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Entropy

Josephson Currents and Gap Enhancement in Graph Arrays of Superconductive Islands

M. Lucci, Davide Cassi, Vittorio Merlo, Roberto Russo, G. Salina, Matteo Cirillo

Published Jun 25, 2021• 5 citations
Publisher

Abstract

Evidence is reported that topological effects in graph-shaped arrays of superconducting islands can condition superconducting energy gap and transition temperature. The carriers giving rise to the new phase are couples of electrons (Cooper pairs) which, in the superconducting state, behave as predicted for bosons in our structures. The presented results have been obtained both on star and double comb-shaped arrays and the coupling between the islands is provided by Josephson junctions whose potential can be tuned by external magnetic field or temperature. Our peculiar technique for probing distribution on the islands is such that the hopping of bosons between the different islands occurs because their thermal energy is of the same order of the Josephson coupling energy between the islands. Both for star and double comb graph topologies the results are in qualitative and quantitative agreement with theoretical predictions.

DOI
10.3390/e23070811

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Evidence is reported that topological effects in graph-shaped arrays of superconducting islands can condition superconducting energy gap and transition temperature. The carriers giving rise to the new phase are couples of electrons (Cooper pairs) which, in the superconducting state, behave as predicted for bosons in our structures. The presented results have been obtained both on star and double comb-shaped arrays and the coupling between the islands is provided by Josephson junctions whose potential can be tuned by external magnetic field or temperature. Our peculiar technique for probing distribution on the islands is such that the hopping of bosons between the different islands occurs because their thermal energy is of the same order of the Josephson coupling energy between the islands. Both for star and double comb graph topologies the results are in qualitative and quantitative agreement with theoretical predictions.
Measurements indicating that planar networks of superconductive islands connected by Josephson junctions display long-range quantum coherence are reported. The networks consist of superconducting islands connected by Josephson junctions and have a tree-like topological structure containing no loops. Enhancements of superconductive gaps over specific branches of the networks and sharp increases in pair currents are the main signatures of the coherent states. In order to unambiguously attribute the observed effects to branches being embedded in the networks, comparisons with geometrically equivalent-but isolated-counterparts are reported. Tuning the Josephson coupling energy by an external magnetic field generates increases in the Josephson currents, along the above-mentioned specific branches, which follow a functional dependence typical of phase transitions. Results are presented for double comb and star geometry networks, and in both cases, the observed effects provide positive quantitative evidence of the predictions of existing theoretical models.
We investigate the properties of Josephson junction networks with inhomogeneous architecture. The networks are shaped as quare comb planar lattices on which Josephson junctions link superconducting islands arranged in the plane to generate the pertinent topology. Compared to the behavior of reference linear arrays, the temperature dependencies of the Josephson currents of the branches of the network exhibit relevant differences. The observed phenomena evidence new and surprising behavior of superconducting Josephson arrays as well as remarkable similarities with bosonic junction arrays.
We report on phenomena observed in planar integrated networks obtained connecting superconducting island by Josephson tunnel junctions. These networks, identifiable as tree-like graphs, have branches consisting of series arrays of Josephson junctions which can be individually current biased and characterized. Both Josephson supercurrents and gap parameters of the arrays embedded in the graph structures display properties significantly different from those of "reference" arrays fabricated on the same chips and having identical geometrical shape. The temperature and magnetic field dependencies of the Josephson current of the embedded arrays both show a singular behavior when a critical value is reached by the Josephson characteristic energy. The gap parameter of the junctions generating the embedded arrays is higher than that of the junctions forming the reference geometrical arrays.
We theoretically study superconducting islands based on semiconductor-nanowire Josephson junctions and take into account the presence of subgap quasiparticle excitations in the spectrum of the junction. Our method extends the standard model Hamiltonian for a superconducting charge qubit and replaces the Josephson potential by the Bogoliubov--de Gennes Hamiltonian of the nanowire junction, projected onto the relevant low-energy subgap subspace. This allows us to fully incorporate the coherent dynamics of subgap levels in the junction. The combined effect of spin-orbit coupling and Zeeman energy in the nanowires forming the junction triggers a topological transition, where the subgap levels evolve from finite-energy Andreev bound states into near-zero-energy Majorana bound states. The interplay between the microscopic energy scales governing the nanowire junction (the Josephson energy, the Majorana coupling, and the Majorana energy splitting), with the charging energy of the superconducting island, gives rise to a great variety of physical regimes. Based on this interplay of different energy scales, we fully characterize the microwave response of the junction, from the Cooper pair box to the transmon regimes, and show how the presence of Majoranas can be detected through distinct spectroscopic features. In split-junction geometries, the plasma mode couples to the phase-dispersing subgap levels resulting from Majorana hybridization via a Jaynes--Cummings-like interaction. As a consequence of this interaction, higher order plasma excitations in the junction inherit Majorana properties, including the $4\ensuremath{\pi}$ effect.
Two-dimensional arrays of very-small-capacitance Josephson junctions have been studied. At low temperatures the arrays show a transition from superconducting to insulating behavior when the ratio of charging energy to Josephson-coupling energy exceeds the value 1. Insulating behavior coincides withthe occurrence of a charging gap inside the BCS gap, with an S-shaped I-V characteristic. This so far unobserved S shape is predicted to arise from macroscopic quantum coherent effects including Bloch oscillations.
We show that a Z 3 quantum double can be realized in an array of superconducting wires coupled via Josephson junctions.With a suitably chosen magnetic flux threading the system, the interwire Josephson couplings take the form of a complex Hadamard matrix, which possesses combinatorial gauge symmetry-a local Z 3 symmetry involving permutations and shifts by ±2π/3 of the superconducting phases.The sign of the star potential resulting from the Josephson energy is inverted in this physical realization, leading to a massive degeneracy in the nonzero flux sectors.A dimerization pattern encoded in the capacitances of the array lifts up these degeneracies, resulting in a Z 3 topologically ordered state.Moreover, this dimerization pattern leads to a larger effective vison gap as compared to the canonical case with the usual (uninverted) star term.We further show that our model maps to a quantum three-state Potts model under a duality transformation.We argue, using a combination of bosonization and mean field theory, that altering the dimerization pattern of the capacitances leads to a transition from the Z 3 topological phase into a quantum XY-ordered phase.Our work highlights that combinatorial gauge symmetry can serve as a design principle to build quantum double models using systems with realistic interactions.