I have written an article for JPSJ News & Comments. Have a look at "Nontrivial Topology of Nontopological Nonlinear Waves." See also old ones.

Heat conduction of the breathing Kagome lattice is discussed in relation to the anomalous heat-carrying corner states due to higher-order topology. Especially the use of the effective Hamiltonian for ...

A two-leg ladder is a nice place to discuss Z2× Z2 symmetry with sufficient numerical accuracy. Using a Z4 Berry phases, several phases of bosonic ladders are discussed in relation to the bulk-edge co...

An electromagnetic field in a photonic crystal is described by a hermitian eigenvalue problem with an overlap matrix which may not be positive definite if the system is composed of negative index medi...

A topological pump of SU(Q) interacting fermions is proposed based on Affleck's SU(Q) quantum chains associated with a symmetric breaking term characterized by a parameter P/Q with co-prime integers P...

Chemisorption on graphene and silicene may realize Martini type π-electron network. It implies specific band dispersion. We propose potential materialization by using the molecular orbital constr...

Taking a square root is not trivial. The Dirac equation is invented by the square root of the Kleind-Gordon equation. Then the lattice analog of the operation implies non-trivial　topology and edge/cor...

Using a molecular orbital (MO) construction scheme of the flat band which we are proposing, we found novel random critical states in a series of flat band systems away from the flat band energy. The M...

Topological protection of singularities for the non-Hermitian problem is one of the recent focuses in condensed matter physics. Exceptional points and rings with symmetry constraints are typical examp...

Topological protection for topological systems may change by the inclusion of particle-particle interaction, which is known as "reduction phenomena." Here we have pointed out its possibilities for 1-d...

One of the recent wisdom for topological phases is the use of a classical system as a quantum simulator. The Hofstadter butterfly associated with topological phase transitions is realized in electric ...

Adiabatic connection of the gapped many-body states is a conceptual background of the topological phases. Historical and more than successful examples are given by various fractional quantum Hall stat...

The discriminant is a generalization of the　"b 2- 4 ac" formula that everybody knows, which tells us the degeneracy of the (secular) equation. Then it is natural the discriminant is useful for the stu...

Recent wisdom for the construction of flat bands is applicable even with randomness. Characterization of special features of the random flat bands has been successfully done by using machine learning....

Analyzing a diffusion equation of alternative metals, rapid heat conduction to the heat bath due to edge states is predicted. The edge states are predicted by the bulk topological invariant as a typic...

Once one admits the electronic state is described by the molecular-orbitals (MOs), the system has flat bands when the number of MOs is less than the total number of atoms. Then it is natural the elect...

As widely accepted, the degeneracy of eigenvalues of the Hamiltonian is a singular point, which is the source of the non-trivial topology. Then it is more than natural that the discriminant of the sec...

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...

The Haldane model with Kekulè distortion possesses various phases characterized by different topology with specific boundary states. Competition between the 1st/2nd order topology (1D/0D boundary stat...

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...