Our condensed matter research is based on numerical simulation. This group consists of 9 members; one associate professor, two assistant professors, one ISSP research fellow, one postdocs, three students, and one office administrator.

Main targets are (1) material research using the numerical simulation and (2) development of the simulation scheme.

**Material Simulation**

Diversity in materials is indeed diverse. We know only very small piece of the whole picture. As a powerful means to supplement the piece, material simulations are attracting attention. The role of the simulation is extending because computers are rapidly increasing the power enabling thereby extending the frontier of research.

Electronic excited state initiated by photoabsorotion (leftmost), and the wave function for the hole (middle) and electron (rightmost).

#### Electronic structure from the many-body perturbation theory (*GW* + Bethe-Salpeter equation method)

One of the most important frontiers is in the excited state study. The study is boosted by the development of many-body Green’s function methods to obtain the excitation energy and the wave function of the excited electrons and holes. With these quantities, it is possible to study the dynamics initiated by an electron excitation.

The excited state dynamics has traditionally been studied by using a model empirically determined from experimental data, but the model cannot be improved when the experimental data is scarce. Detailed structural data alone may not be necessarily sufficient; information of electronic structures may be additionally required.

The excited states can be simulated using the time-dependent (TD) density functional theory (DFT). The accuracy of TDDFT depends critically on the modelling of the electron-electron interaction, or the exchange-correlation potential, and the accuracy is generally insufficient when studying excitations accompanying a charge transfer. The Green’s function can reliably describe the charge-transfer excitation although the associated computational time is much longer.

The excited states have been studied in chemistry using wave function theories. The computational time increases very rapidly (mostly exponentially) as the number of electrons is increased, but the size-dependence is milder for the Green’s function method (typically ).

The electron and hole does not independently propagate, but these quasiparticles are interacting in the excited states. The propagation can be described by the many-body Green’s function method. The equation of motion for Green’s function has a form similar to the Bethe-Salpeter equation (BSE) frequently used in high-energy physics, so that the same name is used in condensed matter. BSE is solved after reformulated into an eigenvalue problem. BSE is most frequently formulated using approximations like *GW* approximation, so that the method is called *GW* + BSE.

We study the excited states using the *GW* + BSE simulation together with experimental data available. It is possible to study a system containing up to two hundred atoms. The study is important in predicting the optical spectrum of materials which may work as a luminescence or photovoltaic material.

#### Structure and dynamics at the interface

Interfaces are ultimately important target of materials science because of the existence of large number of phenomena occurring inherently at interfaces. Density functional theory (DFT) is an invaluable means to explore the interface physics.

Materials interfaced with water, or the solution, have long been studied in physics, chemistry, and biology, but there are many unsolved problems because of the complicated nature of water.

* Water has a large static dielectric constant with which to stabilize charged particles, but the dynamic dielectric constant is much smaller. This makes the dynamics complicated

*Hydrogen atoms behave as a quantum particle while others behave classically.

*The interaction consists of van der Waals to covalent components.

*The atomic structures and the phase diagram are still controversial.

#### Physics of the electrode

Electrodes interfaced with water, or the solution, offers fundamental problems while being important in many application fields like fuel-cells which convert chemical energy into electricity. Owing to the development in treating the dielectric response of the solution, this electrochemical interface has become the target of computational study. Our group is trying to deepen understanding of how and why the fuel-cells reaction occurs at the platinum interface and the knowledge is used to reliably predict how other interface can be modified for a more functional electrode.

#### Firefly luciferin

Biomaterials are functional when interfaced with solution. So, the interface is a key to understanding the biofunction. Among many biomaterials, we are currently targeting oxyluciferin molecule which plays a role as the luminescence center of fireflies. There are controversies about the stability of oxyluciferins in solution presumably due to lack of microscopic understanding of the interface. With this in mind we have performed a very time-consuming simulation to find that the previous understanding is too approximate. The water molecules are interfaced complicatedly with oxyluciferin according to the complicated charge distribution within the molecule. Contrary to the previous picture, behavior of water molecules is thus directly concerned with the stability in solution. The next step of this project is then to understand the mechanism of the luminescence.

