Josephson effect in carbon nanotubes with spin-orbit coupling.
|
|
- Bennett Harvey
- 5 years ago
- Views:
Transcription
1 Josephson effect in carbon nanotubes with spin-orbit coupling. Rosa López Interdisciplinary Institute for Cross-Disciplinary Physics and Complex Systems University of Balearic Islands IFISC (CSIC-UIB), Palma de Mallorca, Spain J. S. Lim (IFISC, UIB), R. López, R. Aguado (ICMM, CSIC): arxiv: Phys. Rev. Lett (211) in press, October 211
2 * 2 nm ORBITAL + SPIN Text W. Liang, M. Bockrath and H. Park, PRL, 88, (22) M. R. Buitelaar, A. Bachtold, T. Nussbaumer, M. Iqbal and C. Schönenberger, PRL, 88, (22) Jarillo-Herrero et al.,prl, 94, 15682, (25)
3
4 Periodic Boundary Conditions Nanotubes Sub-bands in 1D. K 1 K 2 Ethan Minot, Tuning the band structure of carbon nanotubes, PhD Thesis, Cornell 24.
5 Modelling Quantum Dot Carbon Nanotubes I Small bandgap nanotubes k = τ 3 k g K K k K and K are degenerate owing to time-reversal symmetry (isospin) τ 3 = ±1 H = v F (k τ 3 σ 1 + k τ σ 2 ) also becomes quantized due to the finite length (quantum dot).
6 Modelling Quantum Dot Carbon Nanotubes II µ orb = edν F /4 B t Large orbital moments couple to parallel magnetic fields H orb = τ 3 µ orb B = τ 3 ν F πb D/2Φ E k = τ 3 k g + Φ AB /DΦ Φ AB = B πd 2 H Z = 1 2 gµ BB τ σ s 3 B Determination of electron orbital magnetic moments in carbon nanotubes, E. D. Minot, Yuval Yaish, Vera Sazonova & Paul L. McEuen, Nature, 428, 536 (24) See News&Views Nanoscale physics: M. Chiao, Big moment for nanotubes (24)
7 SPIN KONDO EFFECT AND ISOSPIN KONDO EFFECT SU(4) SYMMETRY
8 SPIN KONDO ORBITAL KONDO SPIN + ORBITAL
9 Low temperature transport: evidence of SU(4) symmetry Zeeman orbital Experiment: Orbital Kondo effect in Carbon Nanotubes, Pablo Jarillo-Herrero, Jing Kong, Herre S.J. van der Zant, Cees Dekker, Leo P. Kouwenhoven, Silvano De Franceschi, Nature, 434, 484 (25). Theory: SU(4) Kondo effect in carbon nanotubes, Mahn-Soo Choi, Rosa López and Ramón Aguado, PRL, 95,6724 (25)
10 Carbon Nanotube with Spin-orbit coupling I The orbital motion of electrons also couples to a curvature-induced radial electric field. This creates an effective axial magnetic field which polarizes the spins along the NT axis and favors parallel alignment of the spin and orbital magnetic momenta or antiparallel depending on the sign of this spin-orbit coupling. As a result, the fourfold degeneracy breaks into two Kramers doublets (time-reversed electrons pairs). Spin-orbit interaction can be understood as an effective exchange field between Kramers pairs. Coupling of spin and orbital motion of electrons in carbon nanotubes, F. Kuemmeth, S. Ilani, D. C. Ralph & P.L.McEuen, Nature, 452, 448, 28. THEORY: T. Ando, J. Phys. Soc. Jpn. 69, 1757 (2). D. Huertas-hernando et al, Phys. Rev. B, 74, (26). D. V. Bulaev et al, Phys. Rev. B 77, (28) L. Chico et al, Phys. Rev. B, 79, (29). J. Jeong and H. Lee, Phys. Rev. B, 8, 7549 (29). W. Izumida, K. Sato and R. Saito, J. Phys. Soc. Jpn., 78, 7477 (29). B SO = v E
11 Carbon Nanotube with Spin-orbit coupling II The orbital motion of electrons also couples to a curvature-induced radial electric field. This creates an effective axial magnetic field which polarizes the spins along the NT axis and favors parallel alignment of the spin and orbital magnetic momenta or antiparallel depending on the sign of this spin-orbit coupling. As a result, SU(4) degeneracy breaks into two Kramers doublets (time-reversed electrons pairs). Spin-orbit interaction can be understood as an effective exchange field between these Kramers pairs (J-S Lim, R. López, G-L Giorgi, D. Sánchez Phys. Rev. B 83, (211)) H SO = 1 SOτ 3 σ 1 s 3 + SOτ 3 σ s 3 Coupling of spin and orbital motion of electrons in carbon nanotubes, F. Kuemmeth, S. Ilani, D. C. Ralph & P.L.McEuen, Nature, 452, 448, 28.
12 Nanotubes can be contacted with superconducting leads Pillet et al, Nature Physics, 6, 965, (21). J. P. Cleuziou et al, Nature Nanotech., 1, 53, (26)
13 Superconducting Contact Carbon Nanotube QD Superconducting Contact
14 Superconducting Contact Carbon Nanotube QD Superconducting Contact Andreev Bound states (ABS): entangled time-reversed electron-hole Kramers pairs. Recently measured in nanotubes and graphene Pillet et al, Nature Physics, 6, 965, 21 (nanotubes); T. Dirks, et al, Nature Physics, 6 February 211 (graphene)
15 Superconducting Contact Carbon Nanotube QD Superconducting Contact The Josephson current is mainly given by resonant tunneling of Cooper pairs through these bound states
16 Nanotubes can be contacted with superconducting leads Text Different curves correspond to different Vg Quantum supercurrent transistors in carbon nanotubes, Pablo Jarillo-Herrero, Jorden van Dam and Leo Kouwenhoven, Nature 439, 953 (26). For a review, see Hybrid superconductor quantum dot devices, Silvano de Franceschi et al, Nature Nanotechnology, 5, 73 (21)
17 As both phenomena, spin-orbit and the formation of Andreev bound states, are related to time-reversed Kramers pairs, it is interesting to address the following question: what happens to the Josephson effect in QD carbon nanotubes in the presence of spin-orbit?
