QUANTUM TRANSPORT IN BOTTOM-UP SEMICONDUCTOR NANOSTRUCTURES

Transcription

1 QUANTUM TRANSPORT IN BOTTOM-UP SEMICONDUCTOR NANOSTRUCTURES Silvano De Franceschi INAC/SPSMS/LaTEQS: Laboratory of quantum electron transport and superconductivity Silvano De Franceschi GDR Physique Quantique Mésoscopique, Aussois 8-11 décembre 2008

2 Top-down Quantum Dot Devices 2 1 Spathis et al. (poster session) V SD (mv) 0-1 N= V g (mv) Hofheinz, Jehl, Sanquer et al. V g Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/2008 2

3 Semiconductor nanowires: growth and device fabrication Catalytic VLS growth gold particle vapor liquid eutect time nanowire I - V - I + V + SiO 2 Si (p+) 1 μm source L sd W φ V gate drain Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/2008 3

4 Bottom-up semiconductor nanowire LaTEQS 1µm Si nanowires (Mongillo et al.) Aluminum bottom gates InAs/InP core/shell nanowires (Katsaros et al) 1 μm Ni silicide GaN/AlGaN nanowires (Songmuang et al) 1µm Mn-GaAs nanowires (Storace et al) 200 nm Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/2008 4

5 Self-assembled semiconductor quantum dot LaTEQS Ge islands on Si (Katsaros et al) gate source drain Source-drain bias gate gate voltage Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/2008 5

6 Hybrid normal-superconductor devices Josephson effect and Andreev reflection Thin insulating (oxide) interlayer φ S φ D I S = I C sin(φ S - φ D ) S _ I _ S Short (L< L Φ )normal-conductor interlayer L φ S φ D Andreev reflection I S = I C sin(φ S - φ D ) S _ N _ S Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/2008 6

7 Hybrid normal-superconductor devices?? Nano-link S _ DOT _ S How does superconductivity affects transport? Can a supercurrent flow? What is the current-phase relationship? Can superconductivity provide insight on the electronic properties? Many energy scales involved Superconducting gap Δ Charging energy U Level spacing ΔE Lifetime broadening Γ Thouless energy E Th = h/τ D Temperature k B T Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/2008 7

8 Hybrid normal-superconductor devices Metal Nanoparticles in an oxide thin layer: Ralph et al, PRL 95 Atomic-size contacts: Scheer et al., PRL 97; PRL 01. Kasumov et al, Science ) Morpurgo et al., Science Buitelaar et al., PRL 02 Jarillo-Herrero et al., Nature 06 Cleuziou et al., Nature Nanotech. 06 Doh et al. Science 05 van Dam et al. Nature 06 Xiang et al., Nature Nanotech. 06 Sand-Jespersen, PRL 07 Heersche et al. Nature 06 Buizert et al. PRL 07 Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/2008 8

9 Andreev reflection vs Coulomb blockade S-N-S devices based on InAs or InP nanowire DIfferent regimes depending on relative value of the relevant energy scales: Superconducting gap Δ Charging energy U Level spacing ΔE Lifetime broadening Γ Thouless energy E Th = h/τ D Temperature k B T R N /R Q as characteristic parameter (with R N the normal-state resistance and R Q (2e 2 /h) -1 ~26 kω the quantum resistance) Y.-J. Doh, SD, et al. Nano Letters, 8 Dec Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/2008 9

10 n-type InP nanowire (n~10 19 cm -3 ): weak coupling case R N >> R Q (2e 2 /h) -1 ~26 kω => Coulomb blockade di/dv sd vs (V sd,v g ) B= 20 mt sd Charging energy: U ~ 1 mev B= 20 mt U Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

11 n-type InP nanowire (n~10 19 cm -3 ): weak coupling case R N >> R Q (2e 2 /h) -1 ~26 kω di/dv sd vs (V sd,v g ) +2Δ +Δ -Δ -2Δ sd B = 0 B= Δ << 0 U B= 20 mt Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

12 Negative differential conductance due to BCS singularities B = 20 mt B = 0 Δ Δ Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

