Theory of Quantum Transport in Metallic

and Hybrid Nanostructures

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Series II: Mathematics, Physics and Chemistry – Vol. 230

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Andreas Glatz

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Argonne National Laboratory,

Theory of Quantum Transportin Metallic and Hybrid Nanostructures

Veniamin I. Kozub

Valerii M. Vinokur

IL, U.S.A.

Argonne National Laboratory,

IL, U.S.A.

Ioffe Institute,

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Proceedings of the NATO Advanced Research Workshop on

ISBN-10 1-4020-4777-0 (HB)

ISBN-13 978-1-4020-4777-0 (HB)

Theory of Quantum Transport in Metallic and Hybrid Nanostructures

St. Petersburg, Russia

25-29 August 2003

ISBN-10 1-4020-4778-9 (PB)

ISBN-13 978-1-4020-4778-7 (PB)

ISBN-10 1-4020-4779-7 (e-book)

ISBN-13 978-1-4020-4779 -9 (e-book)

Preface

A new science emerges at the intersection of modern physics, computer sci-ence, and material science. The struggle to further miniaturize is putting nano-technology to the verge of creating single-electron and/or single-spin devicesthat operate by moving a single electron (spin) and can serve as transistors,memory cells, and for logic gates. These devices take advantage of quantumphysics that dominates nanometer size scales. The devices that utilize metal-based hybrid nanostructures may possess significant advantages over thoseexploiting purely semiconducting materials. First, the chemistry of metals istypically simpler than that of semiconductors. Second, the electric propertiesof metals are much less sensitive to the structural defects and impurities thanthose of semiconductors. Next, metallic devices allow better electric and ther-mal contacts. Another important plus point is that in metals the electronde Broigle wavelength is smaller by many orders of magnitude as comparedto that in semiconductors. This makes metallic devices more promising withrespect to their size - down to the size of an atom. Further, high bulk andinterface thermal conductance in metallic devices are beneficial for the heatwithdraw. And, last but by no means the least, the high electron velocityin metals promises to accelerate enormously operation rates with respect tothose in semiconductor-based devices. The final note is that metals can ex-hibit strong ferromagnetism and/or superconductivity. While ferromagnetismprovides a new possibility for information storage and processing associatedvia utilizing spin transfer and storage (the corresponding approach is oftenreferred to as spintronics), the superconductivity offers unique opportunitiesfor completely novel class of devices based on quantum coherence.

These devices allow utilizing new computational algorithms based on quan-tum superposition of states, allowing simultaneous representing many differentnumbers (so-called quantum computation). In a quantum computer infor-mation is loaded as a string of ”qubits” (quantum mechanical representa-tion of bits), which are quantum objects that can occupy different quantumstates. A material implementation of qubits requires finding a medium, whichcan keep superpositional states from the destruction by interaction with the

vi Preface

environment (decoherence effect), i.e. the medium which has a long enoughcharacteristic decoherence time. On the other hand, interaction effects arecrucial for reading off the result of computation. Hence, the main problem isto find physical systems allowing coherent operation and a switchable interac-tion with the environment. In this sense the superconductor devices exhibitingproperties of a single macroscopic quantum state are of prime interest.

The abovementioned aspects of nanoscale physics focusing along the prop-erties of metallic and hybrid nanostructures became the focus of the NATOAdvanced Research Workshop held in St.-Petersburg, August 24 - 29, 2003;the scientific contributions of this workshop are presented in this volume.

Significant attention is paid to hybrid nanostructures on the base of ferro-magnets and superconductors including ferromagnet-superconductors hybridsystems. In the latter systems the role of proximity effects is discussed in de-tail. The possible developments in spintronics are demonstrated by studies ofcurrent-induced magnetization switching in multilayered nanopillars and bystudies spin-dependent transport of electrons in shuttle-structures and mag-netic point contacts. Important and unexpected results are presented for singleelectron transport through the vortex core levels and for domain wall super-conductivity in ferromagnetic superconductors and hybrid S/F structures.Widely discussed are correlation effects in nanostructures; in particular, theproblem of the metal-insulator transition in 2D electron systems which - sincethe existence of such a transition contradicts to conventional expectations ofscaling theory of localization is addressed. New realizations of two-channelKondo effect in single electron transistor and ratchet effects in Luttinger liq-uids are reported.

A special attention is paid to the noise phenomenon in nanostructures. Inparticular, non-Gaussian shot noise, higher cumulants of noise, shot noise intransport through localized states were considered. It is demonstrated thatthe detailed studies of noise, in particular studies of the shot noise, canprovide important information about the electron system involved. Severalissues concerning peculiarities of transport in nanostructures and nanoscaledevices are widely discussed in this volume: magnetoresistance caused by non-Markovian effects, transport properties of granular metals at low tempera-tures, and persistent currents in interacting Aharonov-Bohm interfereometersunder acoustic radiation can be mentioned to name the few. To summarize,the investigations reported in this volume, will, by no doubts, signify the im-portant step towards further understanding mechanisms of quantum transportin nanoscale devices.

