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International Journal of Modern Physics B

JOSEPHSON DECOUPLING PHASE IN INHOMOGENEOUS ARRAYS OF SUPERCONDUCTING QUANTUM DOTS

Sujit Sarkar

Published Jul 16, 2012• 0 citations
Publisher

Abstract

A quantum phase analysis of inhomogeneous arrays of superconducting quantum dots (SQD) is presented. Existence of Josephson decoupling (JD) phase is observed at the half-filling. It occurs due to fluctuations of Josephson couplings over the sites. This JD phase is the phase incoherent gapped state of the system. In JD phase superconductivity disappears even in the absence of Coulomb blockade phase. It is also observed that the inhomogeneity of on-site Coulomb charging energy produces the relevant coupling term that yields Coulomb blockade gapped phase. The presence of nearest-neighbor and next-nearest-neighbor Coulomb interaction yields the same physics for inhomogeneous and homogeneous SQD.

DOI
10.1142/s0217979212501081

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A quantum phase analysis of inhomogeneous arrays of superconducting quantum dots (SQD) is presented. Existence of Josephson decoupling (JD) phase is observed at the half-filling. It occurs due to fluctuations of Josephson couplings over the sites. This JD phase is the phase incoherent gapped state of the system. In JD phase superconductivity disappears even in the absence of Coulomb blockade phase. It is also observed that the inhomogeneity of on-site Coulomb charging energy produces the relevant coupling term that yields Coulomb blockade gapped phase. The presence of nearest-neighbor and next-nearest-neighbor Coulomb interaction yields the same physics for inhomogeneous and homogeneous SQD.
We present a study of quantum phase analysis of inhomogeneous and homogeneous arrays of superconducting quantum dots (SQD). We observe the existance of Josephson decouple (JD) phase only at the half filling for inhomogeneous array of SQD due to the fluctuation of Josephson couplings over the sites at half filling. In JD phase superconductivity disappears even in the absence of Coulomb blockade phase. We also observe that fluctuation of on-site Coulomb charging energy produces the relevant coupling term that yields Coulomb blockade gapped phase. The presence of nearest-neighbor and next-nearest-neighbor Coulomb interaction yields the same physics for inhomogeneous and homogeneous SQD.
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 clean superconducting quantum dots (SQD) and also site dependent Josephson couplings, on site charging energies and the intersite interactions in presence of gate voltage. We predict the existence of different fractionally quantized Cooper pair stair case with many interesting physical properties. The appearance of stair case is not only due to the Coulomb blocked phenomena but also for the site dependent Josephson couplings. We also explain physically the absence of other fractionally quantized Cooper pair stair case. The physics of fractionally quantized Cooper pair stair case has close resemblance with the fractionally quantized magnetization plateau of a spin chain system under a magnetic field.
The quantum phase transition in two capacitively coupled arrays of superconducting quantum dots (SQD) by considering the presence of gate voltage in each superconducting island is presented. We show explicitly that the cotunneling process associated with two coupled SQD arrays, near the maximum-charge frustration line is not sufficient to explain the correct quantum phases with physically consistent phase boundaries. We consider an extra cotunneling process along each chain to explain the correct quantum phases with physically consistent phase boundaries. There is no evidence of supersolid phase in our study. The Bethe ansatz and Abelian bosonization method is used to solve the problem.
Mesoscopic Coulomb blockade (MCB) is recognized as a phase-coherent variant of the conventional Coulomb blockade that arises in systems with open contacts. In open quantum dots, MCB is enhanced by a decrease in background conductance. This occurs because the reduction in coupling strength between the quantum dot and the outer reservoir renders the system more closed, thereby facilitating the emergence of conventional Coulomb blockade. In this work, we demonstrate that the MCB in open superconducting islands exhibits an different correlation with coupling strength compared to open quantum dots. Specifically, a decrease in background conductance may result in a weakening of the MCB. This observation indicates that the MCB in superconducting islands originates from the presence of superconducting-normal interfaces.
Inhomogeneities on various length scales suggesting phase separation seem to be a generic feature of hole-doped high-temperature superconducting cuprates. Also firmly established is the d-wave symmetry of the superconducting state. The interplay of superconductivity and phase separation has been noted in previous mean-field studies of correlated electron models. To further explore this issue in a more rigorous approach we have conducted quantum Monte Carlo calculations of a two-dimensional Hubbard model with nearest-neighbor attractive interaction. For a vanishing on-site repulsion, the result agrees with that of Micnas, Ranninger, and Robaszkiewicz [Phys. Rev. B 39, 11 653 (1989)], and indicates that for a given strength of the attractive interaction, homogeneous d-wave superconducting phase can exist only above a critical doping concentration, below which phase separation occurs. A finite on-site repulsion modifies the phase separation behavior. A stronger d-wave pairing correlation is seen in the inhomogeneous phase compared to the homogeneous phase.