The Role of Spin in Ballistic-Mesoscopic Transport

Transcription

1 The Role of Spin in Ballistic-Mesoscopic Transport INT Program Chaos and Interactions: From Nuclei to Quantum Dots Seattle, WA 8/12/2 CM Marcus, Harvard University Supported by ARO-MURI, DARPA, NSF

2 Spin-Orbit Coupling Antilocalization and Parallel Fields in Quantum Dots.7 Structure and a Kondo-like state in Point Contacts Spin injection and Detection Using Point Contacts and Quantum Dots Antilocalization in QD. Comparison to new random matrix theory that includes SO and parallel magnetic field. Asymmetry of SO is measured. Gate control of SO coupling..7 structure in point contacts appears spin related, and vanishes at low temperature. Temperature, bias, and field dependence suggest a Kondolike correlated state at low T. Transverse Focusing in a parallel field New theory allows voltage to read out spin polarization. Demonstrate > 7% polarization in a QPC Quantum dot as a gate-tunable spin filter with ~25% filtering and adjustable polarization.

3 Spin-Orbit Coupling, Antilocalization, and Parallel Fields in Quantum Dots D. Zumbühl, J. Miller, J. Folk Material: Campman,Gossard, UCSB

4 weak localization and antilocalization in 2D systems. weak localization T=3mK 114 antilocalization Resistance (Ω) longitudinal resistance [Ω] T=3mK B perp.

5 spin precision affects phase interference (2π in spin space gives -1 to phase) motion in real space coherent backscattering weak localization motion in spin space coherent backscattering + spin rotation antilocalization

6 Spin-Orbit Coupling in -D (Quantum Dots) B V shape1 Statistics of Conductance V shape2 g (e 2 /h) 1. δg Single trace for each shape Average of ~2 traces 1 B (mt) from Huibers, CMM, et al, PRL (1999).

7 [11] 4µm low density, large dot 8 µm 2 [11] low density weaker SO coupling weak localization (WL) dots are on different wafers CEM2385 n= m -2 average conductance < g > (e^2/h) WL T=3mK B perp [mt] Perpendicular Magnetic Field (mt) 4µm high density, large dot 8 µm 2 high density stronger SO coupling antilocalization (AL) SY4 n= m -2 average conductance g (e 2 /h) 1.1 T=3mK WL+AL B (mt) Perpendicular Magnetic Field (mt)

8 Spin-Orbit Coupling in Quantum Dots H 2 p = + α(pyσ 2m x p Rashba x σ y ) + ρ(p x σ x p y σ Dresselhaus gauge transformation using < v > in quantum dots (Halperin et al., PRL86, 216 (21) 1 H = + m p r A r a r σz a r ( ) Z 2 2 l σ r ε 2 h 2 () 1 y ) identify SO terms with different symmetries r a r a h r r n = h 2λ λ = spin-orbit terms z r r h n 6 λ λ 2 z x1σ λ1 1 x2σ + λ Z lx l x = σ ε z + 2 2λ 2λ () (SO Berry s phase keeps and correl.) (provides spin flips) (spin-orbit + B ) 2 ax associated energy scale E = πκ T 2 A λλ L L a = a x + 1 λ λ2 2 h π E = Z L ET λso IL Aleiner and VI Falko, PRL (21)

9 B field scales zero field intermediate field large field

10 Effects of S-O coupling supressed in small quantum dots T=3mK large dot 8 µm 2 RMT 4µm dots are on the same wafer small dot 1.2 µm 2 RMT 1µm T=3mK

11 high density material (SY4) Variance of Conductance low density material (CEM) var (g) var g [ (e^2/h)^2 ] dg 8 µm 2 RMT.6.8 < g > ( e^2/h ) var g ( (e^2 / h )^2 ) var (g) dg 8 µm 2 RMT < g > ( e^2/h ) var g [ (e^2/h)^2 ] var (g) µm 2 RMT dg < g > ( e^2/h ) var g ( (e^2/h)^2 ) var (g) dg 3 µm 2 RMT < g > ( e^2/h ) Perpendicular Magnetic Field (mt) Perpendicular Magnetic Field (mt)

12 Effect of Parallel Magnetic Field on Antilocalization parameters fixed by B = fit T=3 mk

13 S-O coupling asymmetry range 1< ν so < 2 for 2:1 aspect ratio dot

14 Parallel Field Effects on Antilocalization and Weak Localization D. M. Zumbuhl, CMM, et al (22)

15 Time-Reversal Symmetry Breaking by Parallel Field B δg wl(b ) = δgwl() 1 + γ γ B esc 1 γ B = a B 2 + b B 6 γ esc = N h effective random B due to disorder / surface roughness inversion asymmetry of heterostructures V. Fal ko, T. Jungwirth, PRB 65, 8136 (22) J. Meyer, A. Altlland, B. Altshuler, cond-mat 15623

