### Article

## Quantum phase slip noise

Quantum phase slips (QPSs) generate voltage fluctuations in superconducting nanowires. Employing the Keldysh technique and making use of the phase-charge duality arguments, we develop a theory of QPS-induced voltage noise in such nanowires. We demonstrate that quantum tunneling of the magnetic flux quanta across the wire yields quantum shot noise which obeys Poisson statistics and is characterized by a power-law dependence of its spectrum SΩ on the external bias. In long wires, SΩdecreases with increasing frequency Ω and vanishes beyond a threshold value of Ω at T→0. The quantum coherent nature of QPS noise yields nonmonotonous dependence of SΩ on T at small Ω.

Quantum phase slips (QPS) may produce non-equilibrium voltage fluctuations in current-biased superconducting nanowires. Making use of the Keldysh technique and employing the phase-charge duality arguments we investigate such fluctuations within the four-point measurement scheme and demonstrate that shot noise of the voltage detected in such nanowires may essentially depend on the particular measurement setup. In long wires, the shot noise power decreases with increasing frequency Ω and vanishes beyond a threshold value of Ω at *T*→0.

With rapid development of nanotechnology it became realistic to fabricate artificial nanostructures with dimensions in sub-50 nm scales. The physics of quasi-one-dimensional superconductors of corresponding dimensions is rather interesting [1]. The particular manifestation of size-dependent quantum fluctuations of superconducting order parameter - the quantum phase slip (QPS) – appeared capable to suppress such ‘text-book’ properties of superconductivity as zero resistivity [2] and persistent currents [3].

Here we demonstrate that one can build a superconducting analogue of a single-electron transistor (Cooper pair transistor) without any tunnel junctions. Instead a pair of thin superconducting wires in QPS regime - the quantum phase slip junctions (QPSJ) - can be used (Fig. 1). At sufficiently low temperatures, well below the critical temperature of the superconductor, the clear Coulomb blockade develops at the I-V characteristic of such a system [4,5]. Application of static gate potential efficiently modulates the amplitude of the Coulomb gap. The same device can be considered as the potential candidate for building a quantum standard of electric current [6].

The topic of superconductivity in strongly disordered materials has attractedsignificant attention. These materials appear to be rather promising for fabrication of various nanoscale devices such as bolometers and transition edge sensors of electromagnetic radiation. The vividly debated subject of intrinsic spatial inhomogeneity responsible for thenon-Bardeen–Cooper–Schrieffer relation between the superconducting gap and the pairing potential is crucial both for understanding the fundamental issues of superconductivity in highly disordered superconductors, and for theoperation of corresponding nanoelectronic devices. Here we report an experimental study of theelectron transport properties of narrow NbN nanowires with effective cross sections of the order of the debated inhomogeneity scales. The temperature dependence of the critical current follows the textbook Ginzburg–Landau prediction for thequasi-one-dimensional superconducting channel Ic∼(1-T/Tc)3/2. We find that conventional models based on the thephase slip mechanism provide reasonable fits for the shape of R(T) transitions. Better agreement with R(T) data can be achieved assuming theexistence of short ‘weak links’ with slightly reduced local critical temperature Tc. Hence, one may conclude that an ‘exotic’ intrinsic electronic inhomogeneity either does not exist in our structures, or, if it doesexist, itdoes not affect their resistive state properties, or does not provide any specific impact distinguishablefrom conventional weak links.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.