## Research

There are many quantum phenomena that arise in solids owing to diverse electronic behavior. In our group, we aim to push the boundaries of condensed matter physics by investigating many body electron/atom systems theoretically. As electrons obey fermionic statistics, they exhibit different properties in matter, like metals, semiconductors, and insulators. Other properties also happen due to spontaneous symmetry breaking, like magnetism and superconductivity. Adding to these conventional condensed matter physics research, nowadays topological quantum physics is also expanding as a new field.

Topology is a mathematical branch that classifies shapes according to continuous deformations. With it, an integer called topological invariant can be defined. We can then identify topologically non-trivial substances by applying this method to the hamiltonian and wavefunctions. For example, recently a new kind of material called topological insulators has been discovered, which behaves as a metal only on the surface and as an insulator in the bulk, and this field has seen rapid expansion since. Other states of matter close to topological insulators include anomalous Hall effect, topological crystalline insulators, Weyl semimetals, and others that are also topologically non-trivial. Such systems attract interest as new materials for spintronics.

Other systems attracting attention with topological non-trivial edge states are superconductors (topological superconductors). For them, uncommon quasi-particles that do not allow distinction between creation and annihilation, called Majorana fermions, appear as edge states. The non-local correlation effect that these Majorana fermions have is believed to be useful for future quantum computation. Topological quantum physics has been researched in many systems, like topological insulators, superconductors, superfluid 3He, and cold atoms, leading to the prediction of particles that would display a new kind of statistics, neither fermionic nor bosonic.

We perform research on a broad range within topological quantum phenomena (from electrons in solids to atomic systems in cold atoms), aiming to develop research with internationally recognized excellence to expand the frontiers of quantum physics. Not being restricted to our group, we also collaborate with other mainstream groups inside and outside Japan, actively promoting joint research projects. We welcome motivated students interested in joining active frontline research in collaboration with our staff and graduate students.

## Present main themes

・Topological superconductivity

・Superconducting junctions

・New symmetries in superconductors

・Topological insulators, topological crystalline insulators

・Topological quantum phenomena in bosonic systems

・Weyl semimetals, Dirac semimetals

・Atomic monolayer materials

・Axial current, skyrmions, and other new spintronics

## Research objective

There are uncountable electrons in solids, but they can be classified from the point of view of their symmetry. Magnetism and superconductivity are phenomena understood as systems with spontaneously broken symmetry. For further classification of superconductivity, notions of spin, space parity, and time become necessary. In superconducting nanostructures or in junctions with ferromagnets, broken symmetries play an important role, inducing the creation of exotic states with odd frequency electron pairing.

On the other hand, the single value of the phase held by electronic wavefunction generates quantum phenomena characterized by topological aspects. Up to now, we have known the quantization of vortices in superconductors and superfluids, Aharonov-Bohm effect, quantum Hall effect and fractional quantum Hall effect. Quantum spin Hall systems and topological insulators are similar to quantum Hall systems, with non-trivial insulating state appearing in the bulk, leading to a necessary metal state on the edges due to the transition from a non-trivial to a trivial medium.

Recently, it has been found that a similar edge state arises on the boundary surface of some superconductors. The research of these topologically non-trivial systems is not only of academic interest, but also bear important future prospects regarding the control of dissipationless electron and spin currents.

Our objective is to build up a new research field by looking at topological quantum phenomena with broken symmetries from varied angles. We perform our research on novel quantum effects and properties theoretically, clarifying new symmetries and topological quantum phenomena.

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