Excursions in Ill-Condensed Quantum Matter: From Amorphous Topological Insulators to Fractional Spins PDF
Preview Excursions in Ill-Condensed Quantum Matter: From Amorphous Topological Insulators to Fractional Spins
Springer Theses Recognizing Outstanding Ph.D. Research Adhip Agarwala Excursions in Ill-Condensed Quantum Matter From Amorphous Topological Insulators to Fractional Spins Springer Theses Recognizing Outstanding Ph.D. Research Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected foritsscientificexcellenceandthehighimpactofitscontentsforthepertinentfield of research. For greater accessibility to non-specialists, the published versions includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor explainingthespecialrelevanceoftheworkforthefield.Asawhole,theserieswill provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists. Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria (cid:129) They must be written in good English. (cid:129) ThetopicshouldfallwithintheconfinesofChemistry,Physics,EarthSciences, Engineeringandrelatedinterdisciplinary fields such asMaterials,Nanoscience, Chemical Engineering, Complex Systems and Biophysics. (cid:129) The work reported in the thesis must represent a significant scientific advance. (cid:129) Ifthethesisincludespreviouslypublishedmaterial,permissiontoreproducethis must be gained from the respective copyright holder. (cid:129) They must have been examined and passed during the 12 months prior to nomination. (cid:129) Each thesis should include a foreword by the supervisor outlining the signifi- cance of its content. (cid:129) The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field. More information about this series at http://www.springer.com/series/8790 Adhip Agarwala Excursions in Ill-Condensed Quantum Matter From Amorphous Topological Insulators to Fractional Spins Doctoral Thesis accepted by the Indian Institute of Science, Bangalore, India 123 Author Supervisor Dr. AdhipAgarwala Prof. VijayB. Shenoy InternationalCentreforTheoreticalSciences Department ofPhysics TataInstitute of FundamentalResearch Indian Institute of Science Bangalore, India Bangalore, India ISSN 2190-5053 ISSN 2190-5061 (electronic) SpringerTheses ISBN978-3-030-21510-1 ISBN978-3-030-21511-8 (eBook) https://doi.org/10.1007/978-3-030-21511-8 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart 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 orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. 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, expressed or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland “Why are you digging a hole?” “I’m looking for buried treasure!” “What have you found?” “A few dirty rocks, a weird root, and some disgusting grubs.” “On your first try??” “There’s treasure everywhere!” Bill Watterson, in Calvin and Hobbes (3rd June, 1995) ’ Supervisor s Foreword Much of condensed matter physics focuses on crystals where there is a natural notionofperiodicity.Theideathatalliswellunderstoodfromthepointofviewof electronic physics of crystals was washed away by the tsunami engendered by topological concepts. AdhipAgarwalasetsonajourneytoexplore“illcondensedmatter”,wherethere isnorefugeoftheBrillouinzone.Inthisthesis,heexploresavarietyofproblemsin amorphous systems, fractals, etc. with a view of exploring topological phases in them. He answers several interesting questions: Are topological electronic phases possible in amorphous systems? And, in fractal lattices? Read this thesis and you willbeenlightenednotonlywithanswerstothesequestionsbutonhow“fractional spins” can arise among other things. Thethesisalsocontainsanexcellentexpositionofmanyofthemodernconcepts ofcondensedmatterphysicsincludingtopologicalideas,fermionicsymmetries,etc. Iparticularlyinviteyoungerscientistswishingtodelveintothebasicstoenjoythis presentation by Adhip, one of my best teachers! Bangalore, India Prof. Vijay B. Shenoy June 2019 Centre for Condensed Matter Theory Department of Physics Indian Institute of Science vii Abstract Impurities, disorder, or amorphous systems—the ill condensed matter—are mostly considered inconveniences to our study of materials, which is otherwise heavily based on idealized perfect crystals. Kondo effect and the scaling theory of local- ization are some offundamental and early discoverieswhichhadbrought forth the novelty hidden in impure or disordered systems. Recent advances in condensed matter physics have emphasized the role of topology, spin-orbit coupling, and non-ordinary symmetries such as time reversal, charge conjugation, and sublattice in many physical phenomena. These have irreversibly transformed the essential ideas and purview of condensed matter physics, both in theoretical and experi- mental directions. However, much of these recent developments and their impli- cationsarelimitedto,orbyideaswhichstemfromcleansystems.Thisthesisdeals with various aspects of these recent developments, but when they are unclean— introducingnewideassuchasamorphoustopologicalinsulators,fractalizedmetals, and fractionalized spins. ix Preface Welcome! Welcometothisthesisandtothestoriespresentedinthis.Curiosityoftenleads toterrainswhichareneithersmoothnorclean—andthereforethename“Excursions in ill condensed matter”. Disordered or ill systems have something beautifully mysterious about them. With their “faults, dislocations, defects” they show remarkably rich physics and a myriad of phenomena that have deep implications. Thisthesis,aswillbediscussedatlengthinthefirstchapter,investigatesrecent developments in quantum condensed matter field such as topological phases, spin-orbit coupled systems, etc. in context of ill systems. Thereareeightchapters.Thefirstandthelastservesastheintroductionandthe conclusion, respectively. The first chapter provides a broad overview of quantum condensed matter field and introduces the idea of ill condensed matter. It further places the motivations for various problems and sketches the central results. The secondchapterdiscussestheformalismtoclassifyquadraticHamiltoniansbasedon fewintrinsicsymmetriesandshowshowthegenericstructure ofHamiltonians can be obtained in each of the symmetry classes. Chapter three builds on these results anddemonstratestherealizationofamorphoustopologicalinsulators.Chapterfour reports the surprises in realizing topological phases on fractals—systems which have a non-integer spatial dimension and where bulk and boundary is ill-defined. Chapter five takes another topological system—the Hofstadter butterfly—the spectrum when a square lattice is subjected to a magnetic field, and looks at the effectofrandomlyremoving thelatticebonds. Chaptersix explores impuritiesina spin-orbit coupled system and shows the existence of fractional spins and a cor- respondingnovelKondoeffect.Chaptersevenextendstheclassificationintroduced in the second chapter, to arbitrary interacting systems and obtains the structure of many-body Hamiltonians in different symmetry classes. Chapter eight concludes with a perspective and discussion offuture scope. xi xii Preface Most of the work presented in this thesis is already present in public domain, either through published manuscripts or arXiv preprints. Therefore, not unexpect- edly, they will have close overlap with the content presented in them. Please feel freetogetintouchforanyclarificationsortosendanysuggestions,criticisms,etc. Happy reading! Bangalore, India Adhip Agarwala
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