## Electron Correlation in MetalsSince the discovery of high Tc superconductivity, the role of electron correlation on superconductivity has been an important issue in condensed matter physics. Here the role of electron correlation in metals is explained in detail on the basis of the Fermi liquid theory. The book, originally published in 2004, discusses the following issues: enhancements of electronic specific heat and magnetic susceptibility, effects of electron correlation on transport phenomena such as electric resistivity and Hall coefficient, magnetism, Mott transition and unconventional superconductivity. These originate commonly from the Coulomb repulsion between electrons. In particular, superconductivity in strongly correlated electron systems is discussed with a unified point of view. This book is written to explain interesting physics in metals for undergraduate and graduate students and researchers in condensed matter physics. |

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### Contents

1 | |

2 Fermi liquid theory | 22 |

3 Andersons orthogonality theorem | 29 |

4 sd Hamiltonian and Kondo effect | 49 |

5 Anderson Hamiltonian | 72 |

6 Hubbard Hamiltonian | 103 |

7 Fermi liquid theory of strongly correlated electron systems | 122 |

8 Transport theory based on Fermi liquid theory | 147 |

9 Superconductivity in strongly correlated electron systems | 159 |

Appendix A Feynman relation | 223 |

Appendix B Second quantization | 224 |

Appendix C Interaction representation and thermal Greens function | 226 |

Appendix D Linear response theory | 233 |

Appendix E Transport equation derived by Eliashberg | 238 |

243 | |

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### Common terms and phrases

Anderson Hamiltonian antiferromagnetic assume atom charged particle coefﬁcient conduction electrons correlated electron systems corresponding coulomb interaction coulomb repulsion critical temperature Tc cuprates d-electron damping rate decreases deﬁned degeneracy derivative diagrams doping down-spin effect electron correlation electron interaction electron number electron–hole pair electron–hole pair excitations equation exchange interaction f electrons Fermi energy Fermi liquid theory Fermi surface ﬁeld ﬁrst term FLEX approximation ﬂuctuations free electron given Green’s function ground heavy fermions Hubbard Hamiltonian Hubbard model impurity Kondo localized spin low temperatures magnetic many-body metals momentum Mott insulator Mott transition obtain orthogonality theorem overlap integral parameter Phys possessing potential pseudogap quasi-particles reduced renormalization resistivity respectively result s-wave second term self-consistent self-energy shown in Fig singlet specific heat spin fluctuations spin-triplet strongly correlated electron superconducting superconducting fluctuations T-matrix T2 term under-doped vertex correction wave-function Yamada