The Nanotube SQUID. uhu,, M. Monthioux,, V. Bouchiat, W. Wernsdorfer, CEMES-Toulouse, CRTBT & LLN Grenoble

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1 The Nanotube SQUID J.-P. Cleuziou,, Th. Ondarçuhu uhu,, M. Monthioux,, V. Bouchiat, W. Wernsdorfer, CEMES-Toulouse, CRTBT & LLN Grenoble

2 Outline Sample fabrication Proximity effect in CNT The CNT superconducting transistor The CNT SQUID experiment Current Phase relation of proximity coupled Qdot Application of the device

3 Sample fabrication Nanotube in surfactant (SDS) Deposition by «combing» on functionnalized silica 2.µm Alignment with AFM E beam lithography Lift-off of Paladium/Aluminum bilayer

4 Carbon nanotube SQUID fabrication G1 SWNT Gnd G2 5 nm Forked geometry same nanotube for both arms -> molecular weak link with same chirality & balanced SQUID

5 Proximity effect in SN NT NS junction Al Pd Al Pd Al Pd MetallicSWNT Pd Al S N Qdot N S

6 Proximity Effect (Al Pd 3nm).4K.7K.3K.9 K.5 K di/dv (kω) MAR 2 g V ds (µv) 1 2 3

7 Proximity effect in SN NT NS junction Al/Pd/CNT/Pd/Al 7 6 dv/di (k Ω) K.1 K.15 K.2 K.25 K.3 K.35 K MAR 2 g.4 K.45 K.5 K.55 K.6 K.7 K.8 K V ds ( µv) Pd(3 nm)/al(5 nm) Pd(6 nm)/al(5 nm)

8 The nanotube Josephson transistor S S VG Off On Energy level schematics P. Jarillo-Herrero, et al., Nature 439, (26). E 2 g T1 T2

9 Gate voltage dependence of the switching current V ( µv) V G -9. V I (na)

10 Gate voltage dependence of the switching current V ( µv) V G -9. V -9.6 V -1. V -11. V I (na)

11 Kondo effect in CNT junctions V sd (mv) N-2 2N 2N+2 H z = 5 mt 35 mk Conductance di/dv T e 2 /h U c = 6 mev δe = 9 mev Γ = 1 mev δe = hv F /2L v F = 8.1 x 1 5 m/s Fermi velocity in the CNT L = 186 nm, comparable to CNT length of 2 nm T 1 V G E F

12 Kondo resonance in CNT Qdots 6 4 V sd (mv) α β γ δ di/dv (e 2 /h) K α β γ δ Pi junction V sd (mv)

13 Temperature dependence of the Kondo resonance a di/dv (e 2 /h) K α β γ δ b Pi junction di/dv (e 2 /h) K.8 K.1 K.15 K.2 K.3 K.4 K.5 K.6 K.8 K 1. K c di/dv (e 2 /h) V sd (mv).4 K.12 K.2 K.3 K.4 K.5 K.6 K.8 K 1. K 1.2 K d di/dv max (e 2 /h) V sd (mv) T K =.24 K T K =.1 K V sd (mv) T (K) G(T) = G /[1 + (2 1/s 1)(T/T K ) 2 ] s s=.22

14 Interplay between Kondo effect and superconductivity V sd (mv) N-2 2N 2N+2 H z = 5 mt 35 mk di/dv I (na) e 2 /h H z = dv/di kω

15 Differential conductivity di/dv map versus sidegate voltages 2 1 V sd (mv) Single CNT-junction α β γ δ H z = 5 mt 35 mk V BG = V double Q-dot in parallel V G V G V G2 (V) e 2 /h

16 Differential conductivity di/dv map versus sidegate voltages 2 1 H z = 5 mt 35 mk V BG = V e 2 /h V G2 (V)

17 Differential conductivity di/dv map versus sidegate voltages 2 1 H z = 5 mt 35 mk V BG = -4 V e 2 /h V G2 (V)

18 G1 CNT Carbon nanotube SQUID V BG G2 5 nm I On On V G1 II Off On V G1 III Off Off V G1 V G2 V G2 V G2

19 CNT-SQUID flux modulation characteristics 12 8 Qdots «on» 6 5 V (µv) ( µ ) I (na) V (µv) ( µ ) I (na) Qdots «off» I (pa) ( ) µ H z (mt) I (pa) µ H z (mt)

20 Estimation of the critical current Calculation of the current driven by discreete Andreev states F BCS free energy =.6 mev and N=1 gives I c = 15 na

21 Correlation between normal state conductance and superconducting switching current I sw V BG = -6V di/dv(v G1,V G2 ) map H z = 5 mt I sw (V G1,V G2 ) map H z = I sw (V G1,V G2 ) map H z = 1.3 mt (Φ /2=h/4e) I II III V G2 (V) V G2 (V) V G2 (V) 2 4 e 2 /h na

22 Magnetic Field dependence I (na) I (na) on -1 off Hz (mt) Hz (mt) 6.8 k Ω 12 k Ω

23 π - junction SQUID di/dv(v G1,V G2 ) map H z = 5 mt I sw (V G1,V G2 ) map H z = V BG = V na V G2 (V) V G2 (V) 2 4 e 2 /h

24 π - junction SQUID 3 2 di/dv(v G1,V G2 ) map H z = 5 mt I ( na) V -9.7 V -1. V -1.9 V µ H z (mt) V G2 (V) V G2 (V) π -4% 8% 2 4 e 2 /h

25 initial π junction in Odd proximity coupled Qdots intermediate g Quantum state of Cooper pairs condensate final 4 3 B.I. Spivak and S.A. Kivelson Phys. Rev. B 43, 374 (1991) π-shift in the Creation operators Josephson relation anticommutation I s = I c sin(ϕ+π) generates π-shift = -I c sin(ϕ) Reversal of the Josephson current

26 Double Pi-junction SQUID V G1 π π V G2 π -4-4 π π na -5% 75% π V G2 (V) V G2 (V)

27 Preliminary estimation of the flux sensitivity of CNT-SQUIDs CNT-SQUID characteristics I sw histogram na/φ 15 N = I (na) Count Φ/ Φ I (na) Flux sensitivity: [3.5 pa]/([3 na/φ ]*sqrt[1]) 1-5 Φ when averaging I sw during 1 s at a rate of 1 khz.

28 Magnetization switching of single molecules micro-squid versus nano-squid (CNT-SQUID) Optimising the flux coupling factor 5 nm nanoparticle 2 nm junction substrate molecule stray field.6 nm 1 nm molecule nanotube carbon nanotube junction substrate

29 Estimation of magnetic flux variation for Mn 12 with S = 1 molecule stray field.6 nm molecule 1 nm nanotube carbon nanotube junction substrate The total magnetic flux Φ of a uniformly magnetized sphere, R =.5 nm. Φ = 1 2 µ Φ = 1.1 x 1-4 Φ for Mn 12 with S = 1 m R Flux sensitivity for the CNT-SQUIDs: 1-5 Φ when averaging I sw during 1 s at a rate of 1 khz

30 Summary Interplay between Kondo effect and superconductivity ->The critical current is enhanced for strong Kondo resonances Gate controlled phase current relation -> tunable Pi SQUID ->Supercurrent reversal in proximity coupled Qdot Noise and performance of the SQUID is compatible with single molecule magnetization measurement A tool for Quantum information?