Springer Series in Solid-State Sciences Volume 186 Series editors Bernhard Keimer, Stuttgart, Germany Roberto Merlin, Ann Arbor, MI, USA Hans-Joachim Queisser, Stuttgart, Germany Klaus von Klitzing, Stuttgart, Germany
The Springer Series in Solid-State Sciences consists of fundamental scientific books prepared by leading researchers in the field. They strive to communicate, in a systematic and comprehensive way, the basic principles as well as new developments in theoretical and experimental solid-state physics. More information about this series at http://www.springer.com/series/682
Ferdinando Mancini Roberta Citro Editors The Iron Pnictide Superconductors An Introduction and Overview 123
Editors Ferdinando Mancini International Institute for Advance Scientific Studies Vietri sul Mare, Salerno Italy Roberta Citro Dipartimento di Fisica E.R. Caianiello Università degli Studi di Salerno Fisciano, Salerno Italy ISSN 0171-1873 ISSN 2197-4179 (electronic) Springer Series in Solid-State Sciences ISBN 978-3-319-56116-5 ISBN 978-3-319-56117-2 (ebook) DOI 10.1007/978-3-319-56117-2 Library of Congress Control Number: 2017936466 Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface This volume The Iron Pnictide Superconductors An Introduction and Overview covers different theoretical aspects of the physics of iron-based superconductors ranging from the analytical to numerical and computational ones. It starts from the basic theory modeling many-body physics in Fe-superconductors and other multi-orbital materials to go to the studies on magnetic, superconducting, and nematic order instabilities. Finally, it offers a comprehensive overview of the recent advancements in the theoretical investigations of Mott transition and strong correlations in iron-based superconductors. The book contains the notes of the lectures delivered at the Nineteenth Training Course in the Physics of Strongly Correlated Systems held in Vietri sul Mare (Salerno, Italy) in October 2015. The course consisted of four lectures every morning, held by Professors Bernd Büchner, Massimo Capone, Luca de Medici, Ilya Eremin, and JörgSchmalian, and afternoon activities (seminars delivered by the junior researchers, solving of specific problems, roundtable on hot topics, hands-on training on relevant numerical issues ) aimed principally at promoting discussions between the attendees and the lecturers. The outcome of this type of course was a significant interchange of ideas among the participants thanks to both the enlightening morning lectures and the long afternoon sessions devoted to discussions. The book has both introductory and pedagogical aspects that could be very useful for researchers entering the field of unconventional superconductivity. The readers will strongly benefit from the different overviews on the topic of multi-band superconductivity in iron-based superconductors. We wish to acknowledge the support of those institutions that made the course possible. The main sponsors of the event were the Department of Physics E.R. Caianiello University of Salerno and the International Institute for Advanced Scientific Studies E.R. Caianiello. Salerno, Italy Ferdinando Mancini Roberta Citro v
Contents 1 Iron Based Supercondutors: Introduction to the Volume.... 1 Roberta Citro and Ferdinando Mancini References.... 5 2 Itinerant Magnetic Order and Multiorbital Effects in Iron-Based Superconductors... 7 Felix Ahn, Johannes Knolle and Ilya Eremin 2.1 Introduction... 7 2.2 A Primer: Spin Density Wave and Spin Waves in the Single-Band Hubbard Model... 9 2.3 Selection of Magnetic Order in the Parent Phase of Iron Based Superconductors... 12 2.3.1 Magnetic Frustration... 12 2.3.2 Lifting the Magnetic Ground State Degeneracy at T N... 15 2.4 Orbital Structure of Spin Density Wave State.... 18 2.4.1 Transformation from Orbital to Band Basis.... 20 2.4.2 Spin Density Wave Mean Field Equations... 22 2.4.3 Numerical Results... 25 2.5 Orbital Effects for the Superconducting State... 26 2.5.1 Leading Angular Harmonics Approximation... 30 2.5.2 Superconductivity with the Bare Interactions.... 33 2.6 Spin Waves in Itinerant Multiorbital Systems.... 37 2.6.1 Multiorbital Models - Spin Wave Theory... 38 2.6.2 Itinerant Frustration and Accidental Zero Modes.... 41 2.6.3 Two Orbital Model: Orbital Versus Excitonic Scenario.... 43 2.6.4 Comparison to Experiments.... 47 2.7 Discussion... 49 References.... 49 vii
