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Physical Review Letters

One-Dimensional Mott Insulator Formed by Quantum Vortices in Josephson Junction Arrays

Alexander van Oudenaarden, Johan E. Mooij

Published Jun 24, 1996• 97 citations
Publisher

Abstract

The quantum transport of vortices in very long and narrow arrays of small Josephson junctions has been studied experimentally. The chemical potential of the system can be changed by an external magnetic field. When the vortex density is commensurate with the one-dimensional junction lattice, the vortex mobility vanishes for a finite window of the magnetic field. The localization of the vortices is due to the forming of a one-dimensional Mott insulator.

DOI
10.1103/physrevlett.76.4947

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•Jul 3, 2017•0 citations
The quantum transport of vortices in very long and narrow arrays of small Josephson junctions has been studied experimentally. The chemical potential of the system can be changed by an external magnetic field. When the vortex density is commensurate with the one-dimensional junction lattice, the vortex mobility vanishes for a finite window of the magnetic field. The localization of the vortices is due to the forming of a one-dimensional Mott insulator.
We review experiments on small-capacitance Josephson junctions. When the Josephson junction is fabricated in the configuration of dc superconducting quantum interference device (SQUID), the Josephson coupling can be tuned IN SITU with an external magnetic field. The electrical transport properties of one-dimensional arrays of small-capacitance dc SQUIDs have been investigated in order to study the superconductor-insulator transition. The arrays have also been used to bias a single Josephson junction, and a clear Coulomb blockade of Cooper-pair tunneling has been observed in the single junction.
The single-vortex problem in a strongly correlated bosonic system is investigated self-consistently within the mean-field theory of the Bose-Hubbard model. Near the superfluid--Mott-insulator transition, the vortex core has a tendency toward the Mott-insulating phase, with the core particle density approaching the nearest commensurate value. If the nearest-neighbor repulsion exists, the charge-density wave order may develop locally in the core. The evolution of the vortex configuration from the strong- to weak-coupling regions is studied. This phenomenon can be observed in systems of rotating ultracold atoms in optical lattices and Josephson-junction arrays.
We study the differential resistivity transition of two-dimensional superconducting arrays induced by an external driving current, in the presence of thermal fluctuations and a magnetic field corresponding to fff flux quantum per plaquette. Recent experiments have identified this transition as a dynamic vortex Mott insulator transition at vortex densities near rational values of fff. The critical behavior is determined from a scaling analysis of the current-voltage relation near the transition, obtained by Monte Carlo simulations of a Josephson-junction array model in the vortex representation. For a square-lattice array, the critical exponents obtained near f=1/2f=1/2f=1/2 are consistent with the experimental observations. The same scaling behavior is observed near f=1/3f=1/3f=1/3. For a honeycomb array, although similar results are obtained for f=1/3f=1/3f=1/3, the transition is absent for f=1/2f=1/2f=1/2, consistent with an incommensurate vortex phase.
An array of superconducting proximity islands has been shown to be highly tunable by electric and magnetic fields.Indeed, a small change in the electric and magnetic field can tune the system from a vortex Mott insulator to a vortex metal.This transition from localized to a non-localized state can occur as soon as the density of the superconducting vortices matches the density of the pinning sites in a non defective structure.The possibility of further modulation of non-localized superconducting states via enhancement of the superconducting order parameter or modulation of the Josephson plasma frequency is discussed.Based on the non-bolometric effects associated with the occurrence of non-equilibrium phenomena in this original superconducting networks we discuss also the possible applications of this array for a conceptually new type of radiation detector.
Vortices and vortex lattices play a major role in determining the transport properties of type-II superconductors[1–3], and enable a platform to investigate exotic superconducting physics[4,5]. The study of vortex matter has generally focused on novel states in 2D films and structures, and has recently moved to investigating systems with constrained dimensions and smaller vortex numbers[6–11]. Vortices are responsible, for example, for some electrical transport regimes in superconducting films, as well as the Berezinkskii-Kosterlitz-Thouless phase transition in superconducting films[12]. Unconventional forms of superconductivity, such as the spin triplet pairing predicted in Sr2RuO4, or in topological insulators paired to s-wave superconductors, contain two condensates that may support two vortex lattices, and may display Majorana modes, signatures of which may have been seen in other superconducting systems[13–17]. The vortex-vortex interactions, or inter and intra-condensate couplings in multicondensate systems, are important parameters that characterize the behavior of the systems that display such phenomena[18–20]. In investigating these parameters, a technique that can both probe the energies in a system, as well as manipulate the vortices therein, has long been desired. In this work, we report on progress in determining the energy scales of vortex systems, as well as limited control over the vortex motion. Using a technique based on magnetic force microscopy, we can directly measure the resonant motion of vortices present in a superconducting lattice. We use a scanning magnetic tip to trap a small number of vortices in a superconducting Josephson junction array near the tip. By observing the resonant motion of the configuration of vortices, a map of the location of energy degeneracies between different stable configurations is generated. From this data, we use a simulation to extract the relative strengths of the characteristic energy scales for the system, including the vortex-magnetic field interaction, the vortex-vortex interaction strength, and the chemical potential for the vortices. The simulations for small numbers of vortices fits the data well for multiple field profiles and lattice spacings. The ability to tune the vortex number and configurations by changing the magnetic field profile from the tip, as well as the lattice parameters of the superconducting surface, are key portions of this technique. We demonstrate that the relative strengths of the chemical potential and vortex-vortex interactions can be tuned relative to the vortex-magnetic field energy by changing the lattice spacing of the array. We also show that by moving the tip farther from or closer to the surface, which changes the potential well from the tip, that the configurations of vortices can be modified. From the experiments, we show that this technique can be used to both extract the strengths of the relative energy scales in this system and other superconducting systems, as well as for manipulating the vortex configurations for quantum computation applications.