InAs InAs nanowire nanowire based cooper pair based cooper pair - PDF document

CooPairEnt CooPairEnt www.nanoelectronics.ch InAs InAs nanowire nanowire based cooper pair based cooper pair splitter splitter Sz Csonka Budapest University of Technology and Economics & University of Basel Motivation CooPairEnt CooPairEnt www.nanoelectronics.ch in collaboration with R. Gschwind Cooper pair: Cooper pair: Spin singlet electron pair Spin singlet electron pair Source of mobile, entangled electrons Source of mobile, entangled electrons e.g. J. Torres and T. Martin, Eur. Phys. J. B 12, 319, 322 (1999) http://www.qgd.uzh.ch 1

CooPairEnt CooPairEnt Metallic nanostructures www.nanoelectronics.ch Beckmann et al.; PRL 93, 197003 (2004) Russo et al.; Phys. Rev. Lett. 95 , 027002 (2005) Beckmann et al.; Appl. Phys. A 603 (2007) Cadden-Zimansky et al., Phys. Rev. Lett. 97 , 237003 (2006) Cadden-Zimansky et al., New J. of Phys. 9 , 116 (2007) A. Kleine et al., EPL 87 , 27011 (2009) A. Kleine et al., Nanotechnology 21, 274002 (2010) Andreev entangler CooPairEnt CooPairEnt www.nanoelectronics.ch J. Torres and T. Martin, Eur. Phys. J. B 12, 319{322 (1999) P. Recher, E.V. Sukhorukov, and D. Loss, Phys. Rev. B 63 , 165314 (2001) N. M.Chtchelkatchev et al. Phys. Rev. B 66 , 161320 (2002) P. Recher and D. Loss, Phys. Rev. B 65, 165327 (2002) h d h ( ) C. Bena, S.Vishveshwara et al. PRL 89 , 037901 (2002) O. Sauret, D. Feinberg, T. Martin PRB 70 , 245313 (2004) … 2

Andreev entangler CooPairEnt CooPairEnt www.nanoelectronics.ch Efficient and controlled pair splitting? Efficient and controlled pair splitting? see also: O. Sauret, D. Feinberg, T. Martin PRB 70 , 245313 (2004) … Experiments: Experiments: p L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) Herrmann et al., PRL 104 , 026801 (2010) CooPairEnt CooPairEnt Entangler based on Qdots www.nanoelectronics.ch ~1/U ~1/ Δ ~1 Cooper pair splitting Cooper pair splitting Direct pair tunneling Direct pair tunneling Recher et al. PRB, 63, 165314 (2001) 3

CooPairEnt CooPairEnt Entangler based on Qdots www.nanoelectronics.ch ~1/U ~1/ Δ ~1 Direct pair tunneling Direct pair tunneling Cooper pair splitting Cooper pair splitting Recher et al. PRB, 63, 165314 (2001) CooPairEnt CooPairEnt Device www.nanoelectronics.ch S electrode connected to two tunable QDs S-electrode connected to two tunable QDs • InAs NW: d ≈ 80nm • QDs: U ≈ 2-4meV • superconductor (Ti/Al), w ≈ 200nm • clear subgap feature: Δ ≈ 160 μ V • top gates with surface oxide • very weak ( ≈ 1/1000) cross capacitance • 2 InAs NW QDs separately tuned by top gates (V SG and V TG ) Δ V SG / Δ V TG ; Δ G S ( Δ V SG ) = Δ G S ( Δ V TG ) L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) 4

Measurement principle CooPairEnt CooPairEnt www.nanoelectronics.ch V ac sensing gate tuning gate V SG V TG S S I S I T sensing tuning qdot qdot I/V I/V G =I /V G =I S /V S ac T T ac G nonlocal (V TG ) = G S (V TG ) - ( α+β V TG ) NONLOCAL MEASUREMENT: NONLOCAL MEASUREMENT: current measurement of sensing qdot while sweeping the gate of the tuning qdot Cooper pair splitting contributes to I S ; depends on sensing QD and tuning QD L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) Measurement principle CooPairEnt CooPairEnt www.nanoelectronics.ch 0.4 0.30 0.50 0.29 0.3 0.25 d [mV] S (G 0 ) 0.28 G 0 ) 0.00 0.2 G S V s G S ( 0.27 -0.25 0.1 0.26 -0.50 0.0 0.25 -3 2 1.5 2.0 2.5 3.0 -0.0050 0.0025 V SG (mV) V SG (mV) V SG [V] 0.24 65 70 75 80 85 V TG (mV) 0.0 0.2 0.4 G S [G 0 ] • quantum dot with U ≈ 2-4meV, ε ≈ 1meV • clear subgap feature, gap visible, Δ ≈ 160 μ V • very weak ( ≈ 1/1000) cross capacitance cross capacitance = Δ V SG / Δ V TG ; Δ G S ( Δ V SG ) = Δ G S ( Δ V TG ) L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) 5

