Discrete Breathers in Two-Dimensional Josephson-Junction Arrays J. J. Mazo Departamento de Fı ´sica de la Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain Departamento de Teorı ´a y Simulacio ´n de Sistemas Complejos, Instituto de Ciencia de Materiales de Arago ´n, C.S.I.C.–Universidad de Zaragoza, E-50009 Zaragoza, Spain (Received 13 March 2002; published 18 November 2002) We have proposed theoretically and studied numerically the existence of discrete breathers (intrinsic localized modes) in the dynamics of a two-dimensional Josephson-junction array biased by radio- frequency fields. The solutions are linearly stable in the framework of the Floquet theory and robust in the presence of thermal fluctuations. We have also discussed the conditions for realizing an experi- mental detection of these modes. DOI: 10.1103/PhysRevLett.89.234101 PACS numbers: 05.45.Yv, 74.50.+r Two-dimensional Josephson-junction arrays (2DJJA) are paradigmatic experimental systems for the study of many physical phenomena [1]. As realizations of the XY model, they have been designed for the study of phase transitions in unfrustrated and frustrated two- dimensional systems. Since they are tailored arrays, they have helped us to understand the role of geometry and disorder in granular superconductors. Modeled by coupled pendula, they are important to understand prob- lems of synchronization of oscillators in complex lattices. Since they present vortices and antivortices, from these arrays we have learned from the behavior of those types of nonlinear coherent excitations in the presence of ac and/or dc perturbations and their role in equilibrium and nonequilibrium phase transitions. A different type of coherent localized excitations in nonlinear lattices are the so-called discrete breathers (DB’s) or intrinsic localized modes [2,3]. Physically they are dynamical solutions for which energy remains sharply localized in a few sites of the array. Then, there is not significant radiation of this energy to the rest of the lattice. It is important to emphasize that we are consid- ering perfect and ordered homogeneous systems, the localization being an intrinsic property of such systems. DB’s have been mainly studied in lattices in one dimension and only experimentally found in some quasi-one-dimensional systems. One of such systems is an underdamped JJ ladder array biased by dc external currents. In these superconducting networks, the local- ized states are localized voltage solutions: not all of the junctions have the same voltage although they are all coupled and driven by the same current. Following theo- retical predictions [4–6], DB’s in the ladder were shown to exist for a wide range of parameter values, excited at will and detected by local voltage measurements and a low temperature laser scanning microscopy [7–10]. An interesting issue to address is the role and the possible detection of such excitations in the dynamics of 2D lattices. In this Letter we study this problem and show numerical evidence for the existence of DB’s in the ac dynamics of a 2DJJA. We propose this system as an adequate device to carry out the experimental detection of DB’s in a 2D system. In the array, the localized solution corresponds to the voltage localized solution sketched in Fig. 1. Such a nontrivial solution is driven by external currents and, in spite of the numerous studies on the dynamics of 2DJJA, to our knowledge it has been neither detected nor predicted up to the date. In the classical regime, single JJ’s can be modeled by the resistively and capacitively shunted junction RCSJ model. The normalized current through a junction is given by i N ’ ’ _ ’ sin’: (1) In this equation ’ is the gauge invariant phase difference across the junction. The damping is given by 0 =2I c CR 2 p , where 0 is the flux quantum and I c , C, 0 0 0 0 +V V<0 V>0 i x ext i y ext x ij ϕ y ij ϕ i,j+1) ( i,j) ( ( i+1,j ) i,j) ( FIG. 1 (color online). Sketch of a DB, a voltage localized solution, in a 2DJJA. Junctions are represented by crosses. The dc voltage across any junction is zero except across four of them where it is equal to V or V. VOLUME 89, NUMBER 23 PHYSICAL REVIEW LETTERS 2DECEMBER 2002 234101-1 0031-9007= 02=89(23)=234101(4)$20.00 2002 The American Physical Society 234101-1