Carbon Nanotube Quantum Dot with Superconducting Leads. Kondo Effect and Andreev Reflection in CNT s

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2 Carbon Nanotube Quantum Dot with Superconducting Leads Kondo Effect and Andreev Reflection in CNT s

3 Motivation

4 Motivation S NT S Orsay group: reported enhanced I C R N product S A. Yu. Kasumov et al. N N NT entangler T. Martin... M. Fisher... D. Loss...

5 Introduction

6 Singlewall Multiwall S. Iijima nm 1-2 nm

7 Synthesis: arc discharge L. Forro et al. EPFL

8 Contacting SEM image L Au Ι Vg Vsd

9 Contacts nm 2 µm

10 500 nm AFM picture

11 Measuring setup

12 wire-like behaviour long tube (7.4 mm) ZBA UCF

13 Quantum Dot Physics

14 Quantum dots

15 ( conventional ) Quantum dots planar dot planar double-dot vertical dot

16 quantum dot? 2 µm

17 1d quantum dot (0d( 0d) δe=h/τ round-trip Γ < δe for any quantum dot in addition: ev and kt if we use superconducting electrodes, there is in addition a 6th parameter: D

18 Contacts matter, i.e. G U >> Γ charge box (independent of δe) metal nano-particle U > δe > Γ quantized charge box Tarucha dots Γ > (U,δE) weak link δe > U > Γ strongly interacting quantum dot δe > Γ > U weakly interacting quantum dot carbon nanotubes

19 simplified... First, ideal quantum dot has: de fi easy, if U << Γ easy, if U >> Γ not easy, if U Γ resonant tunneling single-electron tunneling correlated electron transport

20 open nanotube dot G>> U normal leads

21 MWNT open Q-dot Q (δe~( E~Γ>U) Buitelaar et al. PRL 88, (2002) similar to Fabry-Perot of SWNTs: W. Liang et al., Nature 411, p 665 (2001)

22 closed nanotube dot G<< U normal leads

23 single-electron electron tunneling V sd (mv) DE add add addition energy, i.e. sum of: single-electron charging energy U C V g level-spacing de Change V sd Change V g

24 even even even odd odd odd filling of states according to S = 1/2 0 1/2... odd number of electrons: DE add = U C even number of electrons: DE add = U C + de

25 open nanotube dot G~ U (correlated transport) normal leads

26 V sd (mv) rel. open MWNT Q-dotQ When the number of electrons on the quantum dot is odd, spin-flip processes (which screen the spin on the dot) lead to the formation of a narrow resonance in the density-of-states at the Fermi energy of the leads. V g This is called the Kondo effect Related work: J.Nygard et al, Nature 408, 342 (2000)

27 Mark Buitelaar et al. PRL 89, (2002) 50 mk de ~ 0.6 mev U C ~ 0.4 mev G ~ 0.3 mev

28 open dot with superconducting leads

29 Kondo physics + superconductivity Kondo effect Superconductivity Al Kondo effect and superconductivity are many-electron effects can Kondo and superconductivity coexist or do they exclude each other?

30 spin 1/2 Kondo + S-leadsS normal case superconducting case U E F 1. a gap opens in the leads 2. Cooper pairs have S=0 Kondo effect is the screening of the spin-degree of the dot spin by exchange with electrons from Fermi-reservoirs (the leads) Hence: Kondo effect suppressed, but...

31 Kondo effect Superconductivity Cooper pair Energy scale : ~ k b T K S = 0 Cooper pair Energy scale : ~ D S = 0 A cross-over expected at k b T K ~ D

32 V sd (mv) N Kondo ridge A : 0.75 K Kondo ridge B : 1.11 K Kondo ridge C : 0.96 K V sd (mv) V g S A: decreasing conductance B: increasing conductance C: decreasing conductance V g Buitelaar et al. PRL 88, (2002)

33 different Kondo temperature T K =0.71 K T K =0.96 K T K =1.11 K T K =1.86 K

34 Low T K High T K normal state superconducting state = 0.1 mev or 1.16 K Buitelaar et al. PRL 88, (2002)

35 Andreev reflection through a single level

36 finite bias structure

37 Andreev reflection finite bias structure

38 multiple Andreev reflection (MAR) finite bias structure

39 MAR has been explored in weak links and in single atom contacts (break junctions) theory: Cuevas et al. PRB 54, 7366 (99)

40 MAR has been explored in weak links and in single atom contacts (break junctions) but not in quantum dots dot level dot level G ~ D (Γ 3 )

41 theory (non-interacting)

42 2D/2 2D/3

43 2 2 / 2 2 / 3 2 / 4

44 experiment theory

45 experiment theory

46 explanation? 2 /3 2 /2 BCD-DOS modified Kondo

47 Conclusions nanotubes serve as a model system to study physics Kondo physics (co-tunneling) Interplay between Kondo physics & superconductivity (superconducting) correlations through a single level group Web-page nano.org NCCR on Nanoscience

48 Outlook S NT S Orsay group: reported enhanced I C R N product S A. Yu. Kasumov et al. N N NT entangler T. Martin... M. Fisher... D. Loss...

49 Acknowledgment University of Basel A. Bachtold B. Babic W. Belzig C. Bruder M. Buitelaar M. Calame S. Farhangfar J. Furer M. Gräber S. Ifadir M. Iqbal T. Kontos M. Krüger Z. Liu T. Nussbaumer S. Sahoo C. Strunk EPFL László Forró s group Ecole Polytechnique Fédérale de Lausanne national center Swiss National Science Foundation