The quantum geometry in the momentum space of semiconductors and insulators, described by metric valence band Bloch state, has been an intriguing issue owing to its connection various material properties. Because Brillouin zone is periodic, integration over represents average distance between neighboring states, which we call fidelity number. We show that this number can further be expressed real as a marker, local quantity calculated directly from diagonalizing lattice Hamiltonian. A linear...

A bipartite lattice with chiral symmetry is known to host zero-energy flat bands if the numbers of two sublattices are different. We demonstrate that this mechanism producing can be realized on graphene by introducing periodic vacancies. Using first-principles calculations, we elaborate even though pristine does not exactly preserve symmetry, applied holey still produces single or multiple as narrow $\ensuremath{\sim}0.5\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ near Fermi surface throughout...

For graphene nanoribbons with Rashba spin-orbit coupling, the peculiar magnetic response due to presence of a magnetization and geometric confinement are analyzed within tight-binding model. We observe sizable transverse susceptibility that can be considered as gate voltage-induced magnetoelectric torque without need bias voltage, different directions for zigzag armchair ribbons. The local generates non-collinear spin polarization between two edges and/or along ribbon, net averages zero if...

We elaborate that single-layer graphene with periodic vacancies can have a band structure containing nodal lines or loops, opening the possibility of graphene-based electronic spintronic devices novel functionalities. The principle is by removing carbon atoms such lattice becomes nonsymmorphic, every two sublattices in unit cell will map to each other under glide plane operation. This mapping yields degenerate eigenvalues for operation, which guarantees energy bands must stick together...

Geometric frustration is known to completely damage kinetic processes of some the orbitals (and their associated quantum coherence) as produce flat bands in non-interacting systems. The impact introducing additional interaction system such frustrated systems is, however, a highly controversial issue. On one hand, numerical studies on geometrically hard-core boson (equivalent spin-1/2 systems) typically lead glass or solid phases containing only local many-body coherence, indicating...

The opacity of graphene is known to be approximately given by the fine-structure constant $\ensuremath{\alpha}$ times $\ensuremath{\pi}$. We point out fact that roughly independent frequency and polarization light can attributed topological charge Dirac points. As a result, one literally see with naked eye from graphene, moreover it implies topologically protected. A similar analysis suggests 3D insulator thin films any thickness also have $\ensuremath{\pi}\ensuremath{\alpha}$ in infrared...

The opacity of graphene is known to be approximately given by the fine-structure constant $α$ times $π$. We point out fact that roughly independent frequency and polarization light can attributed topological charge Dirac points. As a result, one literally see naked eyes from graphene, moreover it implies topologically protected. A similar analysis suggests 3D insulator thin films any thickness also have $πα$ in infrared region owing surface states, indicating states through an lens. For or...

The quantum geometry in the momentum space of semiconductors and insulators, described by metric valence band Bloch state, has been an intriguing issue owing to its connection various material properties. Because Brillouin zone is periodic, integration over represents average distance between neighboring states, which we call fidelity number. We show that this number can further be expressed real as a marker, local quantity calculated directly from diagonalizing lattice Hamiltonian. A linear...