18 Anderson-like hamiltonian + BCS leads H C = α=l/r,k,τ,s α,k,τ ξ k c αkτs c αkτs α e iφ α c αkτ c α k τ + h.c. H D = τ,s ε τs d τsd τs + U n τs n τ s H T = (τ,s)=(τ,s ) V α c αkτs d τs + h.c., α=l/r,k,τ,s
19 E/ FIG. 2. SO-mediated supercurrent reversal. a, Total (top) function of phase and different B (in Tesla) for Γ =.1 5 near the -π transition at B = B c =.52T. c, ABS vs. φ in π behavior. d, ABS versus V g for different B =,.5, for all V g <. The π transition is robust as V g is varied ( -5 Bc tization -1 in the longitudinal and perpendicular directi to QD -4 confinement -2 [15] and2the finite 4 diameter of t and the SO coupling. B [T] The levels can be approxim ε τ,σ = ε + στ SO + σ Z + τ orb, with Z = and orb = µ orb B (µ s and µ orb are the spin and
20 Calculation: Green s functions in Nambu space. The poles of the retarded Green s function give the Andreev bound states Det[G r d(ω) 1 ]=D + D = E 1(2) ε + ΓE 1(2) 2 E 2 1(2) E 1(2) + ε ± + ΓE 1(2) 2 E 2 1(2) Γ2 2 cos 2 (φ/2) 2 E 2 1(2) =
21 E 1(2) ε + ΓE 1(2) 2 E 2 1(2) E 1(2) + ε ± + ΓE 1(2) 2 E 2 1(2) Γ2 2 cos 2 (φ/2) 2 E 2 1(2) = 1 5 E/ E/ EF -5-1 Bc B [T] -1 E2 E1 Bc B [T] 1 2µ orb B c = SO by studying the A
22 E 1(2) ε + ΓE 1(2) 2 E 2 1(2) E 1(2) + ε ± + ΓE 1(2) 2 E 2 1(2) Γ2 2 cos 2 (φ/2) 2 E 2 1(2) = 1 Each Kramer s doublet produces two ABS (four in total). E/ -1 E2 E1 Bc EF At B=Bc, the ABS corresponding to different Kramers doublets cross. After the crossing, the two ABS below EF belong to the same Kramers doublet. B [T] 1
23 Josephson current in terms of Green s functions (both discrete and continuum contribution calculated on the same footing) I = 2e dω ˆΣ< 2π Tr ˆσ 3 Ĝ a (ω)+ˆσ r Ĝ< (ω) = I dis + I con I dis Discrete Josephson current (resonant Cooper pairs) = eγ2 sin(φ) f(e 2 ) 2 E 2 ( 2 E2 2)D + (E 2) + f(e 1 ) 2 E 1 ( 2 E1 2)D (E 1)
24 I dis Discrete Josephson current (resonant Cooper pairs) = eγ2 sin(φ) E 2 f(e 2 ) 2 ( 2 E 2 2 )D + (E 2) + E 1 f(e 1 ) 2 ( 2 E 2 1 )D (E 1) I dis = 2e f(e ) E 1(2) 1(2) φ E 1(2) The discrete Josephson current is given by the derivative of the occupied (i. e. below EF) ABS with respect to phase
25 I dis = eγ2 sin(φ) f(e 2 ) 2 E 2 ( 2 E2 2)D + (E 2) + f(e 1 ) 2 E 1 ( 2 E1 2)D (E 1) Continuous Josephson current (quasiparticle states above the gap) I con = eγ2 π sin(φ) dω Θ( ω ) f(ω) 2 (ω 2 2 ) 1 D + (ω) + 1 D (ω)
26 Non-interacting regime,4 I J I J disc -,4,2 -pi transition: reversal of the supercurrent due to the combined effect of SO and external magnetic field. This is very unusual in a noninteracting system. I J cont -,2,5 -,5 1 2 B = B =.2 B =.4 B =.6
27 Non-interacting regime II,4 I J I J disc -,4,1 -pi transition: reversal of the supercurrent due to the combined effect of SO and external magnetic field. This is very unusual in a noninteracting system. I J cont -,1,6 -,6 1 2 B =.5 B =.51 B =.52 B =.53 B =.54
28 Non-interacting regime II I J,4 Magnetic field where spinpolarized orbital states become degenerate -,4,1 E/ 5 I J disc -, Bc B [T] I J cont,6 -,6 1 2 B =.5 B =.51 B =.52 B =.53 B =.54
29 1 1 E/6 c -1 B = B =.5 B =.6 EF B [T] After the crossing, the occupied ABS belong to the same Kramers doublet. Importantly, they have opposite derivative with respect to phase which gives discrete supercurrents of opposite sign. Only the continuous current (states above the gap) contributes. This reverses the sign of the supercurrent. 1-1 q/ 2 q/ 2 q/ 2 In standard QDs this happens in the cotunneling regime only, see Supercurrent reversal in quantum dots, J. van Dam et al, Nature 442, 667 (26).
