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Physical review. B, Condensed matter

One-dimensional Mott localization of quantum vortices in Josephson-junction arrays

Alexander van Oudenaarden, B. van Leeuwen, M. P. M. Robbens, Johan E. Mooij

Published May 1, 1998• 9 citations
Publisher

Abstract

The quantum transport of vortices in very long and narrow arrays of small Josephson junctions is studied experimentally. We investigate the forming of a Mott insulator in periodic arrays. When the vortex density is commensurate with the one-dimensional periodic potential, the vortices localize due to the strong repulsive vortex-vortex interaction. We explore the influence of interaction strength, bandwidth, sample geometry, and temperature on the stability of the Mott states.

DOI
10.1103/physrevb.57.11684

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The quantum transport of vortices in very long and narrow arrays of small Josephson junctions is studied experimentally. We investigate the forming of a Mott insulator in periodic arrays. When the vortex density is commensurate with the one-dimensional periodic potential, the vortices localize due to the strong repulsive vortex-vortex interaction. We explore the influence of interaction strength, bandwidth, sample geometry, and temperature on the stability of the Mott states.
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.
Motivated by possible applications to cold atomic gases in a rotating trap, we give an overview of some important concepts in two-dimensional vortex physics. In the context of Josephson junction arrays, we first discuss the crucial role payed by vortices in both the thermal superconducting to normal metal transition, and the zero temperature superconducting to Mott insulator transition. Important notions on vortex dynamics in these arrays are then presented, with emphasis on experimental results indicating the quantum nature of vortex motion at low temperature. We move then to the Fractional Quantum Hall effect, as observed in electronic systems, and introduce the notions of fractional excitations, generalized statistics, and composite Fermions, which have played a key role in the theoretical description of this remarkable phenomenon. Very likely, cold atomic gases in a rotating trap will soon provide a way to explore the bosonic version of the Fractional Quantum Hall effect, and thus shedding new light on these subtle strongly correlated quantum fluids.
Superconductor-semiconductor Josephson junction arrays are a uniquely tunable platform for studying collective quantum phenomena, particularly in the regime where localized Andreev bound states can hybridize across the lattice when the physical separation between adjacent junctions is smaller than their coherence length (ξABS>dJJξ_{\text{ABS}}>d_{\text{JJ}}ξABS​>dJJ​). Here, we investigate three distinct Al-InAs Josephson junction arrays: a square array and super-honeycomb array fabricated within this ξABS>dJJ{ξ_{\text{ABS}}>d_{\text{JJ}}}ξABS​>dJJ​ regime, as well as a larger-spacing super-honeycomb control device designed such that ξABS≲ ⁣ dJJξ_{\text{ABS}}\lesssim\!~d_{\text{JJ}}ξABS​≲ dJJ​. Under an out-of-plane field, critical current peaks emerge at rational filling factors, reflecting stable vortex configurations in the lattices. In the super-honeycomb lattice, vortices localize to distinct non-identical plaquettes at different filling factors, as predicted by frustrated XY model simulations. A rotating in-plane field yields periodic critical current oscillations that reflect the Rashba spin-orbit coupling inherent to the InAs quantum well. Surprisingly, at f=1f = 1f=1, the closely spaced super-honeycomb array exhibits a distinct critical current minimum as the magnitude of the in-plane field increases, a signature absent in the square array and large-spacing super-honeycomb array. These results indicate that this signature is jointly influenced by the unique geometry of the super-honeycomb vortex lattice and by long-range inter-junction hybridization.
Motivated by possible applications to cold atomic gases in a rotating trap, we give an overview of some important concepts in two-dimensional vortex physics. In the context of Josephson junction arrays, we first discuss the crucial role played by vortices in both the thermal superconducting to normal metal transition, and the zero temperature superconducting to Mott insulator transition. Important notions on vortex dynamics in these arrays are then presented, with emphasis on experimental results indicating the quantum nature of vortex motion at low temperature. We move then to the Fractional Quantum Hall effect. as observed in electronic systems, and introduce the notions of fractional excitations, generalized statistics, and composite fermions, which have played a key role in the theoretical description of this remarkable phenomenon. Very likely, cold atomic gases in a rotating trap will soon provide a way to explore the bosonic version of the Fractional Quantum Hall effect, and thus shedding new light on these subtle strongly correlated quantum fluids.
Abstract In Josephson junction arrays, vortices form stable topological excitations. A key step towards the understanding of their properties was the observation made by Eckern and Schmid that in low‐capacitance junction arrays a vortex behaves as a massive particle moving in a periodic potential and subject to dissipation. The mass is low and quantum effects become observable. The present contribution provides a review of these properties together with a discussion of similar scenarios realized in optical lattices.