St. Petersburg, Andreas GlatzJune 2004 Veniamin Kozub

Valerii Vinokur

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

Part I Coherence and Correlation Effects

Phase Measurements in Closed Aharonov-BohmInterferometersAmnon Aharony, Ora Entin-Wohlman, and Yoseph Imry . . . . . . . . . . . . . 3

Berry Phase with Environment: Classical versus QuantumRobert S. Whitney, Yuriy Makhlin, Alexander Shnirman,and Yuval Gefen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Part II Quantum Mesoscopic Phenomena

Electron Transport in Granular MetalsI.S. Beloborodov, K.B. Efetov, A.V. Lopatin, and V.M. Vinokur . . . . . . . 27

Studies of Current-Driven Excitations in Co/Cu/Co TrilayerNanopillarsS. Urazhdin, Norman O. Birge, W.P. Pratt, Jr., and J. Bass . . . . . . . . . . 39

Nanomechanical Effects in Suspended Carbon NanotubesYa.M. Blanter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Transport through Ferromagnet/Superconductor InterfacesZhigang Jiang, Jose Aumentado, Wolfgang Belzig,and Venkat Chandrasekhar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Anomalous Negative Magnetoresistance Causedby Non-Markovian EffectsVadim V. Cheianov, A. P. Dmitriev, and V. Yu. Kachorovskii . . . . . . . . 67

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viii Contents

Persistent Currents in Interacting Aharonov-BohmInterferometersOra Entin-Wohlman, Yoseph Imry, and Amnon Aharony . . . . . . . . . . . . . 77

Experimental Implementations of the Superconductor-Insulator TransitionV.F. Gantmakher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Thermal Fluctuations in One-Dimensional DisorderedQuantum SystemsAndreas Glatz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Coulomb Drag between Quantum Wires: Effect of SmallMomentum TransferL.I. Glazman, M. Pustilnik, E.G. Mishchenko, and A.V. Andreev . . . . . . 119

Signatures of Spin-Charge Separation in Double-Quantum-Wire TunnelingYaroslav Tserkovnyak, Bertrand I. Halperin, Ophir M. Auslaender,and Amir Yacoby . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Transport of Interacting Electrons through a Double BarrierI.V. Gornyi, and D.G. Polyakov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Ratchet Effects in Luttinger LiquidsD.E. Feldman, S. Scheidl, and V.M. Vinokur . . . . . . . . . . . . . . . . . . . . . . . 147

Part III Superconductivity in Nanostructures

Ferromagnetic-Superconducting Hybrid SystemsJ.Y. Gu, Ya.B. Bazaliy, S.D. Bader, and C.Y. You . . . . . . . . . . . . . . . . . . 159

STM Spectroscopy of the Local Density of States in NormalMetal - Superconductor SystemsL. Cretinon, A. Gupta, N. Moussy, B. Pannetier, and H. Courtois . . . . . 173

Quantum Tunneling between Paramagnetic andSuperconducting States of a Nanometer-ScaleSuperconducting Grain Placed in a Magnetic FieldA.V. Lopatin, and V.M. Vinokur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Domain Wall Superconductivity in FerromagneticSuperconductors and Hybrid S/F StructuresA.Yu. Aladyshkin, A.I. Buzdin, A.A. Fraerman, A.S. Mel’nikov,D.A. Ryzhov, and A.V. Sokolov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Contents ix

Rasba Spin-Orbit Interaction in a Ballistic JosephsonJunctionI.V. Krive, L.Y. Gorelik, R.I. Shekhter, and M. Jonson . . . . . . . . . . . . . . 215

Manifestation of Triplet Superconductivity in Superconductor-Ferromagnet StructuresF.S. Bergeret, A.F. Volkov, and K.B. Efetov . . . . . . . . . . . . . . . . . . . . . . . . 229

Part IV Noise and Fluctuation Phenomena

Phase Dependent Current Statistics in a Short-Arm AndreevInterferometerE.V. Bezuglyi, E.N. Bratus, V.S. Shumeiko, and V.M. Vinokur . . . . . . . 241

Semiclassical Theory of Higher Cumulants of NoiseK.E. Nagaev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

Josephson Junctions as Threshold Detectors for Full CountingStatisticsJens Tobiska, and Yuli V. Nazarov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

Energy Dependence of Current Noisein Superconducting/Normal Metal JunctionsM. Houzet, and F. Pistolesi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

Measurement of the Third Moment of Voltage Fluctuationsin a Tunnel JunctionB. Reulet, J. Senzier, L. Spietz, C.M. Wilson, and D.E. Prober . . . . . . . 277

Shot Noise in Mesoscopic Transport Through Localised StatesA.K. Savchenko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

Part V Single Electron Physics

Single Particle Transport in Disordered Andreev WiresN.B. Kopnin, A.S. Mel’nikov, and V.M. Vinokur . . . . . . . . . . . . . . . . . . . . 291

Two-Channel Kondo Effect in a Modified Single ElectronTransistorYuval Oreg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

Spin-Dependent Transport of Electrons in a Shuttle StructureL.Y. Gorelik, S.I. Kulinich, R.I. Shekhter, M. Jonson,and V.M. Vinokur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

