New coherent states in periodic arrays of ultrasmall Josephson junctions

Abstract

An extensive study of the thermodynamics of a two-dimensional periodic array of ultrasmall Josephson junctions with and without a transverse magnetic field is presented. A quantum Monte Carlo algorithm is introduced to study a model that includes the Josephson energy, $E_J$, as well as the charging energy, $E_c$, contributions. The superfluid density, internal energy, and specific heat for different lattice sizes and numbers of Monte Carlo simulation sweeps are studied as a function of the ratio α=$E_c$/$E_J$, the temperature and the magnitude of the magnetic field. When α≠0, it is found that as the temperature is lowered the model has two phase transitions. First, a second-order Berezinskii-Kosterlitz-Thouless (BKT) transition renormalized by the quantum fluctuations represented by a finite α. Below this BKT transition the system has long-range phase coherence; thus it is a state with zero resistance. At lower temperatures, a first-order phase transition appears which is entirely due to the quantum fluctuations that nucleate vortex excitations. Below this ‘‘quantum induced transition’’ (QUIT) the model still has a finite but diminished superfluid density, thus indicating that the QUIT is between two different zero-resistance states, one dominated by thermal fluctuations and the other by quantum fluctuations. A QUIT is found to be more pronounced in the case where there is a magnetic field. The case studied here corresponds in the classical limit to the fully frustrated state. Finally, we discuss the physical properties of this new low-temperature phase as well as the necessary conditions to test this prediction experimentally.