Journal of Superconductivity: Incorporating Novel Magnetism, Vol. 14, No. 5, October 2001 ( C  2001) Bose–Einstein Condensation in Layered Systems under Repulsive Interaction I. T ¸ ifrea 1,2 and I. Grosu 1 Received and accepted 15 July 2001 We study the Bose–Einstein condensation in the case of a dilute bosonic layered system. First we consider the case of a free bosonic layered system and discuss the condensation temperature and the temperature dependence of the chemical potential for two different limits: a quasi- two-dimensional and a quasi-three-dimensional system. In the presence of a repulsive boson– boson interaction, we expect important changes in the condensation temperature. We present a qualitative evaluation of the modified condensation temperature, based on a diagrammatic theory for the normal phase in Bose systems. KEY WORDS: Bose–Einstein condensation; layered systems. 1. INTRODUCTION The idea of explaining superconductivity based on ordinary Bose–Einstein condensation (BEC) is not a new one, and it was introduced in the attempt to give a correct explanation of this phenomenon in standard superconducting metals [1]. More recently, a renewed interest in such a description of super- conductivity was reconsidered in connection with the unusual superconducting and normal phases in high temperature superconductors (HTSC). Mainly, there are two important experimental results leading to the conclusion that BEC is important in the case of HTSC. First, the coherence length associated to the fermionic pair in the superconducting phase is much smaller than in the case of standard supercon- ductors, such that a description of the superconduct- ing state in terms of bosonic degrees of freedom is more appropriate than the usual one. Secondly, recent angle-resolved photoemission experiments (ARPES) [2] showed the presence of a pseudogap in the en- ergy spectrum of the normal state, a feature which was associated by different authors [3] to the presence 1 Department of Theoretical Physics, Babes-Bolyai University, 3400 Cluj, Romania. 2 Present address: Department of Physics, Clemson University, Clemson, South Carolina 29634. of fermionic pairs above the superconducting critical temperature. Besides the fact that a general consensus on the superconducting mechanism is lacking, at the present time it is generally accepted that the superconduct- ing phase involves the charge carriers in the CuO planes. Because of the two-dimensional (2D) char- acter of these planes, a lot of effort was directed to the understanding of general physics in 2D metallic systems. It appears that an important role in the su- perconductivity mechanism is played by the chains that couple the CuO planes, leading to a quasi-2D structure in the case of HTSC. However, the inter- layer coupling between the CuO planes is small, and as a consequence the correct study of HTSC materials can be made by considering a strong anisotropy along the z -axis (we chose the z -axis to be perpendicular to the CuO planes) [4]. In this work, motivated by possible applications in the HTSC theory, we address the problem of BEC in layered systems, in which a repulsive interaction among the component bosons is considered. Previ- ously, the problem was considered by Wen and Kan [4] and by Haerding and Ravndal [5] in connection with general properties of HTSC materials. Our calcula- tion is done under the assumption of a dilute layered Bose gas (the implications of such a condition is dis- cussed later). Basically, in the case of layered system, 563 0896-1107/01/1000-0563/0 C  2001 Plenum Publishing Corporation