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arXiv:0910.5346

Josephson decoupling phase in inhomoheneous arrays of superconducting quantum dots

Sujit Sarkar

Published Oct 28, 2009• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.0910.5346

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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.
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.
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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.
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We consider a quantum dot with mechanical degrees of freedom which is coupled to superconducting electrodes. A Josephson current is generated by applying a phase difference. In the absence of coupling to vibrations, this setup was previously proposed as a detector of magnetic flux and we wish here to address the effect of the phonon coupling to this detection scheme. We compute the charge on the quantum dot and determine its dependence on the phase difference in the presence of phonon coupling and Coulomb interaction. This allows to identify regions in parameter space with the highest charge to phase sensitivity, which are relevant for flux detection. Further insight about the interplay of such couplings and subsequent entanglement properties between electron and phonon degrees of freedom are gained by computing the von Neumann entropy.