Vortex dynamics and phase transitions in a two-dimensional array of Josephson junctions

Appearance of chaos and hyperchaos in evolving pendulum network

The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled oscillators. In this paper, we study the emergence of chaos in chains of locally coupled identical pendulums with constant torque. The study of the scenarios of the emergence (disappearance) and properties of chaos is done as a result of changes in (i) the individual properties of elements due to the influence of dissipation in this problem and (ii) the properties of the entire ensemble under consideration, determined by the number of interacting elements and the strength of the connection between them. It is shown that an increase of dissipation in an ensemble with a fixed coupling force and a number of elements can lead to the appearance of chaos as a result of a cascade of period-doubling bifurcations of periodic rotational motions or as a result of invariant tori destruction bifurcations. Chaos and hyperchaos can occur in an ensemble by adding or excluding one or more elements. Moreover, chaos arises hard since in this case, the control parameter is discrete. The influence of the coupling strength on the occurrence of chaos is specific. The appearance of chaos occurs with small and intermediate coupling and is caused by the overlap of the existence of various out-of-phase rotational mode regions. The boundaries of these areas are determined analytically and confirmed in a numerical experiment. Chaotic regimes in the chain do not exist if the coupling strength is strong enough. The dimension of an observed hyperchaotic regime strongly depends on the number of coupled elements.

Development of in situ two-coil mutual inductance technique in a multifunctional scanning tunneling microscope

Superconducting thin films have been a focal point for intensive research efforts since their reduced dimension allows for a wide variety of quantum phenomena. Many of these films, fabricated in UHV chambers, are highly vulnerable to air exposure, making it difficult to measure intrinsic superconducting properties such as zero resistance and perfect diamagnetism with ex situ experimental techniques. Previously, we developed a multifunctional scanning tunneling microscope (MSTM) containing in situ four-point probe (4PP) electrical transport measurement capability in addition to the usual STM capabilities [Ge et al., Rev. Sci. Instrum. 86, 053903 (2015)]. Here we improve this MSTM via development of both transmission and reflection two-coil mutual inductance techniques for in situ measurement of the diamagnetic response of a superconductor. This addition does not alter the original STM and 4PP functions of the MSTM. We demonstrate the performance of the two-coil mutual inductance setup on a 10-nm-thick NbN thin film grown on a Nb-doped SrTiO₃(111) substrate.

Multistability of synchronous regimes in rotator ensembles

We study collective dynamics in rotator ensembles and focus on the multistability of synchronous regimes in a chain of coupled rotators. We provide a detailed analysis of the number of coexisting regimes and estimate in particular, the synchronization boundary for different types of individual frequency distribution. The number of wave-based regimes coexisting for the same parameters and its dependence on the chain length are estimated. We give an analytical estimation for the synchronization frequency of the in-phase regime for a uniform individual frequency distribution.

Dependence of global superconductivity on inter-island coupling in arrays of long SNS junctions

We present measurements of the superconducting transition temperature, Tc, for arrays of mesoscopic Nb islands patterned on Au films, for large island spacings d. We show that Tc ∼ 1/d(2), and explain this dependence in terms of the quasiclassical prediction that the Thouless energy, rather than the superconducting gap, governs the inter-island coupling at large spacings. We also find that the temperature dependence of the critical current, Ic(T), in our arrays is similar to that of single SNS junctions. However, our results deviate from the quasiclassical theory in that Tc is sensitive to island height, because the islands are mesoscopic.