SpringerBriefs in Physics Massimiliano Di Ventra · Yuriy V. Pershin Memristors and Memelements Mathematics, Physics and Fiction SpringerBriefs in Physics SeriesEditors BalasubramanianAnanthanarayan,CentreforHighEnergyPhysics,Indian InstituteofScience,Bangalore,Karnataka,India EgorBabaev,DepartmentofPhysics,RoyalInstituteofTechnology,Stockholm, Sweden MalcolmBremer,H.H.WillsPhysicsLaboratory,UniversityofBristol,Bristol, UK XavierCalmet,DepartmentofPhysicsandAstronomy,UniversityofSussex, Brighton,UK FrancescaDiLodovico,DepartmentofPhysics,QueenMaryUniversityof London,London,UK PabloD.Esquinazi,InstituteforExperimentalPhysicsII,UniversityofLeipzig, Leipzig,Germany MaartenHoogerland,UniversityofAuckland,Auckland,NewZealand EricLeRu,SchoolofChemicalandPhysicalSciences,VictoriaUniversityof Wellington,Kelburn,Wellington,NewZealand DarioNarducci,UniversityofMilano-Bicocca,Milan,Italy JamesOverduin,TowsonUniversity,Towson,MD,USA VesselinPetkov,Montreal,QC,Canada StefanTheisen,Max-Planck-InstitutfürGravitationsphysik,Golm,Germany CharlesH.T.Wang,DepartmentofPhysics,UniversityofAberdeen, Aberdeen,UK JamesD.Wells,DepartmentofPhysics,UniversityofMichigan,AnnArbor,MI, USA AndrewWhitaker,DepartmentofPhysicsandAstronomy,Queen’sUniversity Belfast,Belfast,UK SpringerBriefsinPhysicsareaseriesofslimhigh-qualitypublicationsencompassing the entire spectrum of physics. 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Pershin Memristors and Memelements Mathematics, Physics and Fiction MassimilianoDiVentra YuriyV.Pershin DepartmentofPhysics DepartmentofPhysicsandAstronomy UniversityofCalifornia,SanDiego UniversityofSouthCarolina LaJolla,CA,USA Columbia,SC,USA ISSN 2191-5423 ISSN 2191-5431 (electronic) SpringerBriefsinPhysics ISBN 978-3-031-25624-0 ISBN 978-3-031-25625-7 (eBook) https://doi.org/10.1007/978-3-031-25625-7 ©TheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerlandAG2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Toourfamilies Preface Doubtisthefatherofinvention. GalileoGalilei(1564–1642) Whythisbook?Becausewehavenowreachedapointinwhichitisreallydifficult toseparaterealityfromfictioninthefieldofmemristorsandothermemorycircuit elements(memelements). Theword“fiction”(thatweputalsointhetitle)mayseemtoostrong,butitisthe correctone.Havingworkedinthisfieldforthepast15years,wehaveseen(atbest) toomanyexaggerations,andquiteafewplainlywrongandoutlandishstatements. Infact,manytimesweagreewithPauli’sfamousquote:Someofthesestatements are“notevenwrong.” Theseinclude“thememristoristhefourthfundamentalcircuitelement”(seriously doubtful!), “the missing memristor was found” (it was not!), “if it’s pinched it’s a memristor” (not true!), “resistance switching memories are memristors” (demon- strablyfalse!),andmanyothertalltalesandmisunderstandingsthatwewillcoverin thisshortbook. Important! We want to make absolutely clear that our issue is not with much scientificallysolidwork(bothexperimentalandtheoretical)thathasbeenproduced bymanyresearchersinthefield. Rather, this book gives us an opportunity to take stock of some of the wrong claims we mention above and help the reader discern between scientifically valid statements and fictional ones. It is our opinion that these statements diminish the importanceof,anddonotlendcredibilitytoanotherwiseflourishingfield. Thatsaid,itisthenclearthatthepresentmonographisnot areviewofthefield. Forthat,therearesomealreadyavailable. There is indeed a small but growing body of literature that is raising serious objections to the above statements and others we will cover in this monograph. However,thesevoicesarestillveryfeebleandsomewhatburiedinthemainstream buzz.Wehopethisbookwillhelpamplifysuchvoices. vii viii Preface Ourtrainingasphysicists(albeittheoreticians)compelsustoseerealityviathe lensesofexperiments,notmathematics.Infact, Mathematicalstatementsdonotnecessarilycorrespondtoaphysicalreality! Itisindeedeasytobecarriedawaybythebeautyandrigorofmathematicsand thinkthatanequationanditsconsequencesrepresentreality.Butthisisnotalways thecase.Forinstance,theconceptofinfinityiswelldefinedinmathematics,butnotin thephysical(experimental)sciences,becausewecannotmeasureinfinitequantities: Ourinstrumentsarefinite. Wewillnonethelessstartfrommathematicalstatementssince,manytimes,these aretheonesthatcreateconfusion.Wewillthenshowthatsomeofthemdonothave a physical counterpart. In fact, we will provide experimental tests to check their veracity. Afterall,ourknowledgeofthephysical,materialworldiswhatwedetectwith oursensesandextensionsofoursenses(measurementinstruments).1Thisbookthen