0020-1685/05/4112- © 2005 Pleiades Publishing, Inc. 1247 Inorganic Materials, Vol. 41, No. 12, 2005, pp. 1247–1255. Translated from Neorganicheskie Materialy, Vol. 41, No. 12, 2005, pp. 1415–1424. Original Russian Text Copyright © 2005 by Yarzhemsky, Nefedov. INTRODUCTION Understanding the mechanism of superconductivity and the role of the electronic structure in this phenom- enon is crucial for practical application of supercon- ductors. It is, therefore, worth briefly reviewing the field. At present, there is no theory of high-T c supercon- ductivity suitable for “ab initio” calculations of super- conducting properties, necessary for confirming assumptions about the pairing potential. At he same time, correct symmetry interpretation of experimental data might provide information on the pairing potential. The Bardin–Cooper–Schrieffer (BCS) theory of superconductivity [1] explains these phenomena in pure metals in terms of electron coupling into spheri- cally symmetric singlet Cooper pairs with zero total momentum by virtue of electron–phonon interaction. Owing to the spherical symmetry, the energy gap does not fully close, which leads to exponential temperature dependences of physical quantities. After the discov- ery of high-T c superconductivity by Bednorz and Müller [2], it has become clear that some concepts in the BCS theory, in particular the symmetry of electron pairs and the pairing potential, must be revised. Char- acteristically, the resistivity of high-T c superconduc- tors (HTSCs) in the normal state is a linear function of temperature, in contrast to the quadratic behavior of resistivity in metals. Note that the unusual temperature dependence of resistivity in La 1.8 Ba 0.2 CuO 4 was found before the discovery of HTSCs [3]. The specific heat of YBaCuO below T c scales as T 2 , but there is a compo- nent proportional to T. These findings provide clear evidence that high-T c materials are unconventional superconductors, i.e., their pairing wavefunction is not fully symmetric. The angle-resolved photoelectron spectra of HTSCs (Fig. 1) [4, 5] and their conductivity spectra [6] show a deep minimum along the diagonals of the base. These experimental data indicate that high-T c superconductiv- ity cannot be described by the s-pairing model and is unconventional. The fact that the pairing function is zero at points and on lines of the Fermi surface leads to power-law behavior of many physical quantities, in par- ticular, specific heat C and NMR relaxation rate 1/T 1 . Symmetry of Two-Electron States in Unconventional Superconductors V. G. Yarzhemsky and V. I. Nefedov Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninskii pr. 31, Moscow, 119991 Russia e-mail: vgyar@igic.ras.ru Received June 16, 2005 Abstract—A group-theoretical approach is developed to constructing two-electron states in the basis of one- electron states of crystals. Such states correspond to Cooper pairs in superconductors and pseudogap states (at T* > T c ). The theory is applied to unconventional superconductors: heavy-fermion and high-T c materials. Com- parison of theoretical results with experimental data is used to gain insight into the structure of two-electron states in these materials. Y S X Γ (a) (b) (c) Y S Γ X X Γ S Y T = T c T c < T < T* T = T* Fig. 1. Fermi surface of a high-T c material (solid lines) at different temperatures; the dashed lines correspond to the superconducting phase [48].