**Negative capacitance**

Solid can be made functional when interfaced with other solid. Ferroelectric materials have a positive capacitance, but this is not the case when the material is transiently changing the polarization. The negative capacitance thereby appearing is unstable and cannot be measured in the bulk as the Landau theory explains, but can be made metastable at an interface. The possibility is investigated at a ferroelectric thin film interfaced with a paraelectric thin film to find that the structure of the negative capacitance can indeed survive against the driving force to form a domain structure, which make the capacitance positive. Negative capacitance has been attracting attention as a means to enhancing the total capacitance of an electronic device.

**Other topics**

We are also investigating materials in collaboration with experimental researchers, such as phase transition of an O2 solid induced by magnetic field and a new topological insulator.

## Development of computational method

To advance the computational materials science, one need to develop novel computational method and intentionally extend the frontier of the simulation; the frontier is always changing when computers speedup. We need to extend the method for (a) solving the many-body Schrodinger equation to obtain the electronic ground and excited states, (b) obtaining the most stable structures, (c) calculating the response to external perturbations, (d) obtaining the thermodynamic states, and so on. Many works have been done also to develop multi-physics methods to bridge macroscopic phenomena with the micros, which is nontrivial for inhomogeneous materials with or without chemical reactions, such as biomaterials.

Density functional theory (DFT) has been accepted as the standard method for the computational materials science. This theory is based on the Hohenber-Kohn theorem which establishes one-to-one correspondence between (a) the ground state and (b) the particle density together with the functionals to relate (a) and (b) developed by many researchers in the past half century. The theory has not been successfully developed for strongly correlated systems and some of the excited states. Because of this, other computational methods other than DFT are also paid attention.

Success of DFT does not immediately mean that we can apply DFT to large systems because of the large gap existing between micro and macro. DFT provides the ground state of a given atomic geometry, but interesting phenomena often occur in systems where many metastable states with equal energy exist. Then it is not trivial to find the most stable, or a thermodynamically stable, structure.

#### Many body wave function theory — tensor decomposition method —

N electron systems in a material can be characterized by the many-body wave function with 3N degrees of freedom. Determining the wave function in the vast Hilbert space is an ultimate goal.

The wave function is specified by the anti-symmetric tensor of degree N. If the degrees of freedom can be encoded very compactly, there may be a way to handle the wave function. As a way of the encoding, there is a technique called tensor decomposition, with which to decompose the original tensor into a product of tensors of lower degrees. This group is developing an algorithm for this purpose.

#### Many-body perturbation method

The electronic structure can be described by the Green’s function for the many-body Schrodinger equation. The Green’s function can be used to describe not only the ground state but also the excited states, which are generated by shining a light. The Green’s function is obtained by solving the Bethe-Salpeter equation for the excited electrons and holes. In practice the equation is reformulated into an eigen problem using some approximations to the Feynman diagrams such as the one called GW. This group develops algorithms for the GW + BSE calculation and also an inhouse code.

#### Interface

When a material is interfaced with another material of large permittivity, such as ferroelectric materials and liquid water, charged particles can be stabilized at the interface because of the dielectrically reduced Coulomb energy. The interface thus provides a field for the exchange of charge (and also exchange of energy), which is applied to various batteries and bio-membranes. When the Coulombic field extends deep inside the materials, the microscopic details occurring at the interface are coupled to the bulk, yielding thereby many interesting phenomena. This is one of the targets of interface science.

In a practical DFT simulation, it is not trivial to describe the long-range Coulombic field. The interfaces thus require methodological development to initiate the study. Actually, many researchers are enjoying the development. Our group is developing a methodology for (a) platinum-solution interface with which to construct a microscopic theory for fuel cells and for (b) the solid-solid interface to deepen understanding on, for example, the space charge layer.

## Education

Sugino group participates in the physics department of the graduate school of the University of Tokyo. http://www.issp.u-tokyo.ac.jp/maincontents/education_en.html

Please visit Department of Physics for details.