Electronic states of a free-standing hydrogenated monolayer boron (HB) sheet were studied via soft x-ray spectroscopies at the B $K$-shell absorption edge and first-principles calculations. The HB sheet is semimetallic with electron and hole pockets at the $Y$ and $\mathrm{\Gamma }$ points, respectively. The electron band results from the B-H-B bonds formed during synthesis from a ${\mathrm{MgB}}_2$ crystal, while the hole band is kept through the process and originates from a honeycomb lattice boron layer or borophene in ${\mathrm{MgB}}_2$. Our results suggest that the HB sheet is a promising two-dimensional material for realizing new boron-based or superconducting nanodevices.

The existence of a topological Dirac nodal loop is predicted for hydrogenated monolayer boron sheets with a nonsymmorphic symmetry. The three-center two-electron bonds in boron compounds restrict the electronic system to be insulating or semimetallic with a Dirac nodal loop. Two types of electronic structures are distinguished by the ${\mathbb{Z}}_2$ topological index and confirmed by first-principles total-energy calculations. The topological taxonomy, developed in this research, can be applied to other two-dimensional materials and to seek novel Dirac fermions.

The search for free-standing 2D materials has been one of the most important subjects in the field of studies on 2D materials and their applications. Recently, a free-standing monolayer of hydrogenated boron (HB) sheet has been synthesized by hydrogenation of borophene. The HB sheet is also called borophane, and its application is actively studied in many aspects. Here, we review recent studies on the electronic structures of polymorphic sheets of borophane. A hydrogenated boron sheet with a hexagonal boron frame was shown to have a semimetallic electronic structure by experimental and theoretical analyses. A tight-binding model that reproduces the electronic structure was given and it allows easy estimation of the properties of the material. Hydrogenated boron sheets with more complicated nonsymmorphic boron frames were also analyzed. Using the symmetry restrictions from the nonsymmorphic symmetry and the filling factor of hydrogenated boron sheets, the existence of a Dirac nodal line was suggested. These studies provide basic insights for research on and device applications of hydrogenated boron sheets.

Moiré materials have become one of the most active fields in material science in recent years due to their high tunability, and their unique properties emerge from the moiré-scale structure modulation. Here, we propose twisted bilayer ${\mathrm{Bi}}_2{\left({\mathrm{Te}}_{1-x}{\mathrm{Se}}_x\right)}_3$ as a moiré material where the moiré-scale modulation induces a topological phase transition. We show, in twisted bilayer ${\mathrm{Bi}}_2{\left({\mathrm{Te}}_{1-x}{\mathrm{Se}}_x\right)}_3$, a topological insulator domain and a normal insulator domain coexist in the moiré lattice structure, and edge states on the domain boundary make nearly flat bands that dominate the material properties. The edge states further contribute to a moiré-scale band inversion, resulting in moiré-scale topological states. There are corresponding moiré-scale edge states and they are so to speak “edge state from edge state,” which is a unique feature of twisted bilayer ${\mathrm{Bi}}_2{\left({\mathrm{Te}}_{1-x}{\mathrm{Se}}_x\right)}_3$. Our result not only proposes characteristic quantum phases in twisted bilayer ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ family, but also suggests the twisting of stacking-sensitive topological materials paves an avenue in the search for novel quantum materials and devices.

The presence of a Dirac nodal line in a time-reversal and inversion symmetric system is dictated by the \(\mathbb{Z}_{2}\) index when spin–orbit interaction is absent. In a first principles calcula...