Bell-inequality checks constitute a probe of entanglement—given a source of entangled particles, their violation is a signature of the nonlocal nature of quantum mechanics. Here, we study a solid-state device producing pairs of entangled electrons, a superconductor emitting Cooper pairs properly split into the two arms of a normal-metallic fork with the help of appropriate filters. We formulate Bell-type inequalities in terms of current-current cross correlators, the natural quantities measured in mesoscopic physics; their violation provides evidence that this device indeed is a source of entangled electrons.

We investigate the feasibility of manipulating individual spin in a superconducting junction where Bogoliubov quasiparticles can be trapped in discrete Andreev levels. We call this system an Andreev quantum dot (AQD) to be contrasted with a common semiconductor quantum dot. We show that the AQD can be brought into a spin-$1/2$ state. The coupling between the spin and superconducting current facilitates manipulation and measurement of this state. We demonstrate that one can operate two inductively coupled AQDs as a XOR gate; this enables quantum computing applications.

The critical temperature $T_c$ of a superconductor/ferromagnet (SF) bilayer can exhibit nonmonotonic dependence on the thickness $d_f$ of the F layer. SF systems have been studied for a long time; according to the experimental situation, a “dirty” limit is often considered which implies that the mean free path in the layers is the second smallest spatial scale after the Fermi wavelength. However, all calculations reported for the dirty limit were done with some additional assumptions, which can be violated in actual experiments. Therefore, we develop a general method (to be exact, two independent methods) for investigating $T_c$ as a function of the bilayer parameters in the dirty case. Comparing our theory with experiment, we obtain good agreement. In the general case, we observe three characteristic types of $T_c{(d}_f)$ behavior: (1) a nonmonotonic decay of $T_c$ to a finite value exhibiting a minimum at particular $d_f;$ (2) a reentrant behavior, characterized by a vanishing of $T_c$ in a certain interval of $d_f$ and finite values otherwise; and (3) a monotonic decay of $T_c$ and a vanishing at finite $d_f.$ Qualitatively, the nonmonotonic behavior of $T_c{(d}_f)$ is explained by the interference of quasiparticles in the F layer, which can be either constructive or destructive depending on the value of $d_f.$

We discuss fluctuations near the second-order phase transition where the free energy has an additional non-Hermitian term. The spectrum of the fluctuations changes when the odd-parity potential amplitude exceeds the critical value corresponding to the $\mathcal{P}\mathcal{T}$-symmetry breakdown in the topological structure of the Hilbert space of the effective non-Hermitian Hamiltonian. We calculate the fluctuation contribution to the differential resistance of a superconducting weak link and find the manifestation of the $\mathcal{P}\mathcal{T}$-symmetry breaking in its temperature evolution. We successfully validate our theory by carrying out measurements of far from equilibrium transport in mesoscale-patterned superconducting wires.

Superconductor-ferromagnet-superconductor (SFS) Josephson junctions are known to exhibit a transition between π and 0 states. In this letter, we find the π-0 phase diagram of an SFS junction...

We investigate glassy dynamical properties of one-component three-dimensional system of particles interacting via pair repulsive potential by the molecular dynamic simulation in the wide region of densities. The glass state is superfragile and it has high glass-forming ability. The glass transition temperature $T_g$ has a pronounced minimum at densities where the frustration is maximal.