Giant Superconducting Proximity Effect in Composite Systems Chun Chen and Yan Chen Dept. of Physics and Lab of Advanced Materials, Fudan University, Shanghai 200433, China Abstract Searching routes to raise the superconducting transition temperature (Tc) is one of the major pursuits of current research in condensed matter physics. Although until now, there is not yet a wide-accepted consensus on the electron-pairing mechanism of cuprate materials and iron-pnictides, condensed matter theorists believe that two relevant quantities: the pairing gap amplitude as well as the phase stiffness determine the Tc of a superconducting material. Turning this logic around, we study a composite system consisting of a realistic underdoped cuprates layer modeled by a t-t’-J model and a metallic layer. Due to the different correlation nature of two layers, the interlayer coupling may lead to giant superconducting proximity effect and the superconducting order parameter at the metallic layer could be greatly enhanced at zero temperature. Formalism Introduction Recently S. Kivelson group at Stanford (PRB 78, 094509 (2008)) proposed a possible route to high-temperature superconductivity in composite systems. They studied a simple two-component model consisting of a metallic layer and an underdoped pairing layer modeled by negative-U Hubbard model, and suggested that Tc of the whole system can be greatly enhanced by increasing the interlayer coupling. D.H. Lee (Physics 1, 19 (2008)) highlighted the importance of this theoretical work and gave a lucid paraphrase as follows by making an analogy to Josephson junction array. The Hamiltonian of the Model We choose the well-established t-t’-J model to describe the pairing layer and the metallic component is modeled by a tight binding Hamiltonian: Using renormalised mean field theory and Gutzwiller approximation, we introduce two renormalised factors to replace the projection operators: t-t’-J layer metallic layer tc J tc’ tf To calculate the superconducting order parameters, we utilize an orthogonal matrix to diagonalize the effective Hamiltonian: As the left panel shows in the limit of large charge energy, the number of Cooper pairs within individual islands are strongly localized and the system becomes insulating, but once this Josephson junction array attached to a nearby metal, superconductivity could be restored. However this negative-U model is over simplified and doped Mott insulator physics has not been seriously considered in such composite systems. Motivated by this new proposal of higher Tc, we study a similar composite system consisting of a realistic underdoped cuprates layer modeled by a t-t’-J model and a metallic layer (illustrated in the above right panel). By using the renormalized mean field theory of t-J model, we examined the pairing gap amplitudes of the two layers at zero temperature. Our results show that by increasing the interlayer coupling, the pairing gap of t-t’-J layer is suppressed while the gap at the metallic layer Δm could be greatly enhanced. The value of Δm could be even greater than the superconducting order parameter of the underdoped cuprates layer. and four distinct mean fields are defined as usual: Density of states After diagonalizing the Hamiltonian, the bare single-particle Green’s function is given by and the density of states can be calculated from the retarded Green’s function: Numerical Results Density of states Superconducting Order Parameters When the hopping between these two layers is strong, the SC order parameter of t-t’-J layer will decrease, while in the metallic layer such a parameter will be enhanced remarkably, which is even greater than that of a single t-t’-J layer. Meanwhile we notice that such a peak of the metallic layer appears in the underdoped region of the superconducting layer. The right panel depicts the SC order parameter as a function of chemical potential. Here resonance peak in the DOS spectra of the composite does not directly correspond to the mean field order parameters of two individual layers , but through a complicated relationship. One salient feature is that the interlayer coupling may split the original single peak. Summary Due to the different correlation nature of composite system, the SC order parameter at the metallic layer could be greatly enhanced. 2. The LDOS spectra show the splitting of the resonance peak because of the interlayer coupling.