We are theoretically studying properties of electrons in solids. Below are the main research subjects.
We are theoretically studying superconductivity, magnetism, charge ordering, or thermoelectric effects in strongly correlated electron systems, such as oxides, pnictides, and organic conductors. In these systems, correlation effects induced by Coulomb repulsion between electrons give rise to various interesting phenomena. The study on the electron correlation effects has a long history, but the discovery of high temperature superconductivity in the cuprates has led to an explosive amount of studies all over the world. More recently, the discovery of high temperature superconductivity in the iron pnictide superconductors has brought up an renewed avenue for the study on electron correlation effects in multi-orbital systems. We are studying these effects using numerical and analytical theoretical methods.
It is in general difficult to treat a many-body problem theoretically, so one often constructs a model Hamiltonian that is simple enough, but still contains the essential physics. For example, for the high Tc cuprate superconductors, the Hubbard model is often studied as a basic Hamiltonian that captures the essential physics. In the Hubbard model, each site corresponds to the Cu atoms, and the electrons can hop from site to site. Each site can be occupied by a maximum of two electrons with different spins, and a double occupancy of a site costs an on-site energy U. Even such a simplified model cannot be solved exactly (except for a one-dimensional system), and one has to use various approximation methods and/or numerical calculation techniques for finite size clusters.
Even when electron correlation plays an important role, the kinetic energy part of the Hamiltonian also plays an important role. In quantum mechanics, the electrons behave as waves, which are characterized by the wave number and the frequency. The dispersion relation between the wave number and the frequency (proportional to the energy) gives the band structure, which is determined by the lattice structure and the elements constructing the material. In order to understand the properties of the materials theoretically, one has to construct models that have the correct band structure. For example, in the iron pnictide superconductors, the five Fe 3d orbitals give rise to heavily entangled bands around the Fermi level, and it is important to take into account this band structure correctly in order to understand the electronic properties of the material.
The aim of our study is to understand the origin of the experimentally observed phenomena theoretically from a microscopic viewpoint, based on a many-body model Hamiltonian. Moreover, we intend to go further, and predict new phenomena or materials in advance of the experiments.
Anderson localisation is the suppression of diffusion by interference in a disordered system. The idea was first proposed by Philip Anderson in 1958 when he was trying to explain experiments on spin resonance in doped semiconductors. Initial research focused on the localisation of electrons in disordered solids but it has since been realised that Anderson localisation can occur for all types of waves including sound, light and even matter waves in ultra-cold atomic gases.
At the beginning of the 1980s it was realised that the transition between the diffusive and localised phase as a result of increasing disorder was in fact a continuous quantum phase transition. This was a major breakthrough that allowed the ideas developed to understand continuous thermal phase transitions, in particular the renormalization group and the related ideas of scaling theory, to be applied to the Anderson transition. Subsequently it was realised that the distribution of wave intensities at the Anderson transition is multifractal, which is a unique and beautiful aspect of the Anderson transition. Anderson localisation also plays an essential role in the quantum Hall effect and the transition between quantum Hall plateaux is a type of Anderson transition.
Anderson localisation and the Anderson transition are very difficult problems to tackle analytically and a completely satisfactory comprehensive analytic theory is still lacking. My own work, in collaboration with colleagues in Japan, the UK, and Germany, is focused on filling this gap by performing high precision numerical simulations. In particular, clarifying qualitative issues related to symmetry, dimensionality etc. and quantitative investigation of critical phenomena and multifractality. This is contributing to both the qualitative and quantitative understanding of Anderson localisation.