30 Gate tunability 1 B =Bc d E/ Vg/ Vg/ Vg/ Vg/ At zero magnetic field, the SO splitted ABS show a diamondlike shape, similarly to spin-slit ABS due to Coulomb Blockade
31 Gate tunability 1 B =Bc d E/ Vg/ Vg/ Vg/ Vg/ At zero magnetic field, the SO splitted ABS show a diamondlike shape, similarly to spin-slit ABS due to Coulomb Blockade E. Vecino, A. Martín Rodero and A. L. Yeyati, Phys. Rev. B, 68,3515, 23
32 Cotunneling regime (fourth order perturbation theory)
33 Kondo regime (slave boson) I dis J = e 2 η=± sin(φ) [(1 + ηα) 2 + 1][(1 + ηα) 2 + cos 2 ( φ 2 )] α = SO 2T K,SU(4) Without SO we recover the results of: Zazunov, Levy-Yeyati and Egger, PRB 81, 1252 (21)
34 Kondo regime
35 I J I J disc,4 -,4,1 -,1,6 CONCLUSIONS The relatively small SO coupling in quantum dot carbon nanotubes induces a -pi transition in the Josephson current when an external magnetic field brings spin-polarized orbital levels to degeneracy. I J cont -,6 1 2 The transition is also tunable by a gate voltage. This is relevant in view of recent transport experiments in quantum dot carbon nanotubes. I c (2e 2 /h V g / SO I dis/i c I( SO = SO =.5TK, SU (4) SU (2) SU(4) SU(2) SO /T K,SU(4) Cotunneling regime: the transition occurs even at zero magnetic field. Kondo regime: the Josephson current is always in the phase for both SU(4) and SU(2) symmetries. J. S. Lim, R. López, R. Aguado Phys. Rev. Lett (211) arxiv:
Tunable Orbital Pseudospin and Multi-level Kondo Effect in Carbon Nanotubes
Tunable Orbital Pseudospin and Multi-level Kondo Effect in Carbon Nanotubes Pablo Jarillo-Herrero, Jing Kong, Herre S.J. van der Zant, Cees Dekker, Leo P. Kouwenhoven, Silvano De Franceschi Kavli Institute
More informationMajorana single-charge transistor. Reinhold Egger Institut für Theoretische Physik
Majorana single-charge transistor Reinhold Egger Institut für Theoretische Physik Overview Coulomb charging effects on quantum transport through Majorana nanowires: Two-terminal device: Majorana singlecharge
More informationKondo effect in multi-level and multi-valley quantum dots. Mikio Eto Faculty of Science and Technology, Keio University, Japan
Kondo effect in multi-level and multi-valley quantum dots Mikio Eto Faculty of Science and Technology, Keio University, Japan Outline 1. Introduction: next three slides for quantum dots 2. Kondo effect
More informationCoupling of spin and orbital motion of electrons in carbon nanotubes
Coupling of spin and orbital motion of electrons in carbon nanotubes Kuemmeth, Ferdinand, et al. "Coupling of spin and orbital motion of electrons in carbon nanotubes." Nature 452.7186 (2008): 448. Ivan
More informationTransport through interacting Majorana devices. Reinhold Egger Institut für Theoretische Physik
Transport through interacting Maorana devices Reinhold Egger Institut für Theoretische Physik Overview Coulomb charging effects on quantum transport through Maorana nanowires: Two-terminal device: Maorana
More informationSPIN-POLARIZED CURRENT IN A MAGNETIC TUNNEL JUNCTION: MESOSCOPIC DIODE BASED ON A QUANTUM DOT
66 Rev.Adv.Mater.Sci. 14(2007) 66-70 W. Rudziński SPIN-POLARIZED CURRENT IN A MAGNETIC TUNNEL JUNCTION: MESOSCOPIC DIODE BASED ON A QUANTUM DOT W. Rudziński Department of Physics, Adam Mickiewicz University,
More informationKondo Physics in Nanostructures. A.Abdelrahman Department of Physics University of Basel Date: 27th Nov. 2006/Monday meeting
Kondo Physics in Nanostructures A.Abdelrahman Department of Physics University of Basel Date: 27th Nov. 2006/Monday meeting Kondo Physics in Nanostructures Kondo Effects in Metals: magnetic impurities
More informationSUPPLEMENTARY INFORMATION
Josephson φ 0 -junction in nanowire quantum dots D. B. Szombati, S. Nadj-Perge, D. Car, S. R. Plissard, E. P. A. M. Bakkers, L. P. Kouwenhoven 1. Breaking of the chiral symmetry in quantum dots 2. Characterization
More informationTransport through Andreev Bound States in a Superconductor-Quantum Dot-Graphene System
Transport through Andreev Bound States in a Superconductor-Quantum Dot-Graphene System Nadya Mason Travis Dirk, Yung-Fu Chen, Cesar Chialvo Taylor Hughes, Siddhartha Lal, Bruno Uchoa Paul Goldbart University
More informationThree-terminal quantum-dot thermoelectrics
Three-terminal quantum-dot thermoelectrics Björn Sothmann Université de Genève Collaborators: R. Sánchez, A. N. Jordan, M. Büttiker 5.11.2013 Outline Introduction Quantum dots and Coulomb blockade Quantum
More informationSuperconducting properties of carbon nanotubes
Superconducting properties of carbon nanotubes Reinhold Egger Institut für Theoretische Physik Heinrich-Heine Universität Düsseldorf A. De Martino, F. Siano Overview Superconductivity in ropes of nanotubes
More informationTemperature dependence of Andreev spectra in a superconducting carbon nanotube quantum dot
Temperature dependence of Andreev spectra in a superconducting carbon nanotube quantum dot A. Kumar, M. Gaim, D. Steininger, A. Levy Yeyati, A. Martín-Rodero, A. K. Hüttel, and C. Strunk Phys. Rev. B 89,
More informationsingle-electron electron tunneling (SET)
single-electron electron tunneling (SET) classical dots (SET islands): level spacing is NOT important; only the charging energy (=classical effect, many electrons on the island) quantum dots: : level spacing
More informationSupplementary Information
Supplementary Information Quantum supercurrent transistors in carbon nanotubes Pablo Jarillo-Herrero, Jorden A. van Dam, Leo P. Kouwenhoven Device Fabrication The nanotubes were grown by chemical vapour
More informationCan electron pairing promote the Kondo state?
