Low-Temperature Thermal and Vibrational Properties of Disordered Solids A Half-Century of Universal “Anomalies” of Glasses B1948 Governing Asia TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk BB11994488__11--AAookkii..iinndddd 66 99//2222//22001144 44::2244::5577 PPMM Low-Temperature Thermal and Vibrational Properties of Disordered Solids A Half-Century of Universal “Anomalies” of Glasses Editor Miguel A Ramos Universidad Autonóma de Madrid, Spain World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO Published by World Scientific Publishing Europe Ltd. 57 Shelton Street, Covent Garden, London WC2H 9HE Head office: 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 Library of Congress Control Number: 2022942058 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. LOW-TEMPERATURE THERMAL AND VIBRATIONAL PROPERTIES OF DISORDERED SOLIDS A Half-Century of Universal “Anomalies” of Glasses Copyright © 2023 by World Scientific Publishing Europe 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 978-1-80061-257-0 (hardcover) ISBN 978-1-80061-258-7 (ebook for institutions) ISBN 978-1-80061-259-4 (ebook for individuals) For any available supplementary material, please visit https://www.worldscientific.com/worldscibooks/10.1142/Q0371#t=suppl Desk Editor: Joseph Ang Typeset by Stallion Press Email: [email protected] Printed in Singapore JJoosseepphh -- QQ00337711 -- LLooww--TTeemmppeerraattuurree TThheerrmmaall aanndd VViibbrraattiioonnaall PPrrooppeerrttiieess..iinndddd 11 2277//77//22002222 11::4433::1144 ppmm July27,2022 19:24 Low-TemperatureThermalandVibrational...-9inx6in b4719-fm pagev (cid:2)c 2023 World Scientific Publishing Company https://doi.org/10.1142/9781800612587 fmatter Preface About 50 years ago, a seminal paper by Zeller and Pohl established that specific heat and thermal conductivity at low temperatures in amorphous solids were unexpectedly very different from the behavior found in their crystalline counterparts. Only one year later, two independent works, one written by W.A. Phillips, another one by Anderson, Halperin, and Varma, postulated what is usually known as the Tunneling Model. A simple assumption about the general existence of a random distribution of two-level systems in non-crystalline solids appeared to successfully account for the “anomalous” behavior of thermal properties, as well as acoustic or dielectric properties investigated thereafter, at least below 1 K. Aftertheabovementioned publicationbyZellerandPohlin1971, two decades of intensive research followed, especially focused on thermal and acoustic properties at very low temperatures. Then, the phenomenology of glasses (amorphous solids) seemed clear and well understood within the Tunneling Model. A few good review books summarized all those results and findings. Nevertheless, in the second half of this “half-century of universal anomalies of glasses”, someother research directions andunexpected results started to arise, especially around the feature known as the “boson peak”, well beyond the range covered by the successful Tunneling Model. Furthermore, even the apparent success of this model in its range of applicability was seriously questioned. To address all these most recent advances in a comprehensive way is the goal of this book. With the generous contributions of v July27,2022 19:24 Low-TemperatureThermalandVibrational...-9inx6in b4719-fm pagevi vi Low-Temperature Thermal and Vibrational Properties of Disordered Solids several reputed scientists in the field, and ranging from experimental to theoretical physics, this book aims to offer a timely review of low-temperaturethermalandvibrationalpropertiesofglasses,andof disorderedsolids in general. From thevery beginning,ithas beenmy intention that the book should provide a coherent, but at the same time unbiased,broadsurvey of thetopic. Most chapters werewritten by prominent researchers in each discipline, though sometimes with differentviewsorapproachesonthemostcontroversialissues,suchas theverynatureofthe“bosonpeak”,theroleofultrastableglasses,or the glassy behavior found in crystalline solids with different degrees of disorder. The contents of the book are described in detail in the introductory first chapter and will not be repeated here. Ithas notbeenan easy task to coordinateand editthis collective book, especially hampered by the global pandemic that we have suffered during the last two years. Some changes and unwanted decisions hadtobemadealongtheway. Finally, wereached thegoal. For this, I am very grateful not only to all the contributors but also to those colleagues who encouraged me to move on and/or revised some chapters of the book, namely, Andr´es Cano, Stephen Elliott, Anthony Leggett, Herbert Schober, Sebasti´an Vieira, and Alessio Zaccone. I also thank the editors of World Scientific Publications for their patience and understanding. I do hope that this book will be useful for both experienced researchers in the field and younger researchers who are beginning to dive into the complex sea of low-temperature properties and low- frequency dynamics of glasses or non-crystalline solids. Miguel A´ngel Ramos Universidad Aut´onoma de Madrid, Spain July27,2022 19:24 Low-TemperatureThermalandVibrational...