Dependence of the superconducting critical temperature on the number of layers in a homologous series of high-Tccuprates

Abstract

We study a model of n-layer high-temperature cuprates of homologous series like HgBa 2 Ca n−1 Cu n O 2+2n+␦ to explain the dependence of the critical temperature T c ͑n͒ on the number n of Cu-O planes in the elementary cell. Focusing on the description of the high-temperature superconducting system in terms of the collective phase variables, we have considered a semimicroscopic anisotropic three-dimensional vector XY model of stacked copper-oxide layers with adjustable parameters representing microscopic in-plane and out-of-plane phase stiffnesses. The model captures the layered composition and block structure along the c axis of homologous series. Implementing the spherical closure relation for vector variables we have approximately solved the phase XY model with the help of the transfer matrix method and calculated T c ͑n͒ for arbitrary block size n, elucidating the role of the c-axis anisotropy and its influence on the critical temperature. Furthermore, we accommodate inhomogeneous charge distribution among planes characterized by the charge imbalance coefficient R being the function of number of layers n. By making a physically justified assumption regarding the doping dependence of the microscopic phase stiffnesses, we have calculated the values of the parameter R as a function of block size n in reasonable agreement with the nuclear magnetic resonance data of the carrier distribution in multilayered high-T c cuprates.

Theory of Antiferromagnetic Order in High-Tc Oxides: An Approach Based on Ginzburg–Landau Expansion

“…Several authors have studied the effects of interlayer coupling to understand these features from theoretical point of view. [17][18][19][20] Another important aspect of the multilayered systems is the coexistence of superconductivity and antiferromagnetism in a certain region of the phase diagram. [21][22][23] Such phenomenon has been studied theoretically also using t-J model.…”

The Existence of the 60 K Plateau in the YBa2Cu3O6+yPhase Diagram: the Role of Oxygen Ordering and Charge Imbalance

“…The problem reduces then to the evaluation of a determinant of the A N ⊥ (k) matrix (for technical details, we refer readers to Refs. [8,11]). Finally, we arrive at the expression for the critical temperature…”

“…However, in order to describe YBCO phase diagram, it is necessary to relate the model parameters to the amount of oxygen doping. Therefore, we are using a phenomenological dependence of in-plane microscopic phase stiffness of CuO 2 plane on charge (hole) concentration, which was successfully used to describe properties of superconducting homologous series [8]. Furthermore, the dependence between charge concentration and oxygen amount in YBCO was determined experimentally by Tallon et al and found out to be roughly linear in the superconducting region (charge concentration changes from δ = 0.05 for y = 0.4 to δ = 0.17 for y = 1) [12].…”

“…As in Ref. [8], we perform "reverse engineering" approach, i.e. we try to find values of the model parameters that reproduce experimentally observed T c (y) dependence.…”

Charge Imbalance Effects on Interlayer Hopping and Fermi Surfaces in Multilayered High-TcCuprates

“…[23][24][25][26] The interlayer hopping is indispensable for the bulk SC state, even if each CuO 2 plane shows superconductivity. [27][28][29][30][31][32][33] Here, we note two kinds of interlayer hoppings in the multilayered cuprates.…”