Recently, it has been shown that multiterminal superconducting nanostructures may possess topological properties that involve Berry curvatures in the parametric space of the superconducting phases of the terminals, and associated Chern numbers that are manifested in quantized transconductances of the nanostructure. In this paper, we investigate how the continuous spectrum that is intrinsically present in superconductors, affects these properties. We model the nanostructure within scattering formalism deriving the action and the response function that permits a redefinition of Berry curvature for continuous spectrum. We have found that the redefined Berry curvature may have a nontopological phase-independent contribution that adds a nonquantized part to the transconductances. This contribution vanishes for a time-reversible scattering matrix. We have found compact expressions for the redefined Berry curvature for the cases of weak energy dependence of the scattering matrix and investigated the vicinity of Weyl singularities in the spectrum.@en

The technology of superconductor-semiconductor nanowire devices has matured in recent years. This makes it feasible to make more complex and sophisticated devices. We investigate multiterminal superconductor-semiconductor wires to access the feasibility of another topological phenomenon: Weyl singularities in their spectrum. We have found an abundance of Weyl singularities for devices with an intermediate size of the electrodes. We describe their properties and the ways the singularities emerge and disappear upon variation of the setup parameters.@en

We propose a scheme to perform braiding and all other unitary operations with Majorana modes in one dimension that, in contrast to previous proposals, is solely based on resonant manipulation involving the first excited state extended over the modes. The detection of the population of the excited state also enables initialization and read-out. We provide an elaborated illustration of the scheme with a concrete device.@en

We study the quantum corrections to the conductivity of the two-dimensional disordered interacting electron system in the diffusive regime due to inelastic scattering off rare magnetic impurities. We focus on the case of very different g factors for electrons and magnetic impurities. Within the Born approximation for the inelastic scattering off magnetic impurities we find additional temperature-dependent corrections to the conductivity of the Altshuler-Aronov type. Our results demonstrate that the low-temperature transport in interacting disordered electron systems with rare magnetic impurities is more interesting than it was commonly believed on the basis of treatment of magnetic impurity spins as classical ones.@en

One of the pillars of the scientific method is the fact that... Oh wait, it’s a different one. One of the pillars of the technological development is the fact that if the existing design does not achieve the goal or cannot be applied in new conditions, one could propose a totally different design that may achieve the goal. The only constraints in this way being the laws of physics. This is the main message of the lecture by Richard Feynman on tiny machines. The role of different designs can also be noted on a purely theoretical level. There, changing the well-known model can have far reaching consequences on its properties and possible applications. One of the main goals in the focus of modern quantum technology is realization of a quantum computer. The appeal of this device is in the difference from the classical analogous computer, being reasonable proposals for error correction. Another aspect is that one may use topological quantum states that are robust by themselves against certain noises. There is a lot of effort in trying different approaches and designs to experimentally realize and detect these states. Two main approaches are to either realize topological compounds or combine topologically trivial compounds to effectively realize non-trivial topological properties. There have been advances in both topological and non-topological quantum computation. One of the most famous examples being the achieved quantum supremacy (or, after censorship, quantum advantage). Despite that, the technology is still far away from being used at home. Also, during the process of development of technology other things may come about on the way. Anyhow, regardless of the outcome, the way itself is always more important than the resulting point. In this thesis we discuss certain theoretical findings discovered on the way.@en