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 transistor The CNT SQUID experiment Current Phase relation of proximity coupled Qdot Application of the device
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
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
Proximity effect in SN NT NS junction Al Pd Al Pd Al Pd MetallicSWNT Pd Al S N Qdot N S
14 12 1 Proximity Effect (Al Pd 3nm).4K.7K.3K.9 K.5 K di/dv (kω) 8 6 4 2 MAR 2 g -3-2 -1 V ds (µv) 1 2 3
Proximity effect in SN NT NS junction Al/Pd/CNT/Pd/Al 7 6 dv/di (k Ω) 5 4 3 2 1.4 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 -2-15 -1-5 5 1 15 2 V ds ( µv) Pd(3 nm)/al(5 nm) Pd(6 nm)/al(5 nm)
The nanotube Josephson transistor S S VG Off On Energy level schematics P. Jarillo-Herrero, et al., Nature 439, 953-956 (26). E 2 g T1 T2
Gate voltage dependence of the switching current 8 6 4 V ( µv) 2-2 -4 V G -9. V -6-8 -.8 -.6 -.4 -.2.2.4.6.8 I (na)
Gate voltage dependence of the switching current V ( µv) 8 6 4 2-2 -4-6 V G -9. V -9.6 V -1. V -11. V -8 -.8 -.6 -.4 -.2.2.4.6.8 I (na)
Kondo effect in CNT junctions V sd (mv) 6 4 2-2 2N-2 2N 2N+2 H z = 5 mt 35 mk -4-6 -3-2 -1 1 2 3 Conductance di/dv T 2 2 4 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
Kondo resonance in CNT Qdots 6 4 V sd (mv) 2-2 -4 α β γ δ di/dv (e 2 /h) 1.6 1.4 1.2 1.8.6.4.2-6 -3-2 -1 1 2 3.1 K α β γ δ Pi junction -4-2 2 4 V sd (mv)
Temperature dependence of the Kondo resonance a di/dv (e 2 /h) 1.6 1.4 1.2 1.8.6.4.1 K α β γ δ b Pi junction di/dv (e 2 /h).2.18.16.14.12.4 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).2 1.2 1.8.6.4-4 -2 2 4 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).1 -.15 -.1 -.5.5.1.15 V sd (mv) 1.2 1.8.6.4.2 T K =.24 K T K =.1 K.2 -.15 -.1 -.5.5.1.15.1.1 1 V sd (mv) T (K) G(T) = G /[1 + (2 1/s 1)(T/T K ) 2 ] s s=.22
Interplay between Kondo effect and superconductivity V sd (mv) 6 4 2-2 2N-2 2N 2N+2 H z = 5 mt 35 mk di/dv I (na) -4-6 3-3 -2-1 1 2 3 2 1-1 2 4 e 2 /h H z = -2-3 -3-2 -1 1 2 3 dv/di 6.5 18 kω
Differential conductivity di/dv map versus sidegate voltages 2 1 V sd (mv) 6 4 2-2 -4 Single CNT-junction α β γ δ H z = 5 mt 35 mk V BG = V -6-3 -2-1 1 2 3 double Q-dot in parallel V G1-1 -2 V G2-2 -1 1 2 V G2 (V) 2 4 6 e 2 /h
Differential conductivity di/dv map versus sidegate voltages 2 1 H z = 5 mt 35 mk V BG = V -1-2 2 6 4 e 2 /h -2-1 1 2 V G2 (V)
Differential conductivity di/dv map versus sidegate voltages 2 1 H z = 5 mt 35 mk V BG = -4 V -1-2 2 4 6 e 2 /h -2-1 1 2 V G2 (V)
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
CNT-SQUID flux modulation characteristics 12 8 Qdots «on» 6 5 V (µv) ( µ ) 4-4 -8 I (na) 4 3 2 1 V (µv) ( µ ) 12 8 6 4 2-2 -4-6 -6-4 -2 2 4 6 I (na) Qdots «off» I (pa) ( ) 6 5 4 3 2 1 5 1 15 2 µ H z (mt) -8-6 -4-2 2 4 6 I (pa) 5 1 15 2 µ H z (mt)
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
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) 3 3 3 2 2 2 1 1 I 1-1 -1 II -1-2 -3-2 -3 III -2-3 -3-2 -1 1 2 3 V G2 (V) -3-2 -1 1 2 3 V G2 (V) -3-2 -1 1 2 3 V G2 (V) 2 4 e 2 /h 2 4 6 na
Magnetic Field dependence I (na) 6 4 2-2 I (na) 1 5-5 -4 on -1 off -6 5 1 15 2 25 3 35 Hz (mt) 5 1 15 2 25 3 35 Hz (mt) 6.8 k Ω 12 k Ω
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 3-4 2 1-8 -12-16.5 1 na 4 8 12 16 2 24 V G2 (V) -1-2 -3-3 -2-1 1 2 3 V G2 (V) 2 4 e 2 /h
π - junction SQUID 3 2 di/dv(v G1,V G2 ) map H z = 5 mt I ( na) 1.8.6.4 1-1.2-4 -8. V -9.7 V -1. V -1.9 V -1 1 2 3 4 5 6 7 µ H z (mt) -2-3 -3-2 -1 1 2 3 V G2 (V) -8-12 -16 4 8 12 16 2 24 V G2 (V) π -4% 8% 2 4 e 2 /h
initial π junction in Odd proximity coupled Qdots intermediate 2 1 2 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
Double Pi-junction SQUID V G1 π π V G2 π -4-4 π π -8-8.2.4 na -5% 75% π 2 24 28 V G2 (V) 2 24 28 V G2 (V)
Preliminary estimation of the flux sensitivity of CNT-SQUIDs CNT-SQUID characteristics I sw histogram 2 1.8 3 na/φ 15 N = 56 1.6 1 I (na) 1.4 1.2 Count 5 1.8.2.4.6.8 1 Φ/ Φ 1.41 1.42 1.43 1.44 1.45 1.46 1.47 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.
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
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
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?