Insulating Josephson Junction Chains as Pinned Luttinger Liquids

Abstract

Quantum physics in one spatial dimension is remarkably rich, yet even with strong interactions and disorder, surprisingly tractable. This is due to the fact that the low-energy physics of nearly all one-dimensional systems can be cast in terms of the Luttinger liquid, a key concept that parallels that of the Fermi liquid in higher dimensions. Although there have been many theoretical proposals to use linear chains and ladders of Josephson junctions to create novel quantum phases and devices, only modest progress has been made experimentally. One major roadblock has been understanding the role of disorder in such systems. We present experimental results that establish the insulating state of linear chains of sub-micron Josephson junctions as Luttinger liquids pinned by random offset charges, providing a one-dimensional implementation of the Bose glass, strongly validating the quantum many-body theory of one-dimensional disordered systems. The ubiquity of such an electronic glass in Josephson-junction chains has important implications for their proposed use as a fundamental current standard, which is based on synchronisation of coherent tunnelling of flux quanta (quantum phase slips).The combined effects of interaction and disorder in superfluid bosonic condensates can have drastic consequences, leading to the Mott insulator [1,2] and BoseAnderson glass [3][4][5]. The latter is thought to describe helium-4 in porous media, cold atoms in disordered optical potentials, disordered magnetic insulators, and thin superconducting films. The prototypical Bose-Hubbard model without disorder predicts a Beresinskii-KosterlitzThouless quantum phase transition between superfluid and Mott insulator. Experimental implementation using arrays of Josephson junctions has been explored [6][7][8], however, the possibility of the insulating glass has not been considered.One-dimensional arrays of Josephson junctions are notable for application as a fundamental current standard [9,10], which is based on synchronisation of a 'dual' Josephson effect, envisioned to arise from coherent quantum tunnelling of flux quanta, or so-called quantum phase slips [11][12][13][14][15]. Unlike the Mott insulator, the insulating glass is compressible, therefore AC synchronisation of charge may not be possible. Although the presence of offset charge disorder is well-established for small superconducting islands, it has not been sufficiently addressed in regards to dual Josephson effects.We have measured critical voltages for a large number of simple chains of sub-micron Josephson junctions with significantly varying energy scales. We observe universal scaling of critical voltage with single-junction Bloch bandwidth. Our measurements reveal a localisation length exponent that steepens with Luttinger parameter, K, arising from precursor fluctuations as one approaches the Bose glass-superfluid quantum phase transition. This contrasts with the fixed exponent found for classical pinning of charge density waves [16], vortex lattices [17] and disordered spin syst...

Superconductor-insulator transition in disordered Josephson-junction chains

“…In a recent preprint 80 , an experimental study of the depinning in JJ chains deeply in the localized phase has been carried out. The authors have found an agreement with theoretical expectations based on the Luttingerliquid picture in the presence of disorder, which is in correspondence with our model.…”

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.…”

Weak- versus strong-disorder superfluid—Bose glass transition in one dimension

“…In the presence of disorder, such a SF ground state is generally expected to be unstable towards localization, thus forming the so-called Bose glass (BG) phase [7][8][9]: an inhomogeneous gapless compressible fluid with exponentially suppressed correlations. Disordered interacting chains can be experimentally realized using spin ladders [10,11], ultra-cold atoms [12][13][14] and arrays of disordered Josephson junctions [15][16][17]. Broadly speaking, Luttinger liquid physics is expected to occur in various contexts [18], e.g.…”