Phase and Charge reentrant phase transitions in two capacitively coupled Josephson arrays with ultra-small junction

Abstract

We have studied the phase diagram of two capacitively coupled Josephson junction arrays with charging energy, $E_c$, and Josephson coupling energy, $E_J$. Our results are obtained using a path integral Quantum Monte Carlo algorithm. The parameter that quantifies the quantum fluctuations in the i-th array is defined by ${\alpha }_i\equiv \frac{E_{c_i}}{E_{J_i}}$. Depending on the value of ${\alpha }_i$, each independent array may be in the semiclassical or in the quantum regime: We find that thermal fluctuations are important when $\alpha \lesssim 1.5$ and the quantum fluctuations dominate when $2.0\lesssim \alpha$. We have extensively studied the interplay between vortex and charge dominated individual array phases. The two arrays are coupled via the capacitance $C_{\mathrm{inter}}$ at each site of the lattices. We find a {\it reentrant transition} in ${\rm Y}(T,\alpha )$, at low temperatures, when one of the arrays is in the semiclassical limit (i.e. ${\alpha }_1=0.5$) and the quantum array has $2.0\le {\alpha }_2\le 2.5$, for the values considered for the interlayer capacitance. In addition, when $3.0\le {\alpha }_2<4.0$, and for all the inter-layer couplings considered above, a {\it novel} reentrant phase transition occurs in the charge degrees of freedom, i.e. there is a reentrant insulating-conducting transition at low temperatures. We obtain the corresponding phase diagrams and found some features that resemble those seen in experiments with 2D JJA.

25 Latex pages including 8 encapsulated poscript figures. Accepted for publication in Phys. Rev B (Nov. 2004 Issue)

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