One of my main research interests is in electron-correlation problems in solids. Strong electron-correlation effects, originating from a strong Coulomb interaction between electrons, are intractable with a standard theory of solids but are considered to be responsible for various interesting phenomena, such as magnetism, the Mott metal-insulator transition, and high-temperature superconductivity. The understanding as well as the quantitative description of the electron-correlation effects is not only a challenge in fundamental physics but holds a potential for future technological applications.

During the last few decades, the dynamical mean-field theory (DMFT) has turned out to be a useful tool to address these problems. Among its achievements, the DMFT succeeded in describing the Mott metal-insulator transition in infinite dimensions, reasonably reproduced the Curie temperature in iron and nickel, and, through its cluster extension, reproduced a phase diagram similar to that of copper-oxide high-temperature superconductors. Development of a more realistic calculation scheme in conjunction with density functional theory (DFT) is also underway in the field.

Another topic of my recent research is quasicrystals, which are solids consisting of aperiodically ordered atoms. The aperiodic order of quasicrystals leads to nontrivial consequences on the electrons moving in them, resulting in electron states and properties distinct from those of conventional (periodic) crystals and amorphous. Many fundamental problems remain unexplored in this field.

In this circumstance I have focused my efforts on the following issues (numbers in [ ] refer to Publication list):

• Effect of Hund's coupling in multiorbital systems
  While Hund's coupling is known to play important roles in highly localized electron systems, its role in itinerant electron systems has been less explored. We have developed efficient algorithms to deal with Hund's coupling in the quantum Monte Carlo methods, with proposing the Hubbard-Stratonovich-type transformation [1], perturbation-series expansion algorithm [3,4], and double-vertex update algorithm [17]. With these methods, we found a Hund-induced superconductivity of an s-wave spin-triplet orbital-antisymmetric pairing [1,2] and itinerant ferromagnetism relevant to that in elementary transition metals like iron and nickel [5,Thesis], and revealed nonlocal correlation effects of Hund's coupling [18].


• Mott metal-insulator transition and pseudogap state in the two-dimensional Hubbard model
  The two-dimensional Hubbard model is considered to be a minimal model of high-Tc superconducting cuprates. There exist two different singularities in its electronic structure; a pole of the single-electron Green's function and a pole of the self-energy. The former pole defines the Fermi surface (characterizing a metallic property) while the latter pole generates a correlation-induced gap like the Mott gap (charactering an insulating property). We clarified the evolution of these pole singularities with carrier doping from the undoped Mott insulator (with only the latter pole) to an overdoped Fermi-liquid metal (with only the former pole) [6,7,9,16,33,Slides]. Between them, there is an anomalous metallic state with these two poles coexisting in momentum space. We found that this anomalous metallic state has an unusual "s-wave" pseudogap, in which the gap shifts to the unoccupied side in the nodal region. The structure well explains the experiments of electronic Raman responses on top of other spectroscopic experiments, suggesting the importance of measuring momentum-resolved unoccupied spectra in cuprates [9,10,13,14,Slides,Review].


• Real-frequency structure of the self-energy and superconducting gap function in unconventional superconductors
  It was a study on the frequency dependence of the superconducting gap function that established the phonon-mediated mechanism of conventional superconductors. Then, the frequency dependence may hold a key to the high-Tc superconducting mechanism in cuprates as well. By scrutinizing this property in the two-dimensional Hubbard model, we found a hidden fermionic excitation at the origin of both the pseudogap and high-Tc superconductivity [22,26,30,35]. We also revealed a direct microscopic relationship between the Mott insulator and high-Tc superconductor in their self-energy structure. These results led us to a unified view of the Mott insulator, high-Tc superconductor, and pseudogap metal in terms of the self-energy pole [36,Slides,Review].


• Schemes bridging first-principles and many-body-model calculations and its application to real materials
  We proposed a first-principles way to calculate the onsite interactions to be used in the DMFT [12]. We have also applied the DFT+DMFT method to various materials such as an iron pnictide [8], alkali-doped fullerides [19,23,28], Sr₂RuO₄ [27], CaIrO₃ [38,42], and pyrochlore iridates [40] and ruthenates [46].


• Extension of DMFT to more realistic situations, such as multioribital [1,3,4,17], cluster [11,24], and dynamical interaction.


• Superconductivity in quasicrystals
  Quasicrystal is a solid comprised of aperiodically but regularly arranged atoms. Because of the lack of the periodicity, there is no well-defined momentum space (w.r.t. the relative coordinate) and hence no Fermi surface, either. Because our standard understanding of superconductivity (i.e., BCS theory) is based on the pairing of electrons on the Fermi surface, the first question is whether superconductivity can occur in quasicrystals or not. With numerical simulations, we showed that superconductivity indeed occurs, which shows interesting inhomogeneity reflecting the self-similarity of the underlying quasicrystalline lattice [29,37]. Our subsequent studies have revealed interesting properties of this type of superconductor [41,44]. We expect further novel physics will emerge when the fractal and superconductivity meet! [Slides]
  



• Hyperuniform electron states
  Hyperuniformity is a framework to classify point distributions in a space and quantify the regularity of such distributions. Using a generalization of the hyperuniformity to a scalar field, we could quantify the regularity of the charge distributions on the Penrose [50] and Ammann-Beenker tilings [55], as well as in one-dimensional Aubry-Andre-Harper (AAH) and Fibonacci models [49,52]. In particular, in the AAH model, we found that a phase transition occurs between two inhomogeneous charge distributions, where the hyperuniformity class changes [52]. Notice that the translational symmetry, which is associated with a charge-ordering transition in periodic systems, is absent from the first place in the quasiperiodic system. Such a change of the spatial pattern may be utilized to tune the properties of quasicrystals, and the hyperuniformity may play a key role in characterizing it.
  


Coordinates of Penrose tiling