16 Variance of Conductance dependence on Parallel Magnetic Field high density material (SY4) 7x1-6 7x1-6 var g ( (e^2/h)^2 ) var (g) (e 2/ h) µm B par ( mt ) 3.5x1-3 var g ( (e^2/h)^2 ) var (g) (e 2/ h) B par ( mt ) 1.2 µm Parallel Magnetic Field (mt) RMT RMT var g ( (e^2/h)^2 ) var (g) (e 2/ h) 2 var (g) (e2/ h) 2 6x1-6 var g ( (e^2/h)^2 ) (J. A. Folk et al., PRL 86, 212 (21)) low density material (CEM) B par ( mt ) B par ( mt ) 8 µm 2 RMT 3 µm 2 RMT 5 Parallel Magnetic Field (mt)

17 Symmetry of Conductance Fluctuations (Movie) B = 5T.4 V V g -1 mt B perp. +1 mt

18 Effect of Temperature in Antilocalization regime Increased dephasing at higher T. No significant change in SO coupling with T.

19 Using a center gate to Control spin-orbit coupling T=3mK

20 .7 Structure and a Kondo-like state in Point Contacts S. Cronenwett, H. Lynch, D. Goldhaber-Gordon, L. Kouwenhoven, N. Wingreen, K. Hirose Material: Umansky, Heiblum, Weizmann

21 1D System.7 Structure in a Quantum Point Contact

22 Low Temperature Higher Temperature Lo V g V g

23 Critical Questions: What is the characteristic time scale on which the spin is oriented in a particular direction?

24 Nonlinear Transport T =T = 8mK 75 mk, B = TB= T T== 6.6K mk, B =B= T T=8mK T = 75 mk, BB=8T =8T g g (2e2/h) g (2e2/h) g (2e2/h) 3 g 1 g 1-1 Vsd (mv) Vsd Vsd (mv) Vsd 1-1 Vsd (mv) Vsd 1

25 Temperature dependence of zero bias anomaly (at various gate voltages)

26 Kondo-like scaling in a quantum point contact

27 Kondo Temperature and Transport Features

28 In-Plane Field Dependence of Zero Bias Anomaly of a QPC gµb < T K T > T K

29 Spin injection and Detection Using Point Contacts and Quantum Dots J. A. Folk, R. M. Potok Material: Umansky, Heiblum, Weizmann

30 QUANTUM POINT CONTACTS AS SPIN INJECTORS AND SPIN DETECTORS R. M. Potok, J. A. Folk, C. M. Marcus, V. Umansky cond-mat (22).

31 QUANTUM POINT CONTACTS AS SPIN INJECTORS AND SPIN DETECTORS

32 SPIN EMISSION FROM A POLARIZED QUANTUM DOT µ QPC Collector QD Emitter J. A. Folk, R. M. Potok, C. M. Marcus, V. Umansky (in preparation)

33 Injector: PC at 2e 2 /h Collector: PC at.5 e 2 /h No dependence of V BC on V gate Injector: DOT at 2e 2 /h, 2e 2 /h Collector: PC at.5 e 2 /h Fluctuation of V BC when the dot is completed and a parallel field is applied

34 Polarized against field Polarized along field QUANTUM DOT AS SWITCHABLE SPIN FILTER 25% % 25%

35 Mesoscopic Spin Fluctuations collector QPC not spin selective no Zeeman splitting all configurations show UCF

36 Statistics of Fluctuating Polarized Current from a Quantum Dot with P. W. Brouwer

37 SUMMARY Spin-Orbit Coupling Antilocalization and Parallel Fields in Quantum Dots.7 Structure and a Kondo-like state in Point Contacts Spin injection and Detection Using Point Contacts and Quantum Dots Antilocalization in QD. Comparison to new random matrix theory that includes SO and parallel magnetic field. Asymmetry of SO is measured. Gate control of SO coupling..7 structure in point contacts appears spin related and vanishes at low temperature. Temperature, bias, and field dependence suggest a Kondolike correlated state at low T. Transverse Focusing in a parallel field New theory allows voltage to read out spin polarization. Demonstrate > 8% polarization in a QPC Quantum dot as a gate-tunable spin filter with ~25% filtering and adjustable polarization.