Superinsulators, Bose Metals and High-Tc Superconductors: The Quantum Physics of Emergent Magnetic Monopoles PDF
Preview Superinsulators, Bose Metals and High-Tc Superconductors: The Quantum Physics of Emergent Magnetic Monopoles
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Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Control Number: 2022936285 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. SUPERINSULATORS, BOSE METALS AND HIGH-Tc SUPERCONDUCTORS The Quantum Physics of Emergent Magnetic Monopoles Copyright © 2022 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 978-981-125-095-8 (hardcover) ISBN 978-981-125-096-5 (ebook for institutions) ISBN 978-981-125-097-2 (ebook for individuals) For any available supplementary material, please visit https://www.worldscientific.com/worldscibooks/10.1142/12688#t=suppl Desk Editor: Ng Kah Fee Typeset by Stallion Press Email: [email protected] Printed in Singapore KKaahhFFeeee -- 1122668888 -- SSuuppeerriinnssuullaattoorrss,, BBoossee MMeettaallss aanndd HHiigghh--TTcc SSuuppeerrccoonndduuccttoorrss..iinndddd 22 77//44//22002222 1122::1155::2255 ppmm April7,2022 12:43 Superinsulators,BoseMetalsandHigh-Tc...-9inx6in b4596-fm pagev To my parents, who made it possible, to my wife, who shared this journey, to my kids, who embark on their own. v B1948 Governing Asia TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk BB11994488__11--AAookkii..iinndddd 66 99//2222//22001144 44::2244::5577 PPMM April7,2022 12:43 Superinsulators,BoseMetalsandHigh-Tc...-9inx6in b4596-fm pagevii Preface Physics courses go a long way to teach students that, while single elec- tric charges are abundant, magnetic charges appear always in insepara- ble dipoles. Magnetic monopoles in a classical gauge theory would entail inadmissiblesingularitieswithinfinite energydensity. Ittookthe geniusof Dirac inthe 1930sto showthat quantummechanicschangesthe game. He showed that, in a quantum theory of electromagnetism, these singularities are unobservable coordinate singularities if the product of all electric and magnetic charges is an integer multiple of the Planck constant h, the main numerical constant governing quantum behaviour. Quantum electromag- netism with magnetic monopoles is thus perfectly consistent. Indeed, grand unified quantum field theories of the electromagnetic, weak and strong interactions do admit fundamental magnetic monopoles, in which the singularities are replaced by tiny inner cores containing very heavyelementaryparticles. Suchfundamentalmonopolesaresoheavythat they could have been produced only in the Big Bang. However, even after four decades ofintensive and dedicated searches,no trace of them has ever been found. This is notthe endofthe storythough. LighterDirac monopolescould be realized as excitations in emergent condensed matter systems, where the typical energyscales are 12to 13 ordersof magnitude smaller than the grand-unifiedscaleofallelementaryinteractions. Notonlycantheyexistas isolated excitations, but, being light bosons, under appropriate conditions they can Bose condense. A condensate of electric charge is a superconduc- tor, carrying current with no resistance. Correspondingly, a condensate of magneticmonopolesisthedualstate,asuperinsulator,opposinganinfinite resistance to electric currents. vii April7,2022 12:43 Superinsulators,BoseMetalsandHigh-Tc...-9inx6in b4596-fm pageviii viii Superinsulators, Bose Metals and High-Tc Superconductors While a condensate shows the most dramatic consequences of emer- gent magnetic monopoles, single excitations also have an important effect. Indeed, they may constitute a trap for pairs of electrons, leading thus to a real-space-localized and very strong pairing mechanism which may be relevant for high-Tc superconductors. Magnetic monopoles and related topological field theories have played a dominant role in my physics career, from my PhD thesis on monopole- induced proton decay catalysis to the first prediction of superinsulation in the mid-90s. In this book I have attempted to assemble a coherentpicture of the physics of emergent Dirac monopoles in condensed matter systems, focusingonboththeobservedandtheasyetpotentialnewstatesofmatter they induce. A warm thank you goes to all collaborators who shared parts of this journey: I have learned a lot from each of them. Carlo A. Trugenberger April7,2022 12:43 Superinsulators,BoseMetalsandHigh-Tc...-9inx6in b4596-fm pageix Contents Preface vii 1. Introduction 1 1.1 Units and notation . . . . . . . . . . . . . . . . . . . . . 5 2. Gauge theories and magnetic monopoles: A first encounter with superinsulators 7 3. Gauge theories in 2+1 dimensions: The Chern–Simons term 17 4. Lattice Chern–Simons term 25 5. Saddle points, topological excitations and instantons 27 5.1 The XY model and vortices . . . . . . . . . . . . . . . . 28 5.2 Quantum wires and phase slips. . . . . . . . . . . . . . . 33 5.3 Compact QED in 2D . . . . . . . . . . . . . . . . . . . . 35 6. Effective Chern–Simons gauge theories of emergent condensed matter systems 41 7. The superconductor-to-insulator transition 51 8. Effective field theory of the SIT tricritical point 59 ix
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