FRONTIERS ARTICLE The Chiral Plaquette Polaron Paradigm (CPPP) for high temperature cuprate superconductors Jamil Tahir-Kheli * , William A. Goddard III * Materials and Process Simulation Center (MC 139-74), California Institute of Technology, Pasadena, CA 91125, United States article info Article history: Received 14 January 2009 In final form 10 February 2009 Available online 13 February 2009 abstract A scientific revolution occurred in 1986–1994 in which the T c for the best superconductors exploded from 23 K (Nb 3 Ge) to 138 K (Hg 0.2 Tl 0.8 Ba 2 Ca 2 Cu 3 O 8.33 ). Despite enormous effort over the last 21 years, the superconducting mechanism remains unknown. All previous attempts assumed that the doped holes were in the CuO 2 plane. We showed recently with improved quantum mechanics (QM) calculations that the hole is out of the CuO 2 plane and delocalized over four Cu atoms in a square Plaquette that forms the basis of our Chiral Plaquette Polaron Paradigm (CPPP). Here, we show how very simple geometric argu- ments provide a qualitative understanding of the broad range of cuprate phenomenology. This simple geometric analysis may be useful in guiding the development of materials for improved superconductors. The CPPP suggests that judicious control of the dopant distribution could possibly lead to a room-temper- ature T c . Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction The discovery of superconductivity in Mercury (T c = 4.2 K) in 1911, was followed by Lead (T c = 6 K) in 1912, Nb (T c = 9.25 K) in 1930, NbN (T c = 16.1 K) in 1941, Nb 3 Sn (T c = 18.1 K) in 1954, and Nb 3 Ge (T c = 23.2 K) in 1971 [1]. This slow evolution seemed to be converging to the fundamental limit of 30 K suggested by Morel and Anderson for phonon pairing [2]. Thus, the unanticipated discovery of a cuprate superconductor with T c = 35 K in La 2x Ba x CuO 4 by Bednorz and Muller in 1986 [3] led to an unprecedented explosion of materials and record-breaking T c ’s with 38 K for La 2x Sr x CuO 4 in 1987, 92 K for YBa 2 Cu 3 O 7 in 1987, and finally culminating in (Hg 0.2 Tl 0.8 )Ba 2 Ca 2 Cu 3 O 8.33 with 138 K in 1993. This increase of T c by 115 K took place in just 6 years. Unfortunately, for the past 15 years, the maximum T c has not budged. We believe that this is be- cause there has been no sound theoretical basis for understanding the current materials that could be used as a guidepost in suggesting new materials and structures. This punctuated evolution of the highest T c superconducting materials has resulted from serendipitous discovery of new mate- rial classes, followed by rapid experimental optimization. Theory has played virtually no role in this process. Indeed, it took 46 years to develop the theory underlying the superconductivity of Hg and Pb (discovered in 1911) and explained in 1957 [by Bardeen, Coo- per, and Schrieffer (BCS)] [4]. Since 1986 there have been tens of thousands of theory papers on the cuprates, yet no theory is generally accepted by the commu- nity and none has successfully suggested a way to systematically improve these materials. The world has already waited half the 46 years it took for BCS to explain classical superconductors. Hope- fully, we will not have to wait another 23 to understand the cuprates. The challenge of explaining cuprate superconductivity goes far beyond merely understanding the mechanism of the pairing inter- action that leads to increased T c because the transport properties for the normal (non-superconducting) state of the cuprates are also anomalous. In classical BCS superconductors, the normal state properties are consistent with the standard concepts of a Fermi surface, density of states, and a temperature dependent scattering rate. Thus, the breakthrough of BCS was to find the correct ground state and excitations for the superconducting phase. No new con- cepts were required to explain the normal phase properties. In contrast, a correct theory of the cuprates must simulta- neously explain why superconductivity occurs, the nature of the pairing, the observed superconducting d x2y2 gap symmetry (called D-wave) where the x- and y-axes are along the planar Cu–O bond directions, the high T c , the doping phase diagram, and the numer- ous anomalies observed in the electronic and magnetic transport properties of the normal state above T c . These anomalies extend over the complete range of doping for which the cuprates are superconductors. We believe understanding the ‘anomalous’ normal state trans- port properties of cuprates is an extremely important problem in itself because one might be able to modify or enhance these prop- erties to create new types of devices coupling electronic, magnetic, 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.02.025 * Corresponding authors. Fax: +1 626 585 0918. E-mail addresses: jamil@wag.caltech.edu (J. Tahir-Kheli), wag@wag.caltech.edu (W.A. Goddard III). Chemical Physics Letters 472 (2009) 153–165 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett