Graphene Quantum Dots

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  • NanoScience and Technology

    Alev DevrimGlPawelPotaszMarekKorkusinskiPawelHawrylak

    Graphene Quantum Dots

  • NanoScience and Technology

    Series editors

    Phaedon Avouris, Yorktown Heights, USABharat Bhushan, Columbus, USADieter Bimberg, Berlin, GermanyKlaus von Klitzing, Stuttgart, GermanyHiroyuki Sakaki, Tokyo, JapanRoland Wiesendanger, Hamburg, Germany

  • The series NanoScience and Technology is focused on the fascinating nano-world,mesoscopic physics, analysis with atomic resolution, nano and quantum-effectdevices, nanomechanics and atomic-scale processes. All the basic aspects andtechnology-oriented developments in this emerging discipline are covered bycomprehensive and timely books. The series constitutes a survey of the relevantspecial topics, which are presented by leading experts in the field. These books willappeal to researchers, engineers, and advanced students.

    More information about this series at http://www.springer.com/series/3705

    http://www.springer.com/series/3705

  • Alev Devrim Gl Pawel PotaszMarek Korkusinski Pawel Hawrylak

    Graphene Quantum Dots

    123

  • Alev Devrim GlDepartment of PhysicsIzmir Institute of TechnologyIzmirTurkey

    Pawel PotaszInstitute of PhysicsWrocaw University of TechnologyWrocawPoland

    Marek KorkusinskiEmerging Technologies Division, QuantumTheory Group

    National Research Council of CanadaOttawa, ONCanada

    Pawel HawrylakDepartment of PhysicsUniversity of OttawaOttawa, ONCanada

    ISSN 1434-4904 ISSN 2197-7127 (electronic)ISBN 978-3-662-44610-2 ISBN 978-3-662-44611-9 (eBook)DOI 10.1007/978-3-662-44611-9

    Library of Congress Control Number: 2014947690

    Springer Heidelberg New York Dordrecht London

    Springer-Verlag Berlin Heidelberg 2014This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part ofthe 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 orinformation storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed. Exempted from this legal reservation are briefexcerpts in connection with reviews or scholarly analysis or material supplied specifically for thepurpose of being entered and executed on a computer system, for exclusive use by the purchaser of thework. Duplication of this publication or parts thereof is permitted only under the provisions ofthe Copyright Law of the Publishers location, in its current version, and permission for use mustalways be obtained from Springer. Permissions for use may be obtained through RightsLink at theCopyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exemptfrom the relevant protective laws and regulations and therefore free for general use.While the advice and information in this book are believed to be true and accurate at the date ofpublication, neither the authors nor the editors nor the publisher can accept any legal responsibility forany errors or omissions that may be made. The publisher makes no warranty, express or implied, withrespect to the material contained herein.

    Printed on acid-free paper

    Springer is part of Springer Science+Business Media (www.springer.com)

  • Preface

    When one of us, PH, arrived at the University of Kentucky to start his Ph.D. withK. Subbaswamy in 1981, graphene in intercalated graphite (GIC) was all the rage.He was given a paper by Wallace describing electronic properties of graphene andgraphite and told to go and talk to Peter Eklunds group who was measuring opticalproperties of intercalated graphite next door. The next 4 years were exciting, withthe standing room only at the graphite sessions at the March Meetings, it seemedthat future belonged to graphene. However, the excitement did not last forever, andafter completing Ph.D. PH went on to work on another class of artificially madematerials, semiconductor heterostructures. The last 30 years has seen the ability ofcontrolling semiconductors moving from heterojunctions and superlattices to three-dimensional control and making semiconductor quantum dots. Today, semicon-ductor quantum dots enable, for example, transistors based on spins of singleelectrons, sources of single and entangled photons, efficient quantum dot lasers,biomarkers, and solar cells with improved efficiency.