13 n-doped InAs nanowires (n~10 19 cm -3 ): strong coupling case R N as low as ~1 KΩ => No Coulomb blockade upercond. Source SiO 2 Normal Supercond. Drain I C = 136 na R N = 417 Ω I C R N = 60 μv ~ Δ 0 /e Δ, ϕ S Δ < Δ (induced gap) (DC Josephson effect) Ψ = Ψ exp( iϕ ), j = S,D R, L j j j Δ, ϕ S V (μv) I R T = 40 mk I C I (na) ~ I = I sin( φ ) where φ ϕ ϕ S C SD LR SD LR SL DR Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

14 S Source Field-effect control of the supercurrent N S Science (2005) Drain V (μv) V g < 0-71 V -61 V -50 V -40 V -30 V -20 V -10 V 0 V I (na) V gate Ic decreases with R N Ic for different devices 10 2 I C (na) R N (kω) 0 4 Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

15 S Source Field-effect control of the supercurrent N S Drain Supercurrent fluctuations correlate with normal-state universal conductance fluctations V g < 0 Electron transport through the nanowire is diffusive and phase coherent => mesoscopic Josephson junctions V (μv) I (na) V gate -71 V -61 V -50 V -40 V -30 V -20 V -10 V 0 V 2 I (na) 0-2 dv/di (kohm) -70 V kω g (V) Theory: Altshuler & Spivak ( 87) 4 2 GN (2e2 /h) Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

16 Phase-coherent diffusive transport in InAs nanowires (normal state) B Device 1 I - V - I + V + rms(g B )= (G(B) - G(B) ) 2 Device 2 L= 440 nm L= 110 nm rms(g B )= 0.3 e 2 /h rms(g B )= 0.29 e 2 /h B I - V - I + V + Note: G is not proportional to L! rms(g) is almost the same [in theory: rms(g B ) ~ (L φ /L) 3/2 e 2 /h] Metal contacts are 500 nm wide => L does not correspond to the distance between them Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

17 Phase-coherent diffusive transport in InAs nanowires (normal state) Autocorrelation function: F(ΔB)= G(B)G(B+ΔB) - G(B) 2 F(ΔB) decays on a field scale B c (i.e.: F(ΔB)=1/2 F(0) for ΔB = B c ) Device 1 Device 2 L= 440 nm L= 110 nm B c = T B c = T => B c is independent of channel length and field direction! L φ ~ wire diameter ~ 100 nm For the long wire rms(g B ) = 2.45 (L φ /L) 3/2 e 2 /h = 2.45 (100/440) 3/2 e 2 /h = 0.3 e 2 /h [van Houten and Beenakker Solid State Physics 91] Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

18 UCF and Andreev reflection Enhancement of rms(g) due to combined UCF and Andreev reflection b 0.8 rms(g g ) (e 2 B=0 30 di/dv (e 2 /h) V g (V) V=0; B=0.1T V (mv) Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

19 n-type InP nanowire (n~10 19 cm -3 ): intermediate coupling case R N ~ R Q => expected competition Andreev reflection Coulomb blockade (+ high-order cotunneling) Andreev regime R N /R Q = 0.77 Δ Δ 500 nm Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

20 n-type InP nanowire (n~10 19 cm -3 ): intermediate coupling case Gate dependence T dependence G/G max ~ cosh -2 [(e(c g /C Σ ) V g,peak - V g )/2.5k B T] From fit: U = e 2 /C Σ ~ 13.2 k B T ~ 30 μev Coulomb blockade affects only the low-bias regime Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

21 n-type InP nanowire (n~10 19 cm -3 ): intermediate coupling case R N ~ R Q but U>>Δ : => Andreev Reflection vs Kondo effect/high-order cotunneling Buitelaar et al. PRL 02 (carbon nanotubes) Buizert et al, PRL 07 (with InAs self-assembled quantum dots) Sand-Jespersen et al. PRL 07 (InAs nanowires) => Single-electron supercurrent transistor and π Josephson junction I S = I C sin(φ SD +π) V L <0 V R <0 S S Source Drain Nature 442, 667 (2006) induced gap Δ* ~ Δ quantum dot induced gap Δ* ~ Δ Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

22 Negative and positive supercurrent Simplest case: single-level quantum dot 4-th order co-tunneling initial intermediate final N=1 S=1/ I s = = I I c c sin( φ sin( φ LR LR ) (π-junction) + π ) initial intermediate final N=2 S= I = s I c sin( φ LR ) (ordinary junction) [Bulaevski, Knzii, Sobbianin, JETP Lett. 25, 290 ( 77);Spivak and Kivelson PRB 43, 3740 ( 91)] Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

