Transport of interacting particles through a flat Bloch band: superconductivity and all-optical switching

In lattice models, destructive interference can lead to formation of localized states, which results in Bloch bands with a constant dispersion, called flat bands. Flat-band systems give a promising platform for high-temperature superconductivity. They also allow potential applications for signal control in electronics and photonics. In this dissertation, we study transport features of interacting fermions and bosons through systems possessing compactly localized flat-band states. We propose and investigate a two-terminal transport setup for studying these states in the context of flat-band superconductivity. Also, we propose a switching concept for photons based on localized states and their sensitivity to interactions. The dissertation consists of an introductory part and three publications, referred to as I, II, and III. The introductory part discusses the essential theoretical background, giving a brief review of the main results, their implications and outlook. The topics covered include a general introduction to flat Bloch bands, superconductive transport, and non-equilibrium Green's functions, with applications to two-terminal transport. In Publication I, we consider a two-terminal setup for studying localized flat-band states with interaction. Focusing on equilibrium transport via the Josephson effect, we show that connecting superconducting leads to the system allows a supercurrent to flow through flat-band states with on-site Fermi-Hubbard interaction. The critical current and critical temperature are found to be linear in interaction strength, a salient feature of the flat bands. We also consider a potential realization of the system in ultracold gases. In Publication II, we consider non-equilibrium superconductive transport through flat-band states with on-site Fermi-Hubbard interaction in the setup proposed in Publication I. The interactions are considered with a mean-field approximation. We solve the stationary state transport by the method of non-equilibrium Green's functions, showing that normal single-particle transport and transport via Andreev reflection and multiple Andreev reflection, involving quasiparticles, are quenched at the flat band. On the other hand, the AC Josephson effect of Cooper pairs is allowed. Hence, we find that pair transport through flat-band states is allowed while single quasiparticles remain localized. In Publication III, we propose an all-optical switching concept based on localized states. We demonstrate the concept with simple systems that have on-site Hubbard interaction. We show that the system allows switching a single photon by a single-photon control pulse, which is the fundamental quantum limit of minimal switching energy. Furthermore, the switching is allowed for arbitrarily small interaction. We also discuss experimental platforms for realizing the switch.