Graphene-based Josephson junction is electrically tunable and can achieve a clean ballistic regime, where the mean free path of the graphene weak link exceeds the junction length. Systematic analysis of the critical current reveals theoretically expected critical current scaling in both diffusive and ballistic regimes. In the long diffusive regime, the critical current scales with the Thouless energy. In the ballistic regime, it scales with the superconductor gap when the junction length is smaller than the coherence length (short junction regime), otherwise it scales with the energy proportional to the inverse junction length (long junction regime). We also show that we can spatially split two electrons of a Cooper pair in graphene-superconductor junctions. In particular, supercurrent can flow through a quantum Hall state, where a Cooper pair splits into opposite edge channels through the electron-hole hybrid modes formed in the superconductor-quantum Hall interfaces.

In this article, we explain our theoretical proposals, ultrafast ways of controlling magnetic properties of solid (magnetization, spin chirality, spin currents, etc.) by laser. We first review the Floquet theorem, which is useful for the prediction of novel laser-induced phenomena, then we turn to our recent results. We cover the following topics: laser-induced magnetization growing process, laser-driven spin chirality and spin current in multiferroics, and topological spin liquid state realized by laser in the honeycomb Kitaev model.

The most time-consuming part of the molecular simulation is the calculation of long-range interactions of the particles, and there is a strong demand to calculate the electrostatic interactions with high accuracy and low computational cost. To address this issue, we have developed the Zero-Multipole summation Method (ZMM). The theoretical foundation of the ZMM, based on an electrostatic neutralization principle, and its applications to several physical systems are demonstrated. Relationships between the ZMM and other electrostatic-interaction calculation methods are also discussed.

We discuss the nonequilibrium dynamics in periodically driven quantum systems thermally isolated from the environment. In the high-frequency regime, the truncation method of the Magnus expansion of the Floquet Hamiltonian has been used in literatures, which predicted several intriguing phenomena due to periodic driving, such as the dynamical localization, the superfluid-Mott transition in ultracold atoms in a shaken optical lattice, and achieving some nontrivial topological properties. On the other hand, some numerical analysis on the exact Floquet eigenstates have revealed that a periodically driven system will eventually heat up to the infinite temperature. The state of infinite temperature shows no interesting phenomenon, which apparently contradicts the prediction by the method of truncation of the Magnus expansion. We show that the heating is exponentially slow in frequency of the driving field, which implies that interesting states predicted by the truncation of the Magnus expansion are actually intermediate long-lived quasi-stationary state before reaching the state of infinite temperature.

We report time-domain observation of spin-charge-separation and charge-fractionalization processes in artificial Tomonaga-Luttinger liquids, which are formed using quantum Hall edge channels. The waveform measurements provide full information for time evolution of the actual one-dimensional electron systems.