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We analyze the origin of the parabolic background of magnetoresistance oscillations measured in finite-width superconducting mesoscopic rings with input and output stubs and in patterned films. The transmission model explaining the sinusoidal oscillation of magnetoresistance is extended to address the parabolic background as a function of the magnetic field. Apart from the interference mechanism activated by the ring, pinned superconducting vortices as topological defects introduce a further interference-based distribution of supercurrents that affects, in turn, the voltmeter-sensed quasiparticles. The onset of vortices changes the topology of the superconducting state in a mesoscopic ring in a such a way that the full magnetoresistance dynamics can be interpreted owing to the interference of the constituents of the order parameter induced by both the ring with its doubly-connected topology and the vortex lattice in it., Comment: 15 pages, 6 figures

The Ginzburg-Landau theory is used to model the order parameter of a finite-size mesoscopic ring to investigate the effects of the onset of screening currents on the transport of incoming ones. The magnetic flux breaks the symmetry of currents between input and output stubs by means of an induced spatial ordering upon diamagnetic and paramagnetic supercurrents circulating in the ring. The distribution of those screening currents drives the interference of incoming/outgoing supercurrents resulting into a sinusoidal variation of resistance as a function of the magnetic flux even if the density of quasiparticles is not modified by the external magnetic field.

Thermal transport in the Si/SiO$_2$ multishell nanotubes is investigated theoretically. The phonon energy spectra are obtained using the atomistic Lattice Dynamics approach. Thermal conductivity is calculated using the Boltzmann transport equation within the relaxation time approximation. Redistribution of the vibrational spectra in multishell nanotubes leads to a decrease of the phonon group velocity and the thermal conductivity as compared to homogeneous Si nanowires. Phonon scattering on the Si/SiO$_2$ interfaces is another key factor of strong reduction of the thermal conductivity in these structures (down to 0.2 W/mK at room temperature). We demonstrate that phonon thermal transport in Si/SiO$_2$ nanotubes can be efficiently suppressed by a proper choice of nanotube's geometrical parameters: lateral cross-section, thickness and number of shells., Comment: 14 pages, 4 figures

Under a strong transport current, the induced voltage in superconductor nanomembranes in a magnetic field with submicron inhomogeneity shows a pulse on a certain interval of the magnetic field. It is a manifestation of a wide phase-slip domain. The topological transition accompanying the phase-slip effect consists in the occurrence of two new loops of weak superconducting currents connecting two regions of superconducting screening currents, which are disconnected in case of vortex-chain dynamics. In the middle of the phase-slip domain, rapid dynamics of the superconducting order parameter consists in decoupling of a spontaneously nucleated vortex-antivortex pair, subsequent motion of a vortex and an antivortex in the opposite directions followed by their annihilation with an antivortex and a vortex from the adjacent pairs. The submicron-scale inhomogeneity of the magnetic field can be achieved through a direct patterning of the magnetic field applied to a planar membrane or using advanced nanostructuring, such as roll-up technology, focused ion-beam deposition or coating carbon nanotubes by superconducting materials. If the applied magnetic field is orthogonal to the axis of a microtube, which carries transport current in the azimuthal direction, the phase-slip regime is characterized by the vortex-antivortex lifetime of 10E-15 s versus 10E-12 s for disconnected vortex dynamics in the half-tubes. The phase-slip dynamics determines the voltage-magnetic field and voltage-current characteristics in nanoarchitectures with multiple disconnected loops of superconducting screening currents.

An inhomogeneous transport current, which is introduced through multiple electrodes in an open Nb microtube, is shown to lead to a controllable branching of the vortex nucleation period. The detailed mechanism of this branching is analyzed using the time-dependent Ginzburg-Landau equation. The relative change of the vortex nucleation period strongly depends on the geometry of multiple electrodes. The average number of vortices occurring in the tube in a nanosecond can be effectively reduced owing to the inhomogeneous transport current, what is important for noise and energy dissipation reduction in superconductor applications, e.g., for an extension of the operation regime of superconductor-based sensors to lower frequencies., Comment: 8 pages, 4 figures

In-plane polarized light experiences a non-trivial topological evolution as it propagates resonantly in a M\"obius ring resonator. The resultant geometric phase varies continuously when changing the light ellipticity, which leads to constructive interference for a non-integer number of wavelengths, and therefore to the occurrence of an arbitrary fractional number of optical modes. The geometric phase in M\"obius-ring resonators is topologically robust and implies excellent intrinsic fault-tolerance., Comment: This paper has been withdrawn by the authors due to a missing of a unified opinion