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arXiv:cond-mat/0205568 · Physical review. B, Condensed matter

Phase diagram of Josephson junction arrays with capacitive disorder

Francesco Paolo Mancini, Pasquale Sodano, Andrea Trombettoni

Published Jan 21, 2003• 11 citations
arXivHTMLPDF

Abstract

We study the phase diagram at finite temperature of Josephson junction arrays with capacitive disorder (i.e., random offset charges and/or random charging energies): in the limit of large particle numbers per junction, this is a remarkable physical realization of the disordered boson Hubbard model. By using a mean-field approximation, we compute the average free energy and the equation for the phase boundary line between the insulating and superconducting phases. We find that the Mott-insulating lobe structure disappears for large variance $(\ensuremath{\sigma}\ensuremath{\gtrsim}e)$ of the offset charges probability distribution. Further, with nearest-neighbor interactions, the insulating lobe around $q=e$ is destroyed even for small values of $\ensuremath{\sigma}.$ In the case of random charging energies, until the variance of the distribution reaches some critical value the superconducting phase increases in comparison to the situation in which all self-capacitances are equal.

DOI
10.1103/physrevb.67.014518

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We study the phase diagram at finite temperature of Josephson junction arrays with capacitive disorder (i.e., random offset charges and/or random charging energies): in the limit of large particle numbers per junction, this is a remarkable physical realization of the disordered boson Hubbard model. By using a mean-field approximation, we compute the average free energy and the equation for the phase boundary line between the insulating and superconducting phases. We find that the Mott-insulating lobe structure disappears for large variance (\ensuremathσ\ensuremath≳e)(\ensuremath{\sigma}\ensuremath{\gtrsim}e)(\ensuremathσ\ensuremath≳e) of the offset charges probability distribution. Further, with nearest-neighbor interactions, the insulating lobe around q=eq=eq=e is destroyed even for small values of \ensuremathσ.\ensuremath{\sigma}.\ensuremathσ. In the case of random charging energies, until the variance of the distribution reaches some critical value the superconducting phase increases in comparison to the situation in which all self-capacitances are equal.
We carry out a quantum Monte Carlo study of Josephson arrays at temperature T=0 in the presence of an offset voltage between array and substrate. With diagonal and nearest-neighbor charge coupling, we find two types of insulating lobes with different types of charge order, and two types of superconducting regions. One is a supersolid with coexisting long-range phase coherence and checkerboard charge order. The supersolid phase is robust at half-filling. With next-nearest-neighbor coupling, there are two types of supersolid phase, one with checkerboard and one with striped charge order. Our phase diagram agrees with mean-field theory and with quantum Monte Carlo results of van Otterlo et al. in comparable regions of parameter space, but differs in detail from that of a Bose-Hubbard model with nearest-neighbor charging energies.
We study the zero-temperature phase diagram of a dissipationless and disorder-free Josephson junction chain. Namely, we determine the critical Josephson energy below which the chain becomes insulating as a function of the ratio of two capacitances: the capacitance of each Josephson junction and the capacitance between each superconducting island and the ground. We develop an imaginary-time path integral quantum Monte Carlo algorithm in the charge representation, which enables us to efficiently handle the electrostatic part of the chain Hamiltonian. We find that a large part of the phase diagram is determined by anharmonic corrections which are not captured by the standard Kosterlitz-Thouless renormalization group description of the transition.
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The low-temperature states of bosonic condensates exhibit fundamental quantum effects at the macroscopic scale. The combined effects of interaction and disorder in these can have drastic consequences, leading to the Mott insulator and Bose-Anderson glass. 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-Kosterlitz-Thouless quantum phase transition between superfluid and Mott insulator. Experimental implementation using arrays of Josephson junctions has been explored, however, the possibility of the insulating glass has not been considered. The ubiquity of such a phase in Josephson-junction arrays would have important implications for their proposed use as a fundamental current standard. Unlike the Mott insulator, the insulating glass is compressible, therefore AC synchronisation of charge may not be possible. 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, 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, vortex lattices, and disordered spin systems, and is in excellent agreement with the quantum theory of one-dimensional disordered bosonic insulators. We thereby demonstrate a unique signature of the charged Bose glass in insulating Josephson-junction chains.
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.
The zero temperature phase diagram for ultracold bosons in a random 1D potential is obtained through a site decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian, whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose glass phase. The different phases—i.e., Mott insulator, superfluid, and Bose glass—are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes is related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.