We report on a novel mechanism of BCS-like superconductivity, mediated by a pair of Bogoliubov quasiparticles (bogolons). It takes place in hybrid systems consisting of a two-dimensional electron gas in a transition metal dichalcogenide monolayer in the vicinity of a Bose–Einstein condensate. Taking a system of two-dimensional indirect excitons as a testing ground of Bose-Einstein condensate we show, that the bogolon-pair-mediated electron pairing mechanism is stronger than phonon-mediated and single bogolon-mediated ones. We develop a microscopic theory of bogolon-pair-mediated superconductivity, based on the Schrieffer–Wolff transformation and the Gor’kov’s equations, study the temperature dependence of the superconducting gap and estimate the critical temperature of superconducting transition for various electron concentrations in the electron gas and the condensate densities.

A single-electron tunneling (SET) device with a nanoscale central island that can move with respect to the bulk source-and drain electrodes allows for a nanoelectromechanical (NEM) coupling between the electrical current through the device and mechanical vibrations of the island. Although an electromechanical "shuttle" instability and the associated phenomenon of single-electron shuttling were predicted more than 15 years ago, both theoretical and experimental studies of NEM-SET structures are still carried out. New functionalities based on quantum coherence, Coulomb correlations and coherent electron-spin dynamics are of particular current interest. In this article we present a short review of recent activities in this area.

We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the possibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analysed in a framework of three-level model. We compute Landau-Zener probabilities for a linear sweep of the gate charge and investigate Rabi oscillations in a periodically driven three-level system under in-and off-resonance conditions. It was shown that the Landau-Zener probabilities reveal two different patterns: "step" and "beats"-like behaviours associated with the quantum interference effects. Control on these two regimes is provided by change of the ratio between two characteristic time scales of the problem. We demonstrate through the analysis of a periodically driven three-level system, that if a direct transition between certain pairs of levels is allowed and fine-tuned to a resonance, the problem is mapped to the two-level Rabi model. If the transition between pair of levels is forbidden, the off-resonance Rabi oscillations involving second order in tunneling processes are predicted. This effect can be observed by measuring a population difference slowly varying in time between the states of the Cooper-pair box characterised by the same parity.

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