Czech Acad. Scien. in Prague, 6 X 2015 Can electron pairing promote the Kondo state? Tadeusz Domański Marie Curie-Skłodowska University, Lublin, Poland http://kft.umcs.lublin.pl/doman/lectures Issues to
More informationCoulomb blockade and single electron tunnelling
Coulomb blockade and single electron tunnelling Andrea Donarini Institute of theoretical physics, University of Regensburg Three terminal device Source System Drain Gate Variation of the electrostatic
More informationIntra- and inter-shell Kondo effects in carbon nanotube quantum dots
Eur. Phys. J. B (2018) 91: 8 https://doi.org/10.1140/epjb/e2017-80547-y Regular Article THE EUROPEAN PHYSICAL JOURNAL B Intra- and inter-shell Kondo effects in carbon nanotube quantum dots Damian Krychowski
More informationTopological Kondo effect in Majorana devices. Reinhold Egger Institut für Theoretische Physik
Topological Kondo effect in Maorana devices Reinhold Egger Institut für Theoretische Physik Overview Coulomb charging effects on quantum transport in a Maorana device: Topological Kondo effect with stable
More informationarxiv: v1 [cond-mat.mes-hall] 2 Sep 2013
Correlation effects and spin dependent transport in carbon nanostructures S. Lipiński, D. Krychowski arxiv:1309.0359v1 [cond-mat.mes-hall] 2 Sep 2013 Institute of Molecular Physics, Polish Academy of Sciences
More informationPersistent orbital degeneracy in carbon nanotubes
PHYSICAL REVIEW B 74, 155431 26 Persistent orbital degeneracy in carbon nanotubes A. Makarovski, 1 L. An, 2 J. Liu, 2 and G. Finkelstein 1 1 Department of Physics, Duke University, Durham, North Carolina
More informationManipulation of Majorana fermions via single charge control
Manipulation of Majorana fermions via single charge control Karsten Flensberg Niels Bohr Institute University of Copenhagen Superconducting hybrids: from conventional to exotic, Villard de Lans, France,
More informationThe Nanotube SQUID. uhu,, M. Monthioux,, V. Bouchiat, W. Wernsdorfer, CEMES-Toulouse, CRTBT & LLN Grenoble
The Nanotube SQUID J.-P. Cleuziou,, Th. Ondarçuhu uhu,, M. Monthioux,, V. Bouchiat, W. Wernsdorfer, CEMES-Toulouse, CRTBT & LLN Grenoble Outline Sample fabrication Proximity effect in CNT The CNT superconducting
More informationSuperconductivity at nanoscale
Superconductivity at nanoscale Superconductivity is the result of the formation of a quantum condensate of paired electrons (Cooper pairs). In small particles, the allowed energy levels are quantized and
More informationQUANTUM TRANSPORT IN BOTTOM-UP SEMICONDUCTOR NANOSTRUCTURES
QUANTUM TRANSPORT IN BOTTOM-UP SEMICONDUCTOR NANOSTRUCTURES Silvano De Franceschi INAC/SPSMS/LaTEQS: Laboratory of quantum electron transport and superconductivity http://www-drfmc.cea.fr/pisp/55/silvano.de_franceschi.html
More informationQuantum dots and Majorana Fermions Karsten Flensberg
Quantum dots and Majorana Fermions Karsten Flensberg Center for Quantum Devices University of Copenhagen Collaborator: Martin Leijnse and R. Egger M. Kjærgaard K. Wölms Outline: - Introduction to Majorana
More informationInteractions and transport in Majorana wires. Alfredo Levy Yeyati
Interactions and transport in Majorana wires Alfredo Levy Yeyati SPICE Workshop: Spin dynamics in the Dirac systems, Mainz 6-9 June 2017 Content Low energy transport theory in Majorana wire junctions,
More informationSUPPLEMENTARY INFORMATION
Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures Eduardo J. H. Lee, Xiaocheng Jiang, Manuel Houzet, Ramón Aguado, Charles M. Lieber, and Silvano De
More informationSpin Superfluidity and Graphene in a Strong Magnetic Field
Spin Superfluidity and Graphene in a Strong Magnetic Field by B. I. Halperin Nano-QT 2016 Kyiv October 11, 2016 Based on work with So Takei (CUNY), Yaroslav Tserkovnyak (UCLA), and Amir Yacoby (Harvard)
More informationFate of the Kondo impurity in a superconducting medium
Karpacz, 2 8 March 214 Fate of the Kondo impurity in a superconducting medium T. Domański M. Curie Skłodowska University Lublin, Poland http://kft.umcs.lublin.pl/doman/lectures Motivation Physical dilemma
More informationSUPPLEMENTARY INFORMATION
SUPPLEMENTARY INFORMATION DOI: 10.1038/NNANO.2012.160 Valley-spin blockade and spin resonance in carbon nanotubes Fei Pei, Edward A. Laird, Gary A. Steele, Leo P. Kouwenhoven Contents 1. Energy levels
More informationConcepts in Spin Electronics
Concepts in Spin Electronics Edited by Sadamichi Maekawa Institutefor Materials Research, Tohoku University, Japan OXFORD UNIVERSITY PRESS Contents List of Contributors xiii 1 Optical phenomena in magnetic
More informationWriting Spin in a Quantum Dot with Ferromagnetic and. Superconducting Electrodes arxiv:cond-mat/ v1 [cond-mat.mes-hall] 14 Jan 2003