viii Contents 3 Nematic Order and Fluctuations in Iron-Based Superconductors...... 53 Una Karahasanovic, Rafael M. Fernandes and Joerg Schmalian 3.1 Introduction... 53 3.1.1 In the Search for Nematic Phases... 54 3.1.2 The Ising Nematic State in Iron-Based Superconductors: Brief Introduction, Current State of the Art and Open Questions.... 54 3.2 Summary of Collective Field Theories of Magnetism.... 56 3.2.1 Hertz-Millis Theory of Magnetism... 56 3.2.2 Introducing the Large-N Approach... 63 3.3 Emergent Nematic Order in Iron Based Systems... 66 3.3.1 Heuristic Picture of the Spin-Driven Nematic Scenario... 66 3.3.2 Order-Parameter Theory of Stripe-density-wave Phase.... 68 3.3.3 Ising-Nematic Order... 73 3.3.4 Sketch of the Phase Diagram.... 74 3.4 Elastic Coupling and Spin-Driven Nematicity in Iron-Based Superconductors... 75 3.4.1 Elastic Theory of a Tetragonal System... 76 3.4.2 Model... 77 3.4.3 u 4 Theory of Nematic Degrees of Freedom... 78 3.4.4 Estimate of the Mean-Field Regime of Nematic Degrees of Freedom... 85 3.5 Physical Observables... 86 3.5.1 Softening of the Elastic Modulus in the Vicinity of the Nematic Transition... 86 3.5.2 Resistivity Anisotropy... 89 3.5.3 Raman Spectroscopy in the Tetragonal Phase... 92 3.5.4 Raman Resonance Mode in the Superconducting State... 105 3.5.5 Magnetic Spectrum... 109 3.6 Nematic Fluctuations and Pairing... 110 References.... 111 4 Modeling Many-Body Physics with Slave-Spin Mean-Field: Mott and Hund s Physics in Fe-Superconductors... 115 Luca de Medici and Massimo Capone 4.1 The Theoretical Description of Iron-Based Superconductors.... 115 4.2 Strong Electronic Correlations... 118 4.2.1 The Band Theory of Solids: A Brief Reminder... 118 4.2.2 Electron Electron Interactions and Correlations.... 122
Contents ix 4.2.3 The Mott Transition and Mott Insulators.... 123 4.2.4 Fermi-Liquids and Effective Mass... 125 4.3 The Hubbard Model... 128 4.3.1 Complement: Single-Band Hubbard Model at Particle-Hole Symmetry.... 130 4.3.2 Which Materials Are Likely to Be Strongly Correlated?... 132 4.4 Slave-Particle Approaches... 133 4.5 The Slave-Spin Formalism and Its Mean-Field.... 135 4.5.1 Mean-Field Approximation... 139 4.5.2 Complement: Derivation of the Gauge c for Arbitrary Filling... 142 4.5.3 Complement: Fermi-Liquid Quasiparticle Weight and Mass Enhancement... 144 4.5.4 The Half-Filled Single-Band Hubbard Model... 145 4.5.5 Complement: Critical U for the Mott Transition in the Single-Orbital Hubbard Model... 146 4.5.6 The Hubbard Model for Finite Doping... 147 4.6 Multi-orbital Correlations: Hund s Coupling.... 148 4.6.1 Complement: Particle-Hole Symmetry in the Multi-orbital Hubbard Model... 151 4.6.2 Extension of the Slave-Spin Formalism to Multi-orbital Hubbard Models.... 151 4.6.3 The N-Orbital Hubbard Model... 153 4.6.4 Complement: Critical U for the Mott Transition in the 2-Orbital Hubbard Model... 155 4.6.5 Effect of Hund s Coupling on the Mott Transition... 157 4.6.6 The Physics of the Mott Gap... 159 4.6.7 Hund s Effect on Orbital Fluctuations and the Narrowing of the Hubbard Bands... 161 4.6.8 Complement: Comparison with DMFT... 165 4.6.9 Complement: Critical U for the Mott Transition in the 2-Orbital Hubbard Model for Large Hund s Coupling J, and Orbital Decoupling... 166 4.6.10 Hund s-induced Orbital Decoupling... 169 4.7 Slave-Spin Modeling of Fe-Based Superconductors... 171 4.8 Concluding Remarks... 178 References.... 183 Index... 187
Contributors Felix Ahn Institut Für Theoretische Festkörperphysik III, Ruhr-Universität Bochum, Bochum, Germany Massimo Capone SISSA, Trieste, Italy Roberta Citro Dipartimento di Fisica E.R. Caianiello, Università degli Studi di Salerno, Fisciano (SA), Italy; IIASS, International Institute for Advanced Scientific Studies E.R. Caianiello, Vietri sul Mare (SA), Italy Luca de Medici ESPCI, Paris, France Ilya Eremin Institut Für Theoretische Festkörperphysik III, Ruhr-Universität Bochum, Bochum, Germany Rafael M. Fernandes School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA Una Karahasanovic Institut für Theorie der Kondensierten Materie and Institut für Festkörperphysik, Karlsruher Institut für Technologie, Karlsruhe, Germany Johannes Knolle TCM Group, Cavendish Laboratory, Cambridge, UK Ferdinando Mancini Dipartimento di Fisica E.R. Caianiello, Università degli Studi di Salerno, Fisciano (SA), Italy; IIASS, International Institute for Advanced Scientific Studies E.R. Caianiello, Vietri sul Mare (SA), Italy Joerg Schmalian Institut für Theorie der Kondensierten Materie and Institut für Festkörperphysik, Karlsruher Institut für Technologie, Karlsruhe, Germany xi