Research

Topology is one of the key concepts in modern condensed matter physics. It was believed that ``topology is robust against perturbation” and is something that is fixed when a material is synthesized. Actually, there is a way to cheat this. In 2009, we found the first example of the so-called Floquet topological insulator. We showed that the Berry curvature, Chern number, and the chiral edge state in almost ANY two dimensional multi-band systems can be controlled or induced by external time periodic fields such as laser. The key idea is that electrons become photo-dressed. They are described by Floquet states, a temporal analogue of Bloch states, and the topology of the quasi-energy bands can be changed as a function of the laser intensity, polarization and frequency. This idea is not limited to an electron-laser system, but can be universally applied to various physical systems, such as electron-coherent phonon, photon-optical wave guide, cold atom-optical lattice etc. In solid state physics, the concept of Floquet states already existed from the 70’s, but our works is pushing it to the frontline by attracting researchers from various backgrounds such as topological insulators , laser physics, nonequilibrium statistical mechanics, helping the field to accelerate its progress. 

We have developed a numerical method to calculate the quantum dynamics of unconventional superconductors (high Tc cuprates and possibly iron pnictides) by combining the quantum kinetic equation with the nonequilibrium FLEX method. This method is complementary to the nonequilibrium dynamical mean field theory (Aoki, Oka, et al. RMP’14) and is able to treat nonlocal correlation such as the paramagnetic fluctuation considered responsible as the pairing glue (at least in the over doped region). This method still needs refinement. After completing this method, we will apply it to study nonlinear device application and ultrafast phenomena in unconventional superconductors.

With Shintaro Takayoshi and Masahiro Sato, we initiated a collaboration to study ultrafast dynamics in quantum magnets. While many of the well studied dynamical processes in magnets such as domain wall motion and skyrmion dynamics can be described within the semiclassical framework (LLG equation), if we want to study ultrafast dynamics (= picosecond time scale), it becomes important to start from a microscopic and quantum mechanical theory. We tried applying tricks such as the Floquet theory that we learned from our study of electron systems to models of quantum spins. One idea which may be experimentaly relevant is the laser induced magnetization curve . In a more recent ariticle, we have shown that it is possible to generate spin current in multiferrioc materials using laser. 

In high energy physics, there is a branch called nonlinear quantum field theory (or strong field physics), where nonlinear processes and the breakdown of the quantum vacuum in strong electro-magnetic fields are being studied.  This area is an old one that partially started from the study by Heisenberg and Euler in 1936, who predicted nonlinear optical responce of the vacuum. In stronger fields, the QED vacuum becomes unstable against production of electron-positron pairs via quantum tunneling, and Schwinger obtained the one-loop expression of the vacuum decay rate.  These processes are one of the main targets in recent pan-European laser projects such as XFEL and ELI. In addition, applications of nonlinear QFT can be found in quark-gluon plasma formation in heavy ion collision experiments as well as in magnetars (neutron star with strong magnetic fields). 

Nonequilibrium quantum phenomenon is an interesting subject that attracts researchers with diverse background. I was lucky enough to start collaboration with string theorists K. Hashimoto and A. Sonoda and gravity theory specialists S. Kinoshita and K. Murata. Our project is based on the usage of the gauge gravity duality that relates quantum field theories to gravitational systems in a higher dimensional space. 

Developing reliable methods to treat nonequilibrium many-body physics is important. I have a simple strategy in doing this: “Pick the most reliable method in equilibrium and extend it to nonequilibrium”. The following is a list of methods that we have developed (thanks to my collaborators). 

1. Bethe ansatz + Landau-Dykhne method: This is a powerful method that enabled me to study the Schwinger effect in the 1D Hubbard model. 
2. Nonequilibrium continuous time QMC: A method developed with P. Werner and A. Millis.
3. Nonequilibrium dynamical mean field theory for the Hubbard model (Aoki et al. RMP 2014): This was mainly developed by P. Werner, M. Eckstein and N. Tsuji. My contribution is limited.
4. Nonequilibrium fluctuation exchange approximation (noneq. FLEX): I tried to develop a method to study unconventional superconductors including Hi Tc cuprates and possibly iron pnictides far from equilibrium. 
5. Floquet TKNN (Kubo) formula: I have extended the linear response theory to Floquet states using the two-time method. Using this formula, I predicted the laser-induced quantum Hall effect (Floquet topological insulator).
6. Floquet DMFT: N. Tsuji combined the DMFT method with the Floquet theory. This is useful in studying laser-induced Mott insulator-to-metal transitions.
7. Floquet + bozonization/fermionization: Nice analytical method to study periodically driven 1D quantum field theories.
8. Heisenberg-Euler effective Lagrangian in gauge/gravity duality: We extended the GKP-Witten dictionary to unstable vacua. We used this method to calculate the decay rate of the hadronic vacuum in SUSY QCD against strong electromagnetic fields.