One-dimensional Josephson junction arrays: Lifting the Coulomb blockade by depinning

Abstract

Experiments with one-dimensional arrays of Josephson junctions in the regime of dominating charging energy show that the Coulomb blockade is lifted at the threshold voltage, which is proportional to the array's length and depends strongly on the Josephson energy. We explain this behavior as de-pinning of the Cooper-pair-charge-density by the applied voltage. We assume strong charge disorder and argue that physics around the de-pinning point is governed by a disordered sine-Gordon-like model. This allows us to employ the well-known theory of charge density wave de-pinning. Our model is in good agreement with the experimental data. One-dimensional Josephson arrays show a diverse range of transport regimes. In the regime of dominating Josephson energy, which attracts a continued experimental interest 1-3 , they are highly conducting. In the regime of Josephson energy smaller or comparable to the charging energy, one-dimensional Josephson arrays show insulating (Coulomb blockade) behavior with activated transport 4 . Above a certain threshold value of the bias voltage, finite current appears even at zero temperature in the insulating regime. Initially, this switching was interpreted in terms of propagation onset of charge solitons 5-7 , i.e., the energy one has to pay in order to push one soliton into the array. However, further experiments showed that the threshold voltage is proportional to the array length and depends strongly on the value of the Josephson energy 1,8 . Here we interpret the experimentally found behavior as de-pinning in presence of strong charge disorder 9 . We argue that the system is described by a model similar to a disordered sine-Gordon model. The only difference is the fact that, instead of the usual cosine potential, we have another periodic function, the lowest Bloch band energy, which depends strongly on the Josephson energy. It is this dependence which gives rise to the dependence of the switching voltage on the Josephson energy. Previously, similar models were derived 1,[6][7][8]10 using an additional phenomenological inductance in each cell of the array, which provided the necessary mass term. In Ref. 11 it was shown, that a mass term is generated in the adiabatic regime due to the Bloch inductance 12 and the phenomenological inductance is not needed. We argue that the adiabatic mechanism is sufficient to describe the system prior and at the de-pinning point.For this work, a series of experiments has been performed on a set of three Josephson junction chains. The three arrays have been fabricated in parallel on the The set of samples contains nominally identical arrays (labeled A255, B255, and C255) comprising each 255 SQUIDs. These arrays had very similar resistances. Nevertheless, slight variations in the junction parameters are reflected in the I-V characteristics 13 . The experiments have been performed in a 3 He/ 4 He dilution refrigerator at 20 mK temperature. A scanning electron microscope (SEM) picture of a section of one of the arrays is shown in the left inset of Fig. 1. All...

Multifractal metal in a disordered Josephson junctions array

“…Unexpectedly, the many-body wavefunction becomes localized at high temperatures T ≥ T M BL : T M BL ∼ E range T E J the classical dynamics of the phase is only weakly affected by the Josephson couplings and is almost periodic indicating that the system is non-ergodic in this regime. The low-temperature behavior of a related disordered system has been recently studied in the context of a Bose glass [27,28]. For numerical analysis reported here we have restricted the allowed charging states by −Q ≤ q ≤ Q with Q = 2.…”

De-pinning of disordered bosonic chains

“…Examples include electrical transport in charge density waves (CDW) [1,2], the critical current of magnetic flux lattices [3,4] in type II superconductors, the propagation of magnetic domain boundaries [5] and crack formation in strained materials [6]. It was recently shown that the onset of electrical transport in one-dimensional arrays of Josephson junctions is also determined by the de-pinning of the charge-configuration along the array [7].…”

Insulating Josephson Junction Chains as Pinned Luttinger Liquids

“…The blue and black dotted lines are the classical expression of the depinning theory, Eqn. (3) [21], for differing Λ, which are already substantially reduced from the red solid line that arises from a model based on independent, coherent QPS (rigid quasicharge, i.e. infinite screening length).…”

“…In this letter we exploit the critical voltage as a probe of localisation (pinning) length N L , which can be determined using a generalised depinning theory. The classical limit of depinning, as applied to JJ chains, has been discussed recently by Vogt et al [21]. Under the assumption of maximal offset charge disorder, with the f i distributed independently for each site, the last term in Eqn.…”