Measurement principle CooPairEnt CooPairEnt www.nanoelectronics.ch 0.4 0.30 0.50 0.29 0.3 0.25 d [mV] S (G 0 ) 0.28 G 0 ) 0.00 0.2 G S V s G S ( 0.27 -0.25 0.1 0.26 -0.50 0.0 0.25 -3 2 1.5 2.0 2.5 3.0 -0.0050 0.0025 V SG (mV) V SG (mV) V SG [V] 0.24 65 70 75 80 85 V TG (mV) 0.0 0.2 0.4 G S [G 0 ] • quantum dot with U ≈ 2-4meV, ε ≈ 1meV • clear subgap feature, gap visible, Δ ≈ 160 μ V • very weak ( ≈ 1/1000) cross capacitance cross capacitance = Δ V SG / Δ V TG ; Δ G S ( Δ V SG ) = Δ G S ( Δ V TG ) L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) Measurement principle CooPairEnt CooPairEnt www.nanoelectronics.ch 0.4 0.30 0.50 0.29 0.3 0.25 d [mV] S (G 0 ) 0.28 G 0 ) 0.00 0.2 G S V s G S ( 0.27 -0.25 0.1 0.26 -0.50 0.0 0.25 -3 2 1.5 2.0 2.5 3.0 -0.0050 0.0025 V SG (mV) V SG (mV) V SG [V] 0.24 65 70 75 80 85 V TG (mV) 0.0 0.2 0.4 G S [G 0 ] • clear subgap feature, gap visible, Δ ≈ 160 μ V • very weak ( ≈ 1/1000) cross capacitance • averaging (~10 2 ) necessary to make signal visible L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) 6

Results CooPairEnt CooPairEnt www.nanoelectronics.ch 1.0 B = 120mT 0.000 0.5 G Nonlocal [G 0 ] -0.004 G T [G 0 ] 0.0 B = 0mT 0.002 1.0 Current in sensor dot (I S ): • positive non local signal iti l l i l -0.002 while sweeping the V TG at B = 0 ! 0.5 • background, G S ~ 0.15 G 0 ⇒ signal few % -0.006 0.0 • B > B c signal changes sign and 0.070 0.075 0.080 0.085 corresponds to the classical circuit V TG [V] response (no fitting parameters) Results CooPairEnt CooPairEnt www.nanoelectronics.ch 1.0 B = 120mT 0.000 0.5 G Nonlocal [G 0 ] G T [G 0 ] -0.004 0.0 B = 0mT 0.002 1.0 Current in sensor dot (I S ): • positive non local signal iti l l i l -0.002 while sweeping the V TG at B = 0 ! 0.5 • background, G S ~ 0.15 G 0 ⇒ signal few % -0.006 0.0 • B > B c signal changes sign and 0.070 0.075 0.080 0.085 corresponds to the classical circuit V TG [V] response (no fitting parameters) 7

CooPairEnt CooPairEnt Explanation www.nanoelectronics.ch Regime: U >> Δ >> T; ε > Δ , Γ ≈ Δ ; ξ ≈ w S Transport happens in pairs of electrons we observe the Cooper pair splitting � Locally separated (entangled) electrons Cooper pair splitting CPS Direct pair tunneling Direct pair tunneling DPT DPT L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) Explanation CooPairEnt CooPairEnt www.nanoelectronics.ch Simple non-interacting tunneling picture (T i <<1) T T T S I S = I DPT + I CPS /2 I I DPT T S T S ~ T · T I I CPS ~ T · T T S T T -3 G 0 ] ] 2 1.0 G Nonlocal [10 G T [G 0 ] � G Nonlocal ~ T T -2 0.5 � Since G T ≈ I T DPT ~T T 2 , G Nonlocal ~G T 1/2 -6 0.0 0.070 0.075 0.080 0.085 L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) 8

CooPairEnt CooPairEnt Explanation www.nanoelectronics.ch Simple non-interacting tunneling picture (T i <<1) T S T T I S = I DPT + I CPS /2 G T ) 1/2 I DPT T S T S I ~ T · T I CPS I ~ T · T T S T T G Nonlocal [10 -2 G 0 ], (G � G Nonlocal ~ T T � Since G T ≈ I DPT ~T T 2 , G Nonlocal ~G T 1/2 L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) Control of Cooper pair splitting CooPairEnt CooPairEnt www.nanoelectronics.ch V TG [V] V TG [V] 0.066 0.068 0.070 0.066 0.068 0.070 0.50 G T [G 0.004 0.000 0.25 -0.004 0 004 0 ] 0.00 0.004 0.000 G Nonlocal [G 0 ] 0.004 0.3 0.000 -0.004 G S [G 0 the sign of the non-local signal depends 0.2 0.004 G Nonlocal [G 0 ] 0.000 0 000 0 ] on the state of the sensing qdot: -0.004 0.1 � dot sensing out of resonance: 0.004 0.000 G Nonlocal follows G T -0.004 0.0 0.066 0.068 0.070 0.001 0.002 Cooper pair splitting V TG [V] V SG [V] � dot sensing in resonance: “classical” filtering of DPT is not efficient L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) 9

Control of Cooper pair splitting CooPairEnt CooPairEnt www.nanoelectronics.ch V TG [V] V TG [V] 0.066 0.068 0.070 0.066 0.068 0.070 0.50 G T [G 0 0.004 0.000 0.25 -0.004 0 004 0 ] 0.00 0.004 0.000 G Nonlocal [G 0 ] 0.004 0.3 0.000 -0.004 G S [G 0 the sign of the non-local signal depends 0.2 0.004 G Nonlocal [G 0 ] 0.000 0 000 0 ] on the state of the sensing qdot: -0.004 0.1 � dot sensing out of resonance: 0.004 0.000 G Nonlocal follows G T -0.004 0.0 0.066 0.068 0.070 0.001 0.002 Cooper pair splitting V TG [V] V SG [V] � dot sensing in resonance: “classical” filtering of DPT is not efficient L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) Temperature dependence CooPairEnt CooPairEnt www.nanoelectronics.ch non local signal • vanishes at ~ 200mK but i h t 200 K b t superconducting gap still visible up to 600mK (T C = 1.2 K) • T dependence on top, left and right side of sensing qdot’s Coulomb blockade q peak • monotonous decay of the nonlocal signal with T L. Hofstetter, S. C. et al., Nature 461 , 960-963 (2009) 10