The use of topological invariants for the characterization of material phases has been quite successful. Non-trivial topology is reflected by physical observables near the boundaries of systems as a b...

Adiabatic insertion of the Aharonov-Bohm flux through two pinholes introduces charge transport between them when the system is topologically non-trivial. This is the Laughlin argument. The defects/pin...

Corner states of the breezing Pyrochlore lattice are protected by the Z4 symmetry as a typical example of the bulk-edge/boundary correspondence using Z4 Berry phase. With on-site Coulomb interaction, ...

Hofstadter's butterfly ＆ TKNN integers (Chern numbers)

A flat band system with interaction that possesses a single "quantum scar", which we have proposed in Kuno-Mizoguchi-Hatsugai, Phys. Rev. B 102, 241115(R) (2020), is extended to a system wit...

Covalent/Metal-organic framework (COF/MOF) is a 2D/3D network compound of organic molecules (linkages) connected by linker molecules. This material possesses a set of flat bands (at least in a tight-b...

Many body interactions may modify the topology of physical systems. We have discussed it for a simple 0-D system with non-hermitian hamiltonian. Have a look at our recent paper, "Correlation effe...

Quantum mechanics tells us particles are waves at the same time. One may then naively expect that the quantum state is extended, especially with translational invariance. However, it is not always tru...

We propose topological semimetals generated by the square-root operation for tight-binding models in two and three dimensions, which we call square-root topological semimetals. The square-root topolog...