Microwave absorption by the Josephson network in a low field: Application to ceramic high temperature superconductors Adam Rycerz * , Jozef Spalek Marian Smoluchowski Institute of Physics, Jagiellonian University, Ulica Reymonta 4, 30-059 Krak ow, Poland Abstract We discuss the applied magnetic field dependence of the microwave absorption by a three-dimensional array of up to 30  30  30 Josephson junctions with a random variation of its parameters including the resistivity and the capacity of each junction. The numerical simulation results for the networks show characteristic microwave absorption anomalies observed in the ceramic samples of high temperature superconductor YBa 2 Cu 3 O 7x . A brief discussion in analytical terms is also provided. Ó 2003 Elsevier Science B.V. All rights reserved. Keywords: Magnetically modulated microwave absorption; Dissipative Josephson network; Inhomogeneous superconductors 1. Introduction Soon after the discovery of high temperature superconductivity it has been established [1,2] that in ceramic samples of YBa 2 Cu 3 O 7x there exists a large nonresonant microwave absorption in zero and low applied magnetic fields that can be asso- ciated with the transition to the superconducting phase. An exemplary field dependence of this ab- sorption is displayed in Fig. 1 [1]. A broad absorp- tion structure is modulated by a noisy signal with a clear evidence of a quasiperiodic substructure. One can also observe nonlinear phenomena [3]. Because of the potential application of ceramic high temperature superconductors in various mi- crowave applications, it is important to study the properties of a general three-dimensional array of Josephson junctions shunted by resistance (R), capacitance (C), and with inductance (L), including some random variations of the junction para- meters. For that purpose we consider a lattice depicted in Fig. 2, where h a ijk labels the phase dif- ference in the direction a ¼ x, y , z, and ðijk Þ locate the junction position in the three-dimensional ar- ray. This model was considered in various simpli- fied situations by a number of authors [4]. Here we consider a three-dimensional granular structure and disregard the circumstance that the grains themselves may have a coupled Josephson struc- ture along the c-axis, perpendicular to the CuO 2 planes [5]. In other words, the intergranular critical * Corresponding author. Tel.: +48-12-632-4888; fax: +48-12- 633-4079. E-mail address: adamr@th.if.uj.edu.pl (A. Rycerz). 0921-4534/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-4534(03)00651-8 Physica C 387 (2003) 97–101 www.elsevier.com/locate/physc