Coherence and Correlations in Transport through Quantum Dots Rolf - PowerPoint PPT Presentation

Coherence and Correlations in Transport through Quantum Dots Rolf J. Haug Abteilung Nanostrukturen Institut für Festkörperphysik and Laboratory for Nano and Quantum Engineering Gottfried Wilhelm Leibniz Universität Hannover Germany nanostrukturen uni hannover

Gottfried Wilhelm Leibniz (1676 – 1716 in Hannover) binary numbers as mentioned in a letter to Rudolf August von Wolfenbüttel in January 1697 (new-year letter) nanostrukturen uni hannover

• spin effects in quantum dots • shot noise measurements Overview nanostrukturen uni hannover

Technology • lithography (GaAs/AlGaAs heterostructures) 1. optical lithography - AFM-Tip I OX + 2. electron beam lithography AFM-Tip _ 2DEG Oxide 3. direct writing with AFM Water 1 µm + Oxide 5 nm GaAs 5 nm AlGaAs 15 nm AlGaAs:Si Heterostructure 15 nm AlGaAs self-organized growth • Depletion GaAs quantum dots (InAs, InP, Ge) lattice mismatch between InAs and AlAs (GaAs): 7% Stranski-Krastanov growth nanostrukturen uni hannover

Other Fields of Research • quantum Hall effect and fractional quantum Hall effect Phys. Rev. Lett. 93, 196801 (2004) 100 ν = 1/3 60 2 ν = 2/5 Phys. Rev. Lett. 92, 156401 (2004) 80 ν = 1/2 C / r 0 (nJ/K) 40 60 R xy (k Ω ) ν = 2/3 Phys. Rev. Lett. 93, 026801 (2004) R xx (k Ω ) ν = 1 1 40 Phys. Rev. B 74, 165325 (2006) 20 20 0 Phys. Rev. B 74, 195324 (2006) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 0 T e (K) 0 2 4 6 8 10 12 B (T) Phys. Rev. B 76, 153311 (2007) • transport in quantum rings Phys. Rev. Lett. 90, 196601 (2003) Appl. Phys. Lett. 91, 133116 (2007) Appl. Phys. Lett. 92, 013126 (2008) 500 nm • transport through double and triple dots Appl. Phys. Lett. 83, 1163 (2003) Appl. Phys. Lett. 85, 806 (2004) Phys. Rev. B (2008) nanostrukturen uni hannover

Spin-Resolved Tunneling through Quantum Dots Δ = μ g B B g = - 0.12 Zeeman energy spin-polarized current in a magnetic field spin-resolved spectroscopy Europhys. Lett. 54, 495 (2001) of the local density of states nanostrukturen uni hannover

Anisotropy of Spin Splitting: Spin-Orbit Interaction disc-like quantum dot GaAs quantum dots spin splitting B ⊥ B // B B ⊥ Bychkov-Rashba (structure, 0,054meV) // dominates over Dresselhaus (bulk, 0.012meV) for dots in 10nm quantum well Phys. Rev. Lett. 94, 226404 (2005) extreme anisotropy: holes in SiGe/Ge structure Phys. Rev. Lett. 96, 086403 (2006) g=6.2 0 nanostrukturen uni hannover

Interaction Effect in High Magnetic Fields strong coupling in InAs quantum dots Fermi edge singularity (Mahan 1967) interaction of charge on dot with states in the emitter E F Phys. Rev. B 62, 12621 (2000) Phys. Rev. B 74, 035329 (2006 ) InAs dots between AlAs barriers nanostrukturen uni hannover

Many Electrons in Magnetic Field single-electron tunneling conductance within Coulomb blockade vanishes for large T Phys. Rev. B 66, 161305(R) (2002) Keller, PRB 64 (2001) Stopa PRL 88 . 256804 (2003) regular tiles – chequer board periodicity of one flux quantum nanostrukturen uni hannover

Spin-Spin Interaction: Kondo Effect Phys. Rev. Lett. 90, 196601 (2003) 0.050 G (e²/h) 0.025 0.000 -140 -120 -100 -80 V B (mV) • spin ½ on dot forms singlet with Kondo spins in leads • transport via virtual state at Fermi energy involving spin flips finite conductance in Coulomb • Kondo, Prog. Theor. Phys. 32, 37 (1964) Glazman and Raikh, JETP Lett. 47, 452 (1988) valley Ng and Lee, Phys. Rev. Lett. 61, 1768 (1988) Goldhaber-Gordon et al., Nature 391, 156 (1998) Cronenwett et al., Science 281, 540 (1998) Schmid et al., Physica B 256, 182 (1998 ) nanostrukturen uni hannover

Spin Polarization in High Magnetic Fields dot: 2 Landau levels edge/core spin down: leads: spin strong amplitude polarized edge spin up: channels weak amplitude Ciorga et al. Phys. Rev. B 61 , R16315 (2000) New J. Phys. 8, 298 (2006) nanostrukturen uni hannover

Spin Blockade versus Kondo Effect Kondo effect spin blockade spin polarized leads necessary both spins in the leads necessary nanostrukturen uni hannover

Transition between Spin Blockade and Kondo Effect in Dots with Many Electrons Kondo spin blockade Phys. Rev. Lett. 96, 046802 (2006) • with increasing B: Phys. Rev. Lett. 96, 176801 (2006) spin blockade increases, Kondo effect decreases • origin: spin polarization of edge • intermediate regime: both effects visible spin structure shell structure nanostrukturen uni hannover

Spin Structures -0.4 V G Source Drain -0.5 1 µm -0.6 -0.7 100 electrons different -0.8 V (mV) spin configurations G -0.9 -1.0 x1 -1.1 -1.2 x20 1.7 1.9 2.1 2.3 2.5 Phys. Rev. Lett. 96, 176801 (2006) B (T) nanostrukturen uni hannover