List of Contributors

Amnon AharonySchool of Physics and AstronomyTel Aviv University69978 Tel AvivIsraelaharony@post.tau.ac.il

Samuel D. BaderArgonne National LaboratoryMaterials Science Division9700 South Cass AveArgonne, IL 60439USAbader@anl.gov

Igor S. BeloborodovArgonne National LaboratoryMaterials Science Division9700 South Cass AveArgonne, IL 60439USAbeloborodov@anl.gov

Eugene V. BezuglyiInstitute for Low TemperaturePhysicsand EngineeringKharkov 61103Ukraineeugene@fy.chalmers.se

Norman O. BirgeDept. of Physics and Astronomy,Center for FundamentalMaterials Research, and Center forSensor MaterialsMichigan State UniversityEast Lansing, MI 48824-2320USAbirge@pa.msu.edu

Yaroslov M. BlanterDepartment of NanoScience andDIMESDelft University of TechnologyLorentzweg 12628CJ DelftThe Netherlandsblanter@tnntw14.tn.tudelft.nl

Venkat ChandrasekharDepartment of Physics and Astron-omyNorthwestern University2145 Sheridan RoadEvanston, IL 60208USAv-chandrasekhar@northwestern.edu

Vadim V. CheianovNORDITABlegdamsvej 17

xi

xii List of Contributors

Copenhagen, DK 2100Denmarkcheianov@nordita.dk

Herve CourtoisCentre de Recherches sur les TresBasses Temperatures - C.N.R.S.and Universite Joseph Fourier25 Avenue des Martyrs38042 GrenobleFrancecourtoih@grenoble.cnrs.fr

Ora Entin-WohlmanSchool of Physics and Astronomy,Tel Aviv University,69978 Tel AvivIsraelentin@post.tau.ac.il

Dmitri E. FeldmanDepartment of PhysicsBrown University184 Hope StreetProvidence, RI 02912USADmitri Feldman@brown.edu

Vsevolod F. GantmakherInstitute of Solid State PhysicsRAS143432, Chernogolovka, MoscowRussiagantm@issp.ac.ru

Yuval GefenDepartment of Condensed MatterPhysicsThe Weizmann Institute of ScienceRehovot 76100Israelyuval.gefen@weizmann.ac.il

Andreas GlatzArgonne National LaboratoryMaterials Science Division9700 South Cass AveArgonne, IL 60439USAglatz@anl.gov

Leonid I. GlazmanWilliam I. Fine Theoretical PhysicsInstituteSchool of Physics and AstronomyUniversity of Minnesota116 Church Street SEMinneapolis, MN 55455USAglazman@umn.edu

Bertrand I. HalperinLyman Laboratory of PhysicsHarvard University17 Oxford StreetCambridge, MA 02138USAhalperin@physics.harvard.edu

Nikolai B. KopninLow Temperature LaboratoryHelsinki University of TechnologyPO BOX 220002015 TKKFinlandkopnin@boojum.hut.fi

Andrei V. LopatinArgonne National LaboratoryMaterials Science Division9700 South Cass AveArgonne, IL 60439USAlopatin@anl.gov

Alexander S. MelnikovInstitute for Physics of Microstruc-tures

List of Contributors xiii

Russian Academy of Sciences603950, Nizhny Novgorod, GSP-105Russiamelnikov@ipm.sci-nnov.ru

Kirill E. NagaevInstitute of Radioengineering andElectronicsRussian Academy of SciencesMokhovaya ulica 11125009 MoscowRussianag@cplire.ru

Yuli V. NazarovDepartment of NanoScienceDelft University of Technology2628 CJ DelftThe NetherlandsY.V.Nazarov@tn.tudelft.nl

Yuval OregDepartment of Condensed MatterPhysicsThe Weizmann Institute of ScienceRehovot 76100Israelyuval.oreg@weizmann.ac.il

Fabio PistolesiLaboratoire de Physique etModelisation des Milieux CondensesCNRS-UJF B.P. 166F-38042 GrenobleFrancefabio.pistolesi@grenoble.cnrs.fr

Dmitri G. PolyakovInstitut fur NanotechnologieForschungszentrum Karlsruhe

76021 KarlsruheGermanypolyakov@int.fzk.de

Daniel E. ProberDepartments of Applied Physics andPhysicsYale UniversityNew Haven, CT 06520USAdaniel.prober@yale.edu

Alexander K. SavchenkoSchool of PhysicsUniversity of ExeterStocker Road, Exeter, EX4 4QLUnited KingdomA.K.Savchenko@ex.ac.uk

Stefan ScheidlInstitut fur Theoretische PhysikUniversitat zu KolnZulpicher Straße 7750937 KolnGermanysts@thp.uni-koeln.de

Robert I. ShekhterDepartment of Applied PhysicsChalmers University of Technologyand Goteborg UniversitySE-412 96 GoteborgSwedenshekhter@fy.chalmers.se

Anatoly F. VolkovTheoretische Physik IIIRuhr-Universitat Bochum44780 BochumGermanyvolkov@tp3.ruhr-uni-bochum.de

Part I

Coherence and Correlation Effects