:-2H-1,5:1,5-μH-B8H10 and propose its existence. This molecule can be regarded as a building block for sheets of topological hydrogen boride (borophane), which was recently theoretically proposed and experimentally discovered. The electronic structure of the cyclic hydrogenated boron molecule is discussed in comparison with that of cyclic hydrogenated carbon molecules

Prediction of a Cyclic Hydrogenated Boron Molecule as a Promising Building Block for Borophane

We have extensively searched for a cyclic hydrogenated boron molecule that has a three-center two-electron bond at the center. Using first-principles calculations, we discovered a stable molecule of 2:4:6:8:-2H-1,5:1,5-μH-B8H10 and propose its existence. This molecule can be regarded as a building block for sheets of topological hydrogen boride (borophane), which was recently theoretically proposed and experimentally discovered. The electronic structure of the cyclic hydrogenated boron molecule is discussed in comparison with that of cyclic hydrogenated carbon molecules