Fractional Quantum Hall Effects – Bertrand I Halperin

Cs´athy Department of Physics and Astronomy, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907, USA [email protected] The use of ultra-low temperature cooling and high hydrostatic pressure tech- niques has significantly expanded our understanding of two-dimensional electron gas confined to GaAs/AlGaAs structures. This chapter reviews a selected set of experiments employing these specialized techniques in the study of the frac- tional quantum Hall states and the charged ordered phases, such as the re-entrant integer quantum Hall states and the quantum Hall nematic.

Topics discussed in- clude a successful cooling technique used, novel odd denominator fractional quan- tum Hall states, new transport results on even denominator fractional quantum Hall states and on re-entrant integer quantum Hall states, and phase transitions observed in half-filled Landau levels. Contents 1. Introduction . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . 2. Cooling Electrons Below 10 mK and Sample State Preparation . . . . . . . . . . . . . . 3. Recently Discovered Fractional Quantum Hall States .

. . . . . . . . . . . . . . . . . . 3.1. ν = 2 + 6/13 and ν = 2 + 2/5 fractional quantum Hall states . . . . . . . . . . . . 3.2. ν = 3 + 1/3 fractional quantum Hall state . . . . . . .

. . . . . . . . . . . . . . . 3.3. ν = 4/11 and 5/13 fractional quantum Hall states . . . . . . . . . . . . . . . . . . 4. Even Denominator Fractional Quantum Hall States . . . . . . . . . . . . . . . . . . . . 4.1. ν = 5/2 fractional quantum Hall state at low electron densities . . . .

. . . . . . 4.2. Energy gap at ν = 5/2 in pristine samples . . . . . . . . . . . . . . . . . . . . . . 4.3. Energy gap at ν = 5/2 in samples with alloy disorder . . . . . . . . . . . . . . .

This page intentionally left blank This page intentionally left blank This page intentionally left blank This page intentionally left blank NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO World Scientific New Developments Fractional Quantum Hall Effects Editors Bertrand I Halperin Harvard University, USA Jainendra K Jain Penn State University, USA Published by World Scientific Publishing Co.

Pte. 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 Cataloging-in-Publication Data Names: Halperin, Bertrand I., editor. | Jain, Jainendra K., editor. Title: Fractional quantum Hall effects : new developments / editors, Bertrand I. Halperin, Harvard University, Jainendra K. Jain, Penn State University. Description: New Jersey : World Scientific, [2020] | Includes bibliographical references and index.

Identifiers: LCCN 2020019145 (print) | LCCN 2020019146 (ebook) | ISBN 9789811217487 (hardcover) | ISBN 9789811218224 (paperback) | ISBN 9789811217494 (ebook) Subjects: LCSH: Quantum Hall effect. Classification: LCC QC612.H3 F73 2020 (print) | LCC QC612.H3 (ebook) | DDC 537.6/226–dc23 LC record available at https://lccn.loc.gov/2020019145 LC ebook record available at https://lccn.loc.gov/2020019146 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2020 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.

For any available supplementary material, please visit https://www.worldscientific.com/worldscibooks/10.1142/11751#t=suppl Printed in Singapore c⃝2020 World Scientific Publishing Company https://doi.org/10.1142/9789811217494 fmatter Contents Foreword K. von Klitzing vii Preface B. I. Halperin and J. K. Jain xi 1. Thirty Years of Composite Fermions and Beyond J. K. Jain 1 2. The Half-Full Landau Level B. I. Halperin 79 3.

This is a short excerpt from the opening of “” by Unknown, quoted for review and introduction purposes. All rights belong to the copyright holders.

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