Scaling of the transition temperature of hole-doped cuprate superconductors with the charge-transfer energy

We use first-principles calculations to extract two essential microscopic parameters, the charge-transfer energy and the inter-cell oxygen-oxygen hopping, which correlate with the maximum superconducting transition temperature Tc,max across the cuprates. We explore the superconducting state in the three-band model of the copper-oxygen planes using cluster Dynamical Mean-Field Theory. We find that the variation in the charge-transfer energy largely accounts for the empirical trend in Tc,max, resolving a long-standing contradiction with theoretical calculations. editor’s choice Copyright c © EPLA, 2012 Introduction. – Despite an immense body of theoretical and experimental work, we have limited microscopic insights of which materials-specific parameters govern the trends in the maximum transition temperature Tc,max across the copper oxide superconductors. Structurally, all the cuprate families have in common CuO2 planes which support superconductivity. They are described by the chemical formula XSn−1(CuO2)n, where n CuO2 planes are interleaved with n− 1 spacer layers S to form a multilayer. These multi-layers are then stacked along the c-axis, separated by a different spacer layer X. Empirically, it is known that Tc,max is strongly materials-dependent, ranging from 40K in La2CuO4 to 138K in HgBa2Ca2Cu3O8. Additionally, Tc,max can be tuned both as a function of doping and the number n of CuO2 planes. Studies linking the known empirical trends to microscopics have generally established that the properties of the apical atoms (O, F or Cl, depending on the cuprate family) are the relevant materials-dependent parameters. However, conclusions vary regarding their effects on electronic properties, especially in multi-layer cuprates where not all CuO2 have apical atoms. Early theoretical work by Ohta, et al., found correlations between Tc and the Madelung potential of the apical oxygen, arguing that the apical potential controls the stability of the ZhangRice singlets [1]. They conclude that d Cu-O , the distance between the Cu and apical O, is uncorrelated with superconductivity. In a more recent DFT study, Pavarini et al., argue that d Cu-O tunes between the single-layer cuprate families, affecting the electronic structure primarily via the one-electron part of the Hamiltonian [2]. Moving the apical oxygens away from the copper oxide plane allows stronger coupling of in-plane O 2p orbitals to the Cu 4s, enhancing the strength of longer ranged hoppings. This effect is characterized by the increase of a range parameter r∼ t′/t, describing the relative strength of the nextnearest-neighbor hopping t′ to nearest-neighbor hopping t in a one-band model. They find that materials with larger r have larger Tc,max. Many-body corrections to t ′ were included by Yin et al. [3]. The development of cluster Dynamical Mean-Field Theory (c-DMFT) combined with first-principles calculations [4,5] has advanced our qualitative and quantitative understanding of the cuprates [6,7]. A satisfactory description of these materials at intermediate energy scales has been achieved, and the consensus is that the cuprates lie in the regime of intermediate correlation strength [8–10] near the Zaanen-Sawatzky-Allen (ZSA) boundary [11]. However, all numerical studies [12–14] contradict the empirical trend of Tc,max with the range parameter r. In this paper, we address the origin of the variation of the experimental Tc,max across the cuprates using recent advances in electronic structure methods. We carry out first-principles calculations of the hole-doped cuprates, extract chemical parameters by downfolding to the 3-band