Macroscopic Coulomb blockade in large Josephson junction arrays

Abstract

We investigate theoretically transport properties of one-and two-dimensional regular Josephson junction arrays (JJAs) in an insulating state. We derive the low-temperature current-voltage characteristics (the I-V dependencies) for the current mediated by the Cooper pair transfer across the system. In the case where the screening length λc associated with the capacitance of the islands to the ground is much larger than the island's size d, we find that transport is governed by the macroscopic Coulomb blockade effect with the gap ∆c well exceeding a single island charging energy Ec. In the limit of λc ≫ L, where L is the linear size of the array, the gap establishes the dependence on the array size, namely, ∆c ≃ Ec(L/d) in 1D and ∆c ≃ Ec ln(L/d) in 2D arrays. We find two transport regimes: at moderate temperatures, Ec < kBT < ∆c, the low bias transport is thermally activated with the resistance R ∝ exp(T0/T ) where the activation energy kBT0 = ∆c. At ultra-low temperatures, kBT < Ec, a JJA falls into a superinsulating state with R ∝ exp[(∆c/Ec) exp(Ec/T )].

Jumps in Current-Voltage Characteristics in Disordered Films

“…Authors of Refs. [4,7] assumed that the HR state is a new collective state -"superinsulator". Their calculation was vigorously disputed in Ref.…”

Low Temperature Transport in Tunnel Junction Arrays: Cascade Energy Relaxation

“…We illustrate the power of our approach applying it to phenomena of overheating [38,39], the Coulomb anomaly [11,31], the transport in the granular systems governed by the cotunneling processes [31,40] and mediated by the electron-hole environment. The concept of the cascade two-stage energy relaxation appears to be of the fundamental importance to revealing the microscopic mechanism of the insulator-to-superinsulator transition and the nature of low temperature transport in the superinsulating state [25][26][27]. We show, finally, that the concept of the cascade energy relaxation resolves the long standing puzzle of temperature-independent pre-exponential factor in variable range hopping conductivity [16][17][18][41][42][43][44][45].…”

“…The low temperature transport in the large JJA arrays was discussed in [?, 25,26] within the framework of the Feynman-Vernon influence functional technique. The charge transfer is realized by the dipole excitations that unbind and further tunnel under the applied bias.…”

“…The role of such bosonic mediator can be taken by ether the electromagnetic environment [1,2,[4][5][6][7][8]21,22] by the neutral dipole excitations [the electron-hole (e-h) pairs] generated by the tunneling carriers [23,24]. By consideration in the spirit of Feynman-Vernon influence functional it was shown [25][26][27] that in the large Josephson junction arrays the low temperature transport is governed by the unbinding neutral dipole excitations and the successive tunneling of the resulting electric charges. In the course of tunneling the propagating charges generate the dipole environment controlling relaxation process.…”

“…In Section 1.4 we explore application of the cascade two-stage energy relaxation mediated transport to different physical systems and phenomena. In particular, we discuss nonequilibrium Coulomb anomaly, negative differential resistance and overheating in single junctions, properties of electron-hole environment in disordered metals, and the mechanism of tunneling transport in a superinsulating state re-deriving the results of [25][26][27] from a different perspective.…”