Journal of Superconductivity: Incorporating Novel Magnetism, Vol. 17, No. 2, April 2004 ( C  2004) Hole Doping and Inhomogeneous Charge Distribution in High T c Cuprates Investigated from First Principles C. Ambrosch-Draxl, 1 E. Y. Sherman, 1 H. Auer, 1 and T. Thonhauser 2 Received 10 August 2003 To understand the link between doping and electronic properties in the high-temperature superconductors, we have performed first-principles calculations for several representatives of high T c compounds. In the single-layer cuprate HgBa 2 CuO 4 the excess oxygen attracts electrons from the CuO 2 plane leading to an increase of the hole concentration in this building block, where the maximum amount of holes is reached when the dopant oxygen shell is closed. The usage of supercells allows to study the inhomogeneous charge distribution as a function of doping, i.e. from the underdoped up to the overdoped regime. Comparison is made with other compounds like Ba-doped La 2 CuO 4 and oxygen-deficient YBa 2 Cu 3 O 7−x . The effects of our findings on superconductivity are discussed. KEY WORDS: high T c , cuprates; hole doping; LAPW. 1. INTRODUCTION The critical temperature in high T c cuprates can be strongly altered by doping, where in most cases the undoped materials are anitferromagnetic insulators, and the metallic state is reached by doping through the replacement of ions or by introduction of excess oxygen. While the doping concentration is governed by the sample preparation, for most of the theoretical models describing the physical properties and the superconducting phase transition the hole content rather than the doping level is the crucial input parameter. The present work is dedicated to establish a link between these two quantities, since a profound understanding of superconductivity can only be achieved by the detailed knowledge of how doping influences the number of carriers in the normal state. In this context, we study where the excess charge goes upon doping, in particular, how the carrier concentration in the copper–oxygen planes is affected. Moreover the question is raised, what the limiting factor for the amount of holes is. 1 Institut f¨ ur Theoretische Physik, Universit ¨ at Graz, Univer- sit ¨ atsplatz 5, Graz, Austria. 2 Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802. This is a crucial point toward the understanding of a universal relationship between the hole content and T c / T max c [1] which is characterized by a linear increase for low doping levels followed by a plateau. To address these questions, we have carried out first-principles studies for a series of high T c cuprates in the framework of density functional theory (DFT). In this work we will mostly concentrate on the simplest representative of the Hg-based high T c compounds, HgBa 2 CuO 4+δ , but will consider results for other cuprates for comparison. The superconducting transition temperature of HgBa 2 CuO 4+δ is close to 97 K at ambient pres- sure which is the highest T c among all single-layer cuprates. No consensus exists among experimental works about the optimal doping concentration δ opt , which ranges from 0.13 [2,3] via 0.18 [4] up to 0.22 [5]. A recent theoretical paper [6] supports the ex- perimental findings of Xiong et al. [5] also providing an explanation for the limit in the number of holes. It was found there that the dopant oxygen behaves fully ionically where the number of charge carriers in the CuO 2 plane reaches its maximum and thus a plateau when the O 2− configuration is formed. In this work, we will study the mean charge carrier concentration as well as the inhomogeneous hole distribution as a function of doping. Focusing 215 0896-1107/04/0400-0215/0 C  2004 Plenum Publishing Corporation