Writing Spin in a Quantum Dot with Ferromagnetic and Superconducting Electrodes arxiv:cond-mat/0303v [cond-mat.mes-hall] 4 Jan 003 Yu Zhu, Qing-feng Sun, and Tsung-han Lin, State Key Laboratory for Mesoscopic
More informationScattering theory of nonlinear thermoelectric transport
Scattering theory of nonlinear thermoelectric transport David Sánchez Institute for Cross-Disciplinary Physics and Complex Systems IFISC (UIB CSIC, Palma de Mallorca, Spain) Workshop on Thermoelectric
More informationObservation and spectroscopy of a two-electron Wigner molecule in an ultraclean carbon nanotube
DOI: 10.1038/NPHYS69 Observation and spectroscopy of a two-electron Wigner molecule in an ultraclean carbon nanotube S. Pecker* 1, F. Kuemmeth*, A. Secchi 3,4, M. Rontani 3, D. C. Ralph 5,6, P. L. McEuen
More informationCharging and Kondo Effects in an Antidot in the Quantum Hall Regime
Semiconductor Physics Group Cavendish Laboratory University of Cambridge Charging and Kondo Effects in an Antidot in the Quantum Hall Regime M. Kataoka C. J. B. Ford M. Y. Simmons D. A. Ritchie University
More informationCarbon Nanotubes part 2 CNT s s as a toy model for basic science. Niels Bohr Institute School 2005
Carbon Nanotubes part 2 CNT s s as a toy model for basic science Niels Bohr Institute School 2005 1 Carbon Nanotubes as a model system 2 Christian Schönenberger University of Basel B. Babic W. Belzig M.
More informationA Tunable Kondo Effect in Quantum Dots
A Tunable Kondo Effect in Quantum Dots Sara M. Cronenwett *#, Tjerk H. Oosterkamp *, and Leo P. Kouwenhoven * * Department of Applied Physics and DIMES, Delft University of Technology, PO Box 546, 26 GA
More informationSpin orbit interaction in graphene monolayers & carbon nanotubes
Spin orbit interaction in graphene monolayers & carbon nanotubes Reinhold Egger Institut für Theoretische Physik, Düsseldorf Alessandro De Martino Andreas Schulz, Artur Hütten MPI Dresden, 25.10.2011 Overview
More informationSuperconducting Proximity Effect in Quantum-Dot Systems
p. 1 Superconducting Proximity Effect in Quantum-Dot Systems Jürgen König Institut für Theoretische Physik Universität Duisburg-Essen Transport through S-N and S-I-S Interfaces BCS superconductivity: pair
More informationDetecting and using Majorana fermions in superconductors
Detecting and using Majorana fermions in superconductors Anton Akhmerov with Carlo Beenakker, Jan Dahlhaus, Fabian Hassler, and Michael Wimmer New J. Phys. 13, 053016 (2011) and arxiv:1105.0315 Superconductor
More informationANDREEV BOUND STATES IN SUPERCONDUCTOR-QUANTUM DOT CHAINS. by Zhaoen Su Bachelor of Science, Lanzhou University, 2011
ANDREEV BOUND STATES IN SUPERCONDUCTOR-QUANTUM DOT CHAINS by Zhaoen Su Bachelor of Science, Lanzhou University, 211 Submitted to the Graduate Faculty of the Kenneth P. Dietrich School of Arts and Sciences
More informationarxiv:cond-mat/ v1 [cond-mat.mes-hall] 2 Mar 2007
Even-odd effect in Andreev Transport through a Carbon Nanotube Quantum Dot arxiv:cond-mat/0703082v1 [cond-mat.mes-hall] 2 Mar 2007 A. Eichler, M. Weiss, S. Oberholzer, and C. Schönenberger Institut für
More informationElectronic transport in low dimensional systems
Electronic transport in low dimensional systems For example: 2D system l
More informationQuantum Processes in Josephson Junctions & Weak Links. J. A. Sauls
CMS Colloquium, Los Alamos National Laboratory, December 9, 2015 Quantum Processes in Josephson Junctions & Weak Links J. A. Sauls Northwestern University e +iφ 2 e +iφ 1 111000 00000000 111111110000000
More informationMesoscopic Nano-Electro-Mechanics of Shuttle Systems
* Mesoscopic Nano-Electro-Mechanics of Shuttle Systems Robert Shekhter University of Gothenburg, Sweden Lecture1: Mechanically assisted single-electronics Lecture2: Quantum coherent nano-electro-mechanics
More informationEnergy Spectrum and Broken spin-surface locking in Topological Insulator quantum dots
Energy Spectrum and Broken spin-surface locking in Topological Insulator quantum dots A. Kundu 1 1 Heinrich-Heine Universität Düsseldorf, Germany The Capri Spring School on Transport in Nanostructures
More informationCarbon Nanotube Quantum Dot with Superconducting Leads. Kondo Effect and Andreev Reflection in CNT s
Carbon Nanotube Quantum Dot with Superconducting Leads Kondo Effect and Andreev Reflection in CNT s Motivation Motivation S NT S Orsay group: reported enhanced I C R N product S A. Yu. Kasumov et al. N
More informationOrbital Kondo anomaly and channel mixing effects in a double quantum dot *
Materials Science-Poland, Vol. 6, No. 3, 008 Orbital Kondo anomaly and channel mixing effects in a double quantum dot * D. SZTENKIEL **, R. ŚWIRKOWICZ Faculty of Physics, Warsaw University of Technology,
More informationCoulomb Blockade and Kondo Effect in Nanostructures