-9inx6in b4719-fm pagevii (cid:2)c 2023 World Scientific Publishing Company https://doi.org/10.1142/9781800612587 fmatter Contents Preface v Chapter 1. Introduction: About 50 Years of Two-Level Systems and Boson Peak 1 Miguel A. Ramos 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 How Universal Are “Universal Anomalies” of Glasses? . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Aim and Contents of this Book . . . . . . . . . . . . . . 13 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Chapter 2. Low-Temperature Specific Heat of Glasses and Disordered Crystals 21 Miguel A. Ramos 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2 The Specific Heat of Glasses vs Crystals . . . . . . . . 25 2.1 The specific heat below 1 K . . . . . . . . . . . . 27 2.2 The specific heat above 1 K . . . . . . . . . . . . 28 3 Glassy Features in Disordered Crystals. . . . . . . . . 32 3.1 Mixed crystals . . . . . . . . . . . . . . . . . . . . . 32 3.2 Orientationally-disordered crystals (“glassy crystals”) . . . . . . . . . . . . . . . . . . 34 3.3 Other disordered crystals with glassy behavior . . . . . . . . . . . . . . . . . . . . . . . . . 35 vii July27,2022 19:24 Low-TemperatureThermalandVibrational...-9inx6in b4719-fm pageviii viii Low-Temperature Thermal and Vibrational Properties of Disordered Solids 4 Low-temperature Specific Heat of Highly-stable Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5 Theories and Models . . . . . . . . . . . . . . . . . . . . 43 5.1 Tunneling Model . . . . . . . . . . . . . . . . . . . 43 5.2 The maximum in Cp/T3 in glasses and in crystals . . . . . . . . . . . . . . . . . . . . . . . . 47 5.3 Soft potential model . . . . . . . . . . . . . . . . . 48 5.4 Other theories and approaches . . . . . . . . . . 51 6 Discussion: How Universal is the Linear Term in the Specific Heat of Glassy Materials . . . . . . . . . . . . 52 7 Conclusion and Outlook . . . . . . . . . . . . . . . . . . 59 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Chapter 3. Thermal Conductivity of Glasses and Disordered Crystals 69 A. I. Krivchikov and A. Jez˙owski 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2 Low-Temperature Thermal Conductivity Data . . . . 70 2.1 Studies in the decade 1971–1980 . . . . . . . . . 70 2.2 Studies in the decade 1981–1990 . . . . . . . . . 72 2.3 Studies in the decade 1991–2000 . . . . . . . . . 73 2.4 Studies in the decade 2001–2010 . . . . . . . . . 75 2.5 Studies in the decade 2011–2020 . . . . . . . . . 76 3 Theoretical Descriptions . . . . . . . . . . . . . . . . . . 78 3.1 Standard Tunneling Model . . . . . . . . . . . . . 79 3.2 Soft-potential model . . . . . . . . . . . . . . . . . 80 4 Recapitulation. . . . . . . . . . . . . . . . . . . . . . . . . 81 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 84 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Chapter 4. Two-Level Systems and the Tunneling Model: A Critical View 113 Clare C. Yu and Herv´e M. Carruzzo 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 113 1.1 Standard model of two-level systems . . . . . . 114 1.2 Crossover region . . . . . . . . . . . . . . . . . . . . 116 July27,2022 19:24 Low-TemperatureThermalandVibrational...-9inx6in b4719-fm pageix Contents ix 2 Beyond the Standard Model of Two-Level Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 2.1 Interacting two-level systems . . . . . . . . . . . 118 2.2 Universally small phonon scattering . . . . . . . 120 2.3 Exceptions to the rule . . . . . . . . . . . . . . . . 126 3 Mysteries about Glasses at Low Temperatures: Open Questions for the Future . . . . . . . . . . . . . . 127 4 Future Outlook . . . . . . . . . . . . . . . . . . . . . . . . 131 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 133 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Chapter 5. Exceptions Leading to a New Theory of Universality: Amorphous Solids without Glassy Properties 141 M. Molina-Ruiz and F. Hellman 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 141 1.1 Fragile and strong glasses . . . . . . . . . . . . . . 143 2 Anomalous Properties of Glasses at Low Temperatures . . . . . . . . . . . . . . . . . . . . . . 144 2.1 Random first-order transition theory . . . . . . 146 2.2 The standard tunneling model . . . . . . . . . . 147 3 Amorphous Solids without Glassy Properties . . . . . 150 3.1 Connection between TLS and structure. . . . . 154 4 Universal and Non-universal Values of TLSs . . . . . 159 4.1 Interaction of TLSs with elastic fields: The coupling constant . . . . . . . . . . . . . . . . 159 4.2 Interaction of TLSs with elastic and electric fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 5 Conclusions and Perspectives . . . . . . . . . . . . . . . 168 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Chapter 6. Vibrational Dynamics of Non-Crystalline Solids 177 Giacomo Baldi, Aldo Fontana and Giulio Monaco 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 178