Unbinding of charge-anticharge pairs in two-dimensional arrays of small tunnel junctions

Abstract

We describe the behavior of charges in two-dimensional arrays of normal-metal tunnel junctions with very small capacitance. A Kosterlitz-Thouless-Berezinskii phase transition with unbinding of chargeanticharge pairs occurs at a transition temperature of about 7V sss e 2 /SnCkBy with C the junction capacitance. We calculate the influence of tunneling conductance; T c is reduced with increasing conductance and no transition occurs for junction conductance above (14 kft) -1 . In the superconducting state a similar transition occurs at a 4 times higher T c . We present the first experimental results on the conductive transition of an array in the normal and superconducting states.

Critical properties of two-dimensional Josephson-junction arrays with zero-point quantum fluctuations

“…1). It has been suggested that in the limit (C s /C m ) → 0 this I-N transition would be of a BKT type [29,30,2,8]. Experimental results have shown, however, that the behavior of the fabricated samples is better explained by a crossover from a normal to an insulating phase [4][5][6].…”

“…A large number of studies, both experimental [2][3][4][5][6][7] and theoretical [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] have been devoted to them. Initially, part of the interest in JJA came from their close relation to one of the most extensively studied theoretical spin models, i.e.…”

Charge Glass in Two-Dimensional Arrays of Capacitively Coupled Grains with Random Offset Charges

“…Nonlinear behavior sets in at a characteristic voltage V c ϳ T ͞j s,T . For larger disorder, the results are supported by a Monte Carlo simulation of the nonlinear conductance leading to V c ϳ T 11n with a very rough estimate n ϳ 1.7.The electrostatic energy of the net mobile charges Q i e ‫ء‬ n i , multiples of an elementary charge e ‫ء‬ , located at the sites i of an array is given by [1,5] E 1 2where e ‫ء‬ e, the electron charge, for a normal grain and e ‫ء‬ 2e for a superconducting grain. C ij is the capacitance matrix and q i represents a net offset charge in a grain induced by charged impurities trapped near the grainsubstrate interface [1,6].…”

“…Recently, however, a closer analysis of the experimental data of different groups revealed that the onset of finite conductance at finite temperatures could be described just as well by thermal activation of free charges [2,3] with an activation energy E a ഠ 1 4 E c when the grains are in the normal state and E a ഠ 1 4 E c 1 D for superconducting grains, where 2D is the superconducting energy gap at zero temperature. This interpretation neglects the logarithmic interaction between charges expected for an ideal array [1,4] and suggests in turn that, in the experimental systems, the interaction is screened by some unknown mechanism and is essentially short ranged. Although disorder effects, in the form of random offset charges which may be trapped near the grain-substrate interface [1], could be a possible explanation for these results, an understanding of how differently prepared systems, and therefore different degrees of disorder, can still lead to the same activated behavior of the linear conductance is still lacking.…”

“…[S0031-9007(98) PACS numbers: 64.70. Pf, 73.40.Gk, 73.40.Rw Two-dimensional arrays of Josephson junctions where the charging energy of the grains is much larger than the Josephson coupling energy are interesting systems where collective charging effects can be studied experimentally in great detail [1][2][3][4]. In these systems, the net charges in the grains have a long range logarithmic interaction when the junction capacitance C is small enough.…”