Coulomb Blockade and Kondo Effect in Nanostructures Marcin M. Wysokioski 1,2 1 Institute of Physics Albert-Ludwigs-Universität Freiburg 2 Institute of Physics Jagiellonian University, Cracow, Poland 2.VI.2010
More informationSUPPLEMENTARY INFORMATION
Electrical control of single hole spins in nanowire quantum dots V. S. Pribiag, S. Nadj-Perge, S. M. Frolov, J. W. G. van den Berg, I. van Weperen., S. R. Plissard, E. P. A. M. Bakkers and L. P. Kouwenhoven
More informationElectronic transport in topological insulators
Electronic transport in topological insulators Reinhold Egger Institut für Theoretische Physik, Düsseldorf Alex Zazunov, Alfredo Levy Yeyati Trieste, November 011 To the memory of my dear friend Please
More informationElectron transport through Shiba states induced by magnetic adsorbates on a superconductor
Electron transport through Shiba states induced by magnetic adsorbates on a superconductor Michael Ruby, Nino Hatter, Benjamin Heinrich Falko Pientka, Yang Peng, Felix von Oppen, Nacho Pascual, Katharina
More informationQuantum Confinement in Graphene
Quantum Confinement in Graphene from quasi-localization to chaotic billards MMM dominikus kölbl 13.10.08 1 / 27 Outline some facts about graphene quasibound states in graphene numerical calculation of
More informationarxiv:cond-mat/ v1 [cond-mat.mes-hall] 2 Feb 1998
Transport through an Interacting Quantum Dot Coupled to Two Superconducting Leads arxiv:cond-mat/9828v [cond-mat.mes-hall] 2 Feb 998 Kicheon Kang Department of Physics, Korea University, Seoul 36-7, Korea
More informationVortices in superconductors& low temperature STM
Vortices in superconductors& low temperature STM José Gabriel Rodrigo Low Temperature Laboratory Universidad Autónoma de Madrid, Spain (LBT-UAM) Cryocourse, 2011 Outline -Vortices in superconductors -Vortices
More informationCotunneling and Kondo effect in quantum dots. Part I/II
& NSC Cotunneling and Kondo effect in quantum dots Part I/II Jens Paaske The Niels Bohr Institute & Nano-Science Center Bad Honnef, September, 2010 Dias 1 Lecture plan Part I 1. Basics of Coulomb blockade
More informationSpin Coherent Phenomena in Quantum Dots Driven by Magnetic Fields
Spin Coherent Phenomena in Quantum Dots Driven by Magnetic Fields Gloria Platero Instituto de Ciencia de Materiales (ICMM), CSIC, Madrid, Spain María Busl (ICMM), Rafael Sánchez,Université de Genève Toulouse,
More informationPhase transitions in Bi-layer quantum Hall systems
Phase transitions in Bi-layer quantum Hall systems Ming-Che Chang Department of Physics Taiwan Normal University Min-Fong Yang Departmant of Physics Tung-Hai University Landau levels Ferromagnetism near
More informationEffet Kondo dans les nanostructures: Morceaux choisis
Effet Kondo dans les nanostructures: Morceaux choisis Pascal SIMON Rencontre du GDR Méso: Aussois du 05 au 08 Octobre 2009 OUTLINE I. The traditional (old-fashioned?) Kondo effect II. Direct access to
More informationThe Physics of Nanoelectronics
The Physics of Nanoelectronics Transport and Fluctuation Phenomena at Low Temperatures Tero T. Heikkilä Low Temperature Laboratory, Aalto University, Finland OXFORD UNIVERSITY PRESS Contents List of symbols
More informationarxiv:cond-mat/ v1 [cond-mat.mes-hall] 27 Nov 2001
Published in: Single-Electron Tunneling and Mesoscopic Devices, edited by H. Koch and H. Lübbig (Springer, Berlin, 1992): pp. 175 179. arxiv:cond-mat/0111505v1 [cond-mat.mes-hall] 27 Nov 2001 Resonant
More informationThe Quantum Spin Hall Effect
The Quantum Spin Hall Effect Shou-Cheng Zhang Stanford University with Andrei Bernevig, Taylor Hughes Science, 314,1757 2006 Molenamp et al, Science, 318, 766 2007 XL Qi, T. Hughes, SCZ preprint The quantum
More informationQuasi-particle current in planar Majorana nanowires
Journal of Physics: Conference Series PAPER OPEN ACCESS Quasi-particle current in planar Majorana nanowires To cite this article: Javier Osca and Llorenç Serra 2015 J. Phys.: Conf. Ser. 647 012063 Related
More informationTopological Kondo Insulator SmB 6. Tetsuya Takimoto
Topological Kondo Insulator SmB 6 J. Phys. Soc. Jpn. 80 123720, (2011). Tetsuya Takimoto Department of Physics, Hanyang University Collaborator: Ki-Hoon Lee (POSTECH) Content 1. Introduction of SmB 6 in-gap
More informationSemiconductors: Applications in spintronics and quantum computation. Tatiana G. Rappoport Advanced Summer School Cinvestav 2005
Semiconductors: Applications in spintronics and quantum computation Advanced Summer School 1 I. Background II. Spintronics Spin generation (magnetic semiconductors) Spin detection III. Spintronics - electron
More informationChapter 8: Coulomb blockade and Kondo physics
Chater 8: Coulomb blockade and Kondo hysics 1) Chater 15 of Cuevas& Scheer. REFERENCES 2) Charge transort and single-electron effects in nanoscale systems, J.M. Thijssen and H.S.J. Van der Zant, Phys.
