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arXiv:1003.2038 · Physical Review B

Quantum phase transition in an array of coupled superconducting quantum dots with charge frustration

Sujit Sarkar

Published Jun 25, 2010• 0 citations
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Abstract

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.

DOI
10.1103/physrevb.81.212505

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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.
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.
The quantum phase transition and the electronic transport in a triangular quantum dot system are investigated using the numerical renormalization group method. We concentrate on the interplay between the interdot capacitive coupling V and the interdot tunnel coupling t . For small t , three dots form a local spin doublet. As t increases, due to the competition between V and t , there exist two first-order transitions with phase sequence spin-doublet-magnetic frustration phase-orbital spin singlet. When t is absent, the evolutions of the total charge on the dots and the linear conductance are of the typical Coulomb-blockade features with increasing gate voltage. While for sufficient t , the antiferromagnetic spin correlation between dots is enhanced, and the conductance is strongly suppressed for the bonding state is almost doubly occupied.
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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 investigate two equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. With increasing interdot coupling, a rich range of behavior is uncovered: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom, followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi-liquid "charge-ordered" phase with finite residual entropy and anomalous transport properties. Physical arguments and numerical renormalization group methods are employed to obtain a detailed understanding of the problem.
We study the quantum phase transition of the one-dimensional phase model in the presence of dissipative frustration, provided by an interaction of the system with the environment through two noncommuting operators. Such a model can be realized in Josephson junction chains with shunt resistances and resistances between the chain and the ground. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a nonmonotonic behavior as a function of the dissipative coupling strength. This result is a consequence of the frustration between (i) one dissipative coupling that quenches the quantum phase fluctuations favoring the ordered phase and (ii) one that quenches the quantum momentum (charge) fluctuations leading to a vanishing phase coherence. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that quantum frustration increases the range in which the phase transition is second order. The nonmonotonic behavior is reflected also in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.