Eur. Phys. J. B 72, 583–589 (2009) DOI: 10.1140/epjb/e2009-00394-9 Regular Article T HE EUROPEAN P HYSICAL JOURNAL B Phase diagram for a t-J bilayer: role of interlayer couplings A. Medhi 1,2, a , S. Basu 2 , and C. Kadolkar 2 1 Department of Basic Sciences and Social Sciences, North-Eastern Hill University, Shillong 791022, India 2 Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, India Received 7 March 2009 / Received in final form 10 April 2009 Published online 20 November 2009 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2009 Abstract. The phase diagram for a t-J bilayer as a function of interplanar hopping, t ⊥ and hole concen- tration, x is presented for a few different values of interplanar exchange, J ⊥ using variational Monte Carlo calculations. The phase diagram shows rich features, such as a coexistence of antiferromagnetism and su- perconductivity at underdoping, planar (d-wave) and interplanar (dz -wave) superconducting correlations for small and large J ⊥ , respectively at optimal and overdoping. Another unusual feature appears in the form of a dome shaped structure in the phase diagram where the superconducting correlations are initially assisted as interplanar hopping is enhanced for small t ⊥ , while larger t ⊥ is found to be detrimental to superconductivity. PACS. 71.10.Fd Lattice fermion models – 74.25.Dw Superconductivity phase diagrams 1 Introduction The study of phase diagrams in the models of correlated electron systems has been in the focus of researchers due to the interesting interplay of strong interactions with exter- nal agencies, e.g. temperature, pressure, doping etc. Spe- cial attention is given to strongly interacting models in two dimensions, e.g. a t-J model because of its relevance to the physics of the cuprate superconductors. Attempts with varied degree of reliability to calculate the ground state properties of a two dimensional t-J model are plenty. They range from using analytical tools [1] to different vari- ants of the Monte Carlo method [2–4]. However, mostly the emphasis has been on planar systems and the physics that plays a crucial role due to presence of two or more layers has received limited attention. In this work, we con- sider a t-J model for bilayer superconductors and examine its ground state properties as a function of interlayer cou- plings, using the variational Monte Carlo (VMC) method. A number of previous studies on this model exist [5–10], which examined its properties mainly within the mean- field approximation. However, a comprehensive study of the phase diagram of the model, by taking into account the strong correlations properly, has been lacking. This forms the motivation for our work. Apart from the above, the work also assumes sig- nificance due to a number of reasons. The momentum a e-mail: amedhi@iitg.ernet.in dependence of the superconducting gap, Δ k has been one of the major issues in the high-T c superconductors. The general conclusion from angle resolved photoemis- sion spectroscopy (ARPES) and tunneling experiments is that Δ k has d-wave symmetry [11,12]. It is maximum near the antinodal (0,π) or (π, 0) points and is zero along the nodal (π,π) direction. However, there exists a number of experimental evidences which suggest that the gap sym- metry is more complex than a simple d-wave. An early report in this regard is the ARPES result for the energy gap in Bi 2 Sr 2 CaCu 2 O 8+x (Bi2212) by Ding et al. [13]. They find that the gap does not vanish along (π,π) direc- tion, instead the node is split into two and lies near the (π,π) line on its either side. Similar result was obtained by Vobornik et al. [14] who found an energy gap of ∼9 meV along the Brillouin zone diagonal for heavily overdoped Bi2212. More recently, analyzing high-resolution spectro- scopic data on Bi2212, Zhao [15] concludes that the diag- onal superconducting gap in the compound is of ∼7 meV. These results are in direct contrast to a d-wave scenario of the superconducting gap. Zhao argues that the pho- toemission and tunneling experiments are surface sensi- tive and hence may not reveal the true gap characteris- tics of the bulk materials. In fact, his results support a gap with an extended s-wave symmetry having eight line nodes. However such evidences contradicting the d-wave scenario seem to be coming only from bilayer materials. A very recent ARPES study on high quality single crystal