23 Summary?? Hybrid nanodevices Relevant energy scales: Δ, U, ΔE, Γ, E Th, k B T R N >> R Q R N << R Q R N ~ R Q Single-electron tunneling, NDC due to BCS density of states (Doh et al. Nano Letters 08) Case of a diffusive normale conductor (ΔE=0) Tunable proximity supercurrent (Doh et al. Science 05) Correlation between Ic fluctuations and UCF Enhance UCF amplitude due to Andreev reflection (at finite bias) Case of a ballistic conductor (quantum dot with finite ΔE) Resonant supercurrent transistor (Jarillo-Herrero et al. Nature 06) Case of a large quantum dot (ΔE~0, U<<Δ) Clear energy scale separation between Coulomb blockade and Andreev reflection (Doh et al. Nano Letters 08) Case of a small quantum dot ( Γ < ~ ΔE, U,Δ ) pi-junction behavior: I S = I C sin(φ SD +π) (van Dam et al., Nature 06) Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

24 Acknowledgements INAC/SPSMS/LaTEQS: M. Mongillo (PhD), G. Katsaros (PD), P. Spathis (PD) open positions available at master, PhD and PD level F. Lefloch, J.L. Thomassin, X. Jehl, M. Sanquer Collaborators on semiconductor nanowires (NWs): J. Van Dam, Y.J. Doh, S. Sapmaz, L. Kouwenhoven (InAs/InP NWs, TU Delft) E. Bakkers, A. Roest (InAs/InP NWs, Philips Eindhoven) S. Rubini, F. Martelli, F. Jabeen (Mn-doped GaAs/InAs NWs, CNR-INFM TASC,Trieste) E. Storace, J. Weis, K. von Klitzing (Mn-doped GaAs/InAs NWs, MPI Stuttgart) X. Jiang, C. Lieber (InAs-InP core-shell NWs, Harvard) R. Songmuang, B. Daudin, B. Gayral (GaN-based NWs, INAC/CNRS) C. Mouchet, E. Rouviere, J.P. Simonato (doped Si NWs, LITEN) P. Gentile, N. Pauc, T. Baron (undoped Si NWs, INAC/LTM) Collaborators on self-assembled semiconductor quantum dots: M. Stoffel, A. Rastelli, O. Schmidt (IFW Dresden) Funding: ANR (chair d excellence & ERC starting grant), EU FP6 (HYSWITCH) Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

25 Fully tunable quantum dot: intermediate tunnel coupling V L V R V = δ μm e B=100 mt 200 nm V R = mv δ V (mv) δ Inelastic cotunneling V L (mv) -390 Can be used for spectroscopy in strong coupling regime [PRL 86, 878 (2001)] Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

26 Fully tunable quantum dot: intermediate tunnel coupling V L V R 1 μm 200 nm Quantum dot parameters: Charging energy: ~ 1 mev 1.5 e B=100 mt V R = mv Level spacing: mev Supercond. gap: 0.14 mev V (mv) δ V L (mv) -390 Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/

27 S Source L R Δ* QD Δ* D Study of Josephson Supercurrent through an interacting QD Nature 442, 667 (2006) V L V R We exploit the independent tunability of nanowire JJs I c,ref = 320 pa (V REF = fixed constant) V REF 2µm Drain I c,qd (na) I c =I c,qd +I c,ref b V (mv) -1 1 negative supercurrent! N N+1 N+2 N+3 N+4 Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/ V L (mv)

28 S L R Δ* QD Δ* D 0.4 π-junction behaviour 5 Source V L I c (na) Φ (Φ 0 ) V REF 2µm Φ Drain V R I c,qd (na) Φ (Φ 0 ) b V (mv) V L (mv) Similar π-behavior seen also in CNT-SQUIDs [Cleuziou et al. (2006)] N N+1 N+2 N+3 N+4 Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/ V L (mv)

29 Phase-coherent diffusive transport in InAs nanowires B=0.1T: UCF drops for kt>e Th B=0: UCF drops for V>E Th This is consistent with a Thouless energy E TH ~ 0.14 mev Silvano De Franceschi Laboratoire de Transport Electronique Quantique et Supraconductivité 17/12/