In this model as applied to Josephson Junction arrays, there is charge-flux duality. Can be described by a Hamiltonian with Josephson couplings between scing island and charging energies for the islands.
In the regime where Ec
There are a number of possible complications in the simple arrays including random charge, and Josephson energies, and flux noise.
They have endeavored to overcome these issues by making JJ arrays with a large number of nearest-neighbor islands. These are arrays where there is a supercell of many tightly connected neighbors. This supercell is connected to its neighboring supercells, by cells that have less interconnects. With these array they can explore of a wide range of JJ parameters and an effective Ej/Ec created which is enhanced over the bare value by factor of N^2.
Michael 1st presented data for array without ground planes and then for arrays conducting ground plane. They found multiple SIT (due to commensurate effects) over a wide range of critical resistances R ~ 3-20 k were observed. "Metallic" phases with very low (typically < 100 mK) characteristic energies were found.
SIT observed at low “critical” Rcr ~ few ohms resemble the “dirty boson” SIT however the duality is lacking for the transitions observed at larger Rcr . On the “insulating” side of the SIT, the R(T) dependences can be fitted with the Arrhenius law R(T)~exp(T0/T), where kBT0 is close to the “Coulomb” gap 2eV* (V* is the offset voltage across the whole array). Michael speculated that this may be a signature of some collective process and/or macroscopic inhomogeneity. The threshold for quasiparticle generation at high bias currents is surprisingly universal for samples with vastly different zero-bias resistances and that this power scales with the array area.
Blogged by Peter Armitage
Important observation presented in this talk is that macroscopically superconducting state can exist in arrays with individual resistance up to MOhm range (due to large factor N increasing effective Josephson energy).
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