More informationSelf-assembled SiGe single hole transistors
Self-assembled SiGe single hole transistors G. Katsaros 1, P. Spathis 1, M. Stoffel 2, F. Fournel 3, M. Mongillo 1, V. Bouchiat 4, F. Lefloch 1, A. Rastelli 2, O. G. Schmidt 2 and S. De Franceschi 1 1
More informationSpin-Polarized Current in Coulomb Blockade and Kondo Regime
Vol. 112 (2007) ACTA PHYSICA POLONICA A No. 2 Proceedings of the XXXVI International School of Semiconducting Compounds, Jaszowiec 2007 Spin-Polarized Current in Coulomb Blockade and Kondo Regime P. Ogrodnik
More informationVortex States in a Non-Abelian Magnetic Field
Vortex States in a Non-Abelian Magnetic Field Predrag Nikolić George Mason University Institute for Quantum Matter @ Johns Hopkins University SESAPS November 10, 2016 Acknowledgments Collin Broholm IQM
More informationExperimental Studies of Single-Molecule Transistors
Experimental Studies of Single-Molecule Transistors Dan Ralph group at Cornell University Janice Wynn Guikema Texas A&M University Condensed Matter Seminar January 18, 2006 p.1 Cornell Image from http://www.cornell.edu/
More informationRashba spin-orbit coupling in the oxide 2D structures: The KTaO 3 (001) Surface
Rashba spin-orbit coupling in the oxide 2D structures: The KTaO 3 (001) Surface Sashi Satpathy Department of Physics University of Missouri, Columbia, USA E Ref: K. V. Shanavas and S. Satpathy, Phys. Rev.
More informationEffects of Interactions in Suspended Graphene
Effects of Interactions in Suspended Graphene Ben Feldman, Andrei Levin, Amir Yacoby, Harvard University Broken and unbroken symmetries in the lowest LL: spin and valley symmetries. FQHE Discussions with
More informationThe 4th Windsor Summer School on Condensed Matter Theory Quantum Transport and Dynamics in Nanostructures Great Park, Windsor, UK, August 6-18, 2007
The 4th Windsor Summer School on Condensed Matter Theory Quantum Transport and Dynamics in Nanostructures Great Park, Windsor, UK, August 6-18, 2007 Kondo Effect in Metals and Quantum Dots Jan von Delft
More informationTopological Quantum Computation with Majorana Zero Modes. Roman Lutchyn. Microsoft Station
Topological Quantum Computation with Majorana Zero Modes Roman Lutchyn Microsoft Station IPAM, 08/28/2018 Outline Majorana zero modes in proximitized nanowires Experimental and material science progress
More informationLecture 26: Nanosystems Superconducting, Magnetic,. What is nano? Size
Lecture 26: Nanosystems Superconducting, Magnetic,. What is nano? Size Quantum Mechanics Structure Properties Recall discussion in Lecture 21 Add new ideas Physics 460 F 2006 Lect 26 1 Outline Electron
More informationInterference: from quantum mechanics to nanotechnology
Interference: from quantum mechanics to nanotechnology Andrea Donarini L. de Broglie P. M. A. Dirac A photon interferes only with itself Double slit experiment: (London, 1801) T. Young Phil. Trans. R.
More informationPG5295 Muitos Corpos 1 Electronic Transport in Quantum dots 2 Kondo effect: Intro/theory. 3 Kondo effect in nanostructures
PG5295 Muitos Corpos 1 Electronic Transport in Quantum dots 2 Kondo effect: Intro/theory. 3 Kondo effect in nanostructures Prof. Luis Gregório Dias DFMT PG5295 Muitos Corpos 1 Electronic Transport in Quantum
More informationPresented by: Göteborg University, Sweden
SMR 1760-3 COLLEGE ON PHYSICS OF NANO-DEVICES 10-21 July 2006 Nanoelectromechanics of Magnetic and Superconducting Tunneling Devices Presented by: Robert Shekhter Göteborg University, Sweden * Mechanically
More informationSIGNATURES OF SPIN-ORBIT DRIVEN ELECTRONIC TRANSPORT IN TRANSITION- METAL-OXIDE INTERFACES
SIGNATURES OF SPIN-ORBIT DRIVEN ELECTRONIC TRANSPORT IN TRANSITION- METAL-OXIDE INTERFACES Nicandro Bovenzi Bad Honnef, 19-22 September 2016 LAO/STO heterostructure: conducting interface between two insulators
More informationQuantum Transport through Coulomb-Blockade Systems
Quantum Transport through Coulomb-Blockade Systems Björn Kubala Institut für Theoretische Physik III Ruhr-Universität Bochum COQUSY6 p.1 Overview Motivation Single-electron box/transistor Coupled single-electron
More information3.45 Paper, Tunneling Magnetoresistance
3.45 Paper, Tunneling Magnetoresistance Brian Neltner May 14, 2004 1 Introduction In the past few decades, there have been great strides in the area of magnetoresistance the effect of magnetic state on
More informationElectron Interactions and Nanotube Fluorescence Spectroscopy C.L. Kane & E.J. Mele
Electron Interactions and Nanotube Fluorescence Spectroscopy C.L. Kane & E.J. Mele Large radius theory of optical transitions in semiconducting nanotubes derived from low energy theory of graphene Phys.