challengesthecommunitytobemoregroundedinrealityratherthanfiction. Weareawarethatthisbook(assomeofourpreviouspublications)mayputusat oddswithmanyresearchersinthisfield.Tothis,wecanonlyanswerbyparaphrasing Aristotle’sfamousquote: Ourdesireistobefriendeverybody,butourbiggestdesirestillistobefriendtruth.2 It is only for this reason that we have written this book. May it then serve as a solidanchorforpresentandfuturestudentsandresearchersinthisfield,whichhas stillalottoofferbothintellectuallyandpractically. LaJolla,CA,USA MassimilianoDiVentra Columbia,SC,USA YuriyV.Pershin December2022 1For a brief and simple introduction to the scientific method see, e.g., the book M. Di Ventra, https://oxford.universitypressscholarship.com/view/10.1093/oso/9780198825623.001. 0001/oso-9780198825623?rskey=4y6M82result=2 The Scientific Method: Reflections from a Practitioner,(OxfordUniversityPress,2018). 2Andthesamephilosopherwouldsay“Truthisthatwhichconformstoreality.” Acknowledgements Wemustfindtimetostopandthankthepeoplewhomakea differenceinourlives. JohnF.Kennedy(1917–1963) Severalpeoplehaveworkedwithustobetterunderstandthefundamentalsandappli- cations of memory elements. In particular, we want to acknowledge the fruitful collaborationswithSeanBearden,DaliborBiolek,FabrizioBonani,DimitriBasov, Alessandro Braggio, Shiva Asapu, Francesco Caravelli, Leonardo Castelano, Yu- Chang Chen, Chih-Chun Chien, Guy Cohen, Timir Datta, Vincent Dowling, Tom Driscoll,IñigoEgusquiza,StevenLaFontaine,FrancescoGiazotto,ClaudioGuar- cello,MikhailKatkov,JinsunKim,MattKrems,LucasLamata,AlexeyMikhaylov, Haik Manukian, Julian Martinez-Rincon, Franco Nori, Yan Ru Pei, Sebastiano Peotta, Paul Pfeiffer, Daniel Primosch, Mikel Sanz, Forrest Sheldon, Sergey Shevchenko, Valeriy Slipko, Enrique Solano, Alexander Stotland, Carsten Timm, FabioTraversa,YuanhangZhang,andXiaoZheng. Wealsowanttothankmanycolleagues(toomanytonamehere)wehavediscussed withovertheyears.Theirfeedbackhasalwaysbeenvaluable.Weparticularlythank Leon Chua for our discussions on the topic of this book at an early stage and withwhomweproposedthenotionofmemcapacitiveandmeminductiveelements. Althoughourresearchideashavecollidedwithhisattimes—duetohisinsistence on concepts whose validity we do not share—we still remember fondly our initial interactions. We are also grateful to the National Science Foundation, the Department of Energy, and the Defense Advanced Research Projects Agency, for supporting our researchinthefield. Finally,specialthanksgotoourfamilieswho,throughtheirpresenceandlove, have provided us with invaluable support and continuous encouragement over the years. ix Contents 1 What’sinaName? .............................................. 1 1.1 TheNotionofMemory ....................................... 1 1.2 ResponseFunctions .......................................... 2 1.3 ResponseFunctionsandMemoryDegreesofFreedom ............ 4 1.4 MemoryElements(Memelements) ............................. 5 1.5 MemoryCapacityandStorage ................................ 6 1.6 WhatDoWeReallyMeasure? ................................. 8 1.6.1 AnExample .......................................... 9 References ...................................................... 10 2 RealityVersusFiction ........................................... 13 2.1 ElementaryPhysicsofFundamentalCircuitElements ............. 13 2.1.1 Resistors ............................................. 14 2.1.2 Capacitors ........................................... 16 2.1.3 Inductors ............................................ 16 2.2 ExperimentalSystemswithMemory ........................... 17 2.3 ThreeTypesofMemoryCircuitElements ....................... 18 2.4 IdealMemelements:AMathematicalFiction? ................... 19 2.5 ResistorsAreNotCapacitors,AreNotInductors! ................ 22 2.6 IfIt’sPinchedIt’s...What? ................................... 23 2.7 NotEvenWrong ............................................ 25 References ...................................................... 27 3 PhysicalConstraintsforIdealMemelements ....................... 29 3.1 ListofPhysicalConstraints ................................... 30 3.1.1 StrongSensitivitytoFluctuations ........................ 30 3.1.2 StochasticCatastrophe ................................. 32 3.1.3 ViolationofLandauerPrinciple ......................... 34 3.1.4 Over-DelayedSwitching ............................... 34 3.1.5 IncompatibilitywithSymmetriesofElectrodynamics ...... 35 3.2 IntrinsicVariabilityofMemristiveResponse .................... 35 References ...................................................... 38 xi