    In this monograph, we describe a new class of quantum dots based on graphene,a single atomic layer of carbon atoms. Since the isolation of a single graphene layerby Novoselov and Geim, we became interested in using only graphene, instead ofdifferent semiconductors, to create graphene quantum dots. By controlling thelateral size, shape, type of edge, doping level, sublattice symmetry, and the numberof layers we hoped to engineer electronic, optical, and magnetic properties ofgraphene. Our initial exploration started in 2006, but came into focus later after webecame aware of a beautiful work by Ezawa and by Palacios and Fernandez-Rossieron triangular graphene quantum dots. This work emphasized the role of sublatticesymmetries and electron-electron interactions in engineering magnetic properties ofgraphene nanostructures, opening the possibility of creating an interesting alter-native to semiconductor spintronics. The second intriguing possibility offered bygraphene is that it is a semimetal with zero-energy gap. By lateral size quantizationthe gap in graphene quantum dots can be tuned from zero to UV. By contrast, insemiconductors, the energy gap can only be larger than the energy gap of the bulkmaterial. In principle, graphene quantum dots allow for design of material with thedesired energy gap. The exciting possibility of convergence and seamless

    v

  • integration of electronics, photonics, and spintronics in a single material, graphene,could lead to a new area of research, carbononics.

    These were some of the ideas we embarked to explore when two of us, ADG andPP joined the Quantum Theory Group led by PH at the NRC Institute for Micro-structural Sciences in 2008. Themonograph is based largely on the Ph.D. thesis of oneof us, Pawel Potasz, shared between NRC and Wrocaw University of Technology.

    After Introduction in Chap. 1, Chap. 2 describes the electronic properties of bulkgraphene, a two dimensional crystal, including fabrication, electronic structure, andeffects of more than one layer. In Chap. 3 fabrication of graphene quantum dots isdescribed while Chap. 4 describes single particle properties of graphene quantumdots, including tight-binding model, effective mass, magnetic field, spin-orbitcoupling, and spin Hall effect. The role of sublattice symmetry and the emergenceof a degenerate shell of electronic states in triangular graphene quantum dots isdescribed. The bilayers and rings, including Mbius ring with topology encoded bygeometry, are described. Chapter 5 introduces electron-electron interactions,including introduction to several tools such as HartreeFock, Hubbard model andConfiguration Interaction method used throughout the monograph. Chapter 6 dis-cusses correlations and magnetic properties in triangular graphene quantum dotsand rings with degenerate electronic shells, including existence of magneticmoment and its melting with charging, and Coulomb and Spin Blockade intransport. Chapter 7 focuses on optical properties of graphene quantum dots,starting with tight-binding model and including self-energy and excitonic correc-tions. Optical spin blockade and optical control of the magnetic moment isdescribed. Comparison with experimental results obtained for colloidal graphenequantum dots is also included.

    We hope the monograph will introduce the reader to this exciting and rapidlyevolving field of graphene quantum dots and carbononics.

    Izmir, Turkey Alev Devrim GlWrocaw, Poland Pawel PotaszOttawa, Canada Marek Korkusinski

    Pawel Hawrylak

    vi Preface

    http://dx.doi.org/10.1007/978-3-662-44611-9_1http://dx.doi.org/10.1007/978-3-662-44611-9_2http://dx.doi.org/10.1007/978-3-662-44611-9_3http://dx.doi.org/10.1007/978-3-662-44611-9_4http://dx.doi.org/10.1007/978-3-662-44611-9_5http://dx.doi.org/10.1007/978-3-662-44611-9_6http://dx.doi.org/10.1007/978-3-662-44611-9_7

  • Contents

    1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    2 GrapheneTwo-Dimensional Crystal . . . . . . . . . . . . . . . . . . . . . . 32.1 Introduction to Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Fabrication of Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

    2.2.1 Mechanical Exfoliation . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Chemical Vapor Decomposition . . . . . . . . . . . . . . . . . . 122.2.3 Thermal Decomposition of SiC . . . . . . . . . . . . . . . . . . . 122.2.4 Reduction of Graphite Oxide (GO) . . . . . . . . . . . . . . . . 13

    2.3 Mechanical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4 Electronic Band Structure of Graphene . . . . . . . . . . . . . . . . . . . 14

    2.4.1 Tight-Binding Model . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.2 Effective Mass Approximation, Dirac Fermions

    and Berrys Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.3 Chirality and Absence of Backscattering . . . . . . . . . . . . 212.4.4 Bilayer Graphene . . . . . . . . . . . .