More informationSpins and spin-orbit coupling in semiconductors, metals, and nanostructures
B. Halperin Spin lecture 1 Spins and spin-orbit coupling in semiconductors, metals, and nanostructures Behavior of non-equilibrium spin populations. Spin relaxation and spin transport. How does one produce
More informationWhen a normal-type (N) conductor is connected to a
ARTICLES PUBLISHED ONLINE: 15 DECEMBER 213 DOI: 1.138/NNANO.213.267 Spin-resolved Andreev levels and parity crossings in hybrid superconductor semiconductor nanostructures Eduardo J. H. Lee 1, Xiaocheng
More informationLecture 8, April 12, 2017
Lecture 8, April 12, 2017 This week (part 2): Semiconductor quantum dots for QIP Introduction to QDs Single spins for qubits Initialization Read-Out Single qubit gates Book on basics: Thomas Ihn, Semiconductor
More informationCharges and Spins in Quantum Dots
Charges and Spins in Quantum Dots L.I. Glazman Yale University Chernogolovka 2007 Outline Confined (0D) Fermi liquid: Electron-electron interaction and ground state properties of a quantum dot Confined
More informationNonlocal transport properties due to Andreev scattering
Charles Univ. in Prague, 5 X 2015 Nonlocal transport properties due to Andreev scattering Tadeusz Domański Marie Curie-Skłodowska University, Lublin, Poland http://kft.umcs.lublin.pl/doman/lectures Outline
More informationZero-bias conductance peak in detached flakes of superconducting 2H-TaS2 probed by STS
Zero-bias conductance peak in detached flakes of superconducting 2H-TaS2 probed by STS J. A. Galvis, L. C., I. Guillamon, S. Vieira, E. Navarro-Moratalla, E. Coronado, H. Suderow, F. Guinea Laboratorio
More informationAditi Mitra New York University
Superconductivity following a quantum quench Aditi Mitra New York University Supported by DOE-BES and NSF- DMR 1 Initially system of free electrons. Quench involves turning on attractive pairing interactions.
More informationFinite-frequency Matsubara FRG for the SIAM
Finite-frequency Matsubara FRG for the SIAM Final status report Christoph Karrasch & Volker Meden Ralf Hedden & Kurt Schönhammer Numerical RG: Robert Peters & Thomas Pruschke Experiments on superconducting
More informationarxiv: v2 [cond-mat.mes-hall] 30 May 2015
Majorana Entanglement Bridge arxiv:53.6399v [cond-mat.mes-hall] 3 May 5 Stephan Plugge, Alex Zazunov, Pasquale Sodano,, 3, 4 and Reinhold Egger, Institut für Theoretische Physik, Heinrich-Heine-Universität,
More informationQuantum Transport and Dissipation
Thomas Dittrich, Peter Hänggi, Gert-Ludwig Ingold, Bernhard Kramer, Gerd Schön and Wilhelm Zwerger Quantum Transport and Dissipation WILEY-VCH Weinheim Berlin New York Chichester Brisbane Singapore Toronto
More informationCoulomb blockade in metallic islands and quantum dots
Coulomb blockade in metallic islands and quantum dots Charging energy and chemical potential of a metallic island Coulomb blockade and single-electron transistors Quantum dots and the constant interaction
More informationCarbon Nanotubes for Coherent Spintronics
Carbon Nanotubes for Coherent Spintronics The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Published Version Accessed
More informationSUPPLEMENTARY INFORMATION
doi:1.138/nature12186 S1. WANNIER DIAGRAM B 1 1 a φ/φ O 1/2 1/3 1/4 1/5 1 E φ/φ O n/n O 1 FIG. S1: Left is a cartoon image of an electron subjected to both a magnetic field, and a square periodic lattice.
More informationCooper-pair splitter: towards an efficient source of spin-entangled EPR pairs
Cooper-pair splitter: towards an efficient source of spin-entangled EPR pairs L. Hofstetter 1, A. Kleine 1, S. Csonka 1,2, A. Geresdi 2, M. Aagesen 3, J. Nygard 3, A. Baumgartner 1, J. Trbovic 1, and C.
More informationHerre van der Zant. interplay between molecular spin and electron transport (molecular spintronics) Gate
transport through the single molecule magnet Mn12 Herre van der Zant H.B. Heersche, Z. de Groot (Delft) C. Romeike, M. Wegewijs (RWTH Aachen) D. Barreca, E. Tondello (Padova) L. Zobbi, A. Cornia (Modena)
More informationSupplementary Information: Electrically Driven Single Electron Spin Resonance in a Slanting Zeeman Field
1 Supplementary Information: Electrically Driven Single Electron Spin Resonance in a Slanting Zeeman Field. Pioro-Ladrière, T. Obata, Y. Tokura, Y.-S. Shin, T. Kubo, K. Yoshida, T. Taniyama, S. Tarucha
More informationModern Physics for Scientists and Engineers International Edition, 4th Edition
Modern Physics for Scientists and Engineers International Edition, 4th Edition http://optics.hanyang.ac.kr/~shsong 1. THE BIRTH OF MODERN PHYSICS 2. SPECIAL THEORY OF RELATIVITY 3. THE EXPERIMENTAL BASIS
More informationWe study spin correlation in a double quantum dot containing a few electrons in each dot ( 10). Clear
Pauli spin blockade in cotunneling transport through a double quantum dot H. W. Liu, 1,,3 T. Fujisawa, 1,4 T. Hayashi, 1 and Y. Hirayama 1, 1 NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya,
More information