DC + AC barrier Shot Noise • electrical current DC nanostrukturen uni hannover

Shot Noise DC + AC DC W. Schottky, Annalen der Physik, 57, 541 (1918) S Poisson = 2eI (single barrier) correlations can suppress noise = α S 2 eI Ugo Fano Fano factor U. Fano, Phys. Rev. 72, 26 (1947) nanostrukturen uni hannover

Shot Noise Measurement τ = 1 Θ E E • direct measurement of current noise x spectrum ( PRB 66, 161303R (2002) ) • reduction of shot noise due to Coulomb blockade Θ Θ 2 α = − • S = α ·2eI with E C 1 τ = 1 ( ) Θ + Θ Θ x 2 C C E C 200 T = 1.5 K 60 60 2 /Hz) E D 150 V sd = 131 mV 40 40 I (pA) measurement resolution: -30 A 100 Δ S ~10 -30 A 2 /Hz 120 mV S=2eI 20 20 S ( 10 1 k Ω resistor @ 300 K: 50 S = 1.6 ·10 -23 A 2 /Hz 100 mV 0 0 0 80 100 120 0 2 4 6 8 10 V SD (mV) f (kHz) nanostrukturen uni hannover

Noise at Fermi Edge Singularity ( ) − γ Θ ∝ − E E E F D B = 15 T 0.6 E F T = 0.4 K E D 0.4 I (nA) ( ) − γ Θ ∝ − V V E th 0.2 PRB 62, 12621 (2000); PRB, 74, 035329 (2006) 0.0 Θ + Θ 2 2 α = E C ( ) Θ + Θ 2 1.0 E C Fano factor α strong 0.9 additional noise suppression 0.8 due to Fermi edge singularity 0.7 0.6 236 238 240 242 V SD (mV) Phys. Rev. B 75, 233304 (2007) nanostrukturen uni hannover

Transport through Coupled Quantum Dots stacks of InAs dots 26. ICPS, IOP 171, 233 (2002) Phys. Rev. Lett. 96, 246803 (2006) nanostrukturen uni hannover

Shot Noise in Transport through Coupled Quantum Dots Fano factor 1.4 1.2 Fano Factor α 1.0 0.8 0.6 -186.5 -187.0 V (mV) enhancement Phys. Rev. Lett. 96, 246803 (2006) nanostrukturen uni hannover

Electron Bunching • compare: electron bunching for single quantum dots – observed for 2 accessible states with different tunnelling rates e.g. Phys. Rev. B 69, 113316 (2004); Gustavsson et al, Phys. Rev. B 74, 195305 (2006); Zachrin et al, Phys. Rev. Lett. 98, 066801 (2007 ) I t nanostrukturen uni hannover

Electron Bunching here: two molecular states for coherently coupled dots – energies aligned: symmetric system and equal rates ⇒ α < 1 – energies detuned: asymmetric distribution and tunnelling rates ⇒ bunching E L = E R E L < E R nanostrukturen uni hannover

Quantum Coherence • theory (Kiesslich, Berlin) • coherent coupling of QDs • dephasing due to phonon absorption and emission • reproduces super-Poissonian noise and temperature dependence ε (mV) Phys. Rev. Lett. 99, 206602 (2007) nanostrukturen uni hannover

Putting Electrons on a String • shot noise caused by randomness of tunneling events 200 2 /Hz) 150 S = α · S 0 100 S(f) (fA 50 0 0 5 10 f (kHz) • suppression of randomness – by driven electron pump – electrons at well defined times → no noise expected nanostrukturen uni hannover

Noise Suppression in an Electron Pump • electrons pumped by actively driven barriers (Blumenthal et al, Nat. Phys. 2007, Kaestner et al, U1 arXiv:0707.0993) U2 ~ • quantized current plateaus I = nef FFT – n electrons per cycle; repetition frequency f E • noise suppressed for quantized pumping I/V 3 400 nm 2 20 I = 2.0 ef 10 I / ef 0 1 I = 1.6 ef 2 / Hz) 20 10 0 0 S (fA 2 / Hz) 10 S (fA 20 I = 1.0 ef 0 10 0 -160 -140 -120 -100 -80 2 4 6 8 10 12 14 U1 (mV) f (kHz) f = 400 MHz Appl. Phys. Lett. 92, 082112 (2008) nanostrukturen uni hannover

Shot Noise and Electron Counting in Quantum Dots coupled dots single dots 1.4 K 2.7 K -0.3 I (nA) -0.2 -0.1 0.0 Fano Factor α 1.5 1.4 K 2.7 K 1.0 0.5 -186.5 -187.0 ε (mV) ε (mV) V SD (mV) Phys. Rev. Lett. 96, 246803 (2006) Phys. Rev. B 66,161303 (2002) Phys. Rev. Lett. 99, 206602 (2007) Phys. Rev. B 69, 113316 (2004) Phys. Rev. B 70, 033305 (2004) Phys. Rev. B 75, 233304 (2007) noise in bimodal electron pump counting statistics Appl. Phys. Lett. 92, 082112 (2008) Phys. Rev. B 76, 155307 (2007) nanostrukturen uni hannover

K. Pierz K. Eberl P. Barthold W. Wegscheider, G. Abstreiter C. Fühner O. Schmidt, U. Denker J. Könemann D. Grützmacher A. Nauen D. Reuter, A.D. Wieck N. Maire M. Rogge H. Frahm V. Fal‘ko, E. McCann F. Hohls B. Altshuler T. Brandes, G. Kiesslich, H. W. Schumacher, E. Schöll B. Kästner nanostrukturen uni hannover