Electronic and magnetic properties of ribbon-shaped nanographite systems with zigzag and armchair edges in a magnetic field are investigated by using a tight-binding model. One of the most remarkable features of these systems is the appearance of edge states, strongly localized near zigzag edges. The edge state in a magnetic field, generating a rational fraction of the magnetic flux $(\phi =p/q)$ in each hexagonal plaquette of the graphite plane, behaves like a zero-field edge state with q internal degrees of freedom. The orbital diamagnetic susceptibility strongly depends on the edge shapes. The reason is found in the analysis of the ring currents, which are very sensitive to the lattice topology near the edge. Moreover, the orbital diamagnetic susceptibility is scaled as a function of the temperature, Fermi energy, and ribbon width. Because the edge states lead to a sharp peak in the density of states at the Fermi level, the graphite ribbons with zigzag edges show Curie-like temperature dependence of the Pauli paramagnetic susceptibility. Hence, there is a crossover from high-temperature diamagnetic to low-temperature paramagnetic behavior in the magnetic susceptibility of nanographite ribbons with zigzag edges.

We present a two-dimensional (2D) lattice model that exhibits a nontrivial topological phase in the absence of the Berry curvature. Instead, the Berry connection provides the topological nontrivial phase in the model, whose integration over the momentum space, the so-called 2D Zak phase, yields a fractional wave polarization in each direction. These fractional wave polarizations manifest themselves as degenerated edge states with opposite parities in the model.

Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of π-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon widt...

Topological photonics has emerged as a novel approach to engineering the flow of light and provides unprecedented means for developing diverse photonic elements, including robust optical waveguides immune to structural imperfections. However, the development of nanoscale standing-wave cavities in topological photonics is rather slow, despite its importance when building densely integrated photonic integrated circuits. In this Letter, we report a photonic crystal nanocavity based on a topological corner state, supported at a 90-deg-angled rim of a two-dimensional photonic crystal. A combination of the bulk-edge and edge-corner correspondences guarantees the presence of the higher-order topological state in a hierarchical manner. We experimentally observe a corner mode that is tightly localized in space while supporting a high $Q$ factor over 2,000, verifying its promise as a nanocavity. These results cast new light on the way to introduce nanocavities in topological photonics platforms.

2D van der Waals ferroelectrics have emerged as an attractive building block with immense potential to provide multifunctionality in nanoelectronics. Although several accomplishments have been reported in ferroelectric switching for out-of-plane ferroelectrics down to the monolayer, a purely in-plane ferroelectric has not been experimentally validated at the monolayer thickness. Herein, an in-plane ferroelectricity is demonstrated for micrometer-size monolayer SnS at room temperature. SnS has been commonly regarded to exhibit the odd–even effect, where the centrosymmetry breaks only in the odd-number layers to exhibit ferroelectricity. Remarkably, however, a robust room temperature ferroelectricity exists in SnS below a critical thickness of 15 layers with both an odd and even number of layers, suggesting the possibility of controlling the stacking sequence of multilayer SnS beyond the limit of ferroelectricity in the monolayer. This work will pave the way for nanoscale ferroelectric applications based on SnS as a platform for in-plane ferroelectrics.