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Coherence and Correlations in Transport through Quantum Dots Rolf J. Haug Abteilung Nanostrukturen Institut fr Festkrperphysik and Laboratory for Nano and Quantum Engineering Gottfried Wilhelm Leibniz Universitt Hannover Germany

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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

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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)

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Overview

  • spin effects in quantum dots
  • shot noise measurements
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Technology

  • lithography (GaAs/AlGaAs heterostructures)
  • 1. optical lithography
  • 2. electron beam lithography
  • 3. direct writing with AFM
  • self-organized growth

quantum dots (InAs, InP, Ge)

lattice mismatch between InAs and AlAs (GaAs): 7% Stranski-Krastanov growth

IOX

  • +

1 µm

5 nm GaAs 5 nm AlGaAs 15 nm AlGaAs:Si 15 nm AlGaAs GaAs

AFM-Tip

Oxide 2DEG

Depletion

AFM-Tip Heterostructure

Oxide

Water

+ _

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500 nm

  • Phys. Rev. Lett. 90, 196601 (2003)
  • Appl. Phys. Lett. 91, 133116 (2007)
  • Appl. Phys. Lett. 92, 013126 (2008)
  • Appl. Phys. Lett. 83, 1163 (2003)
  • Appl. Phys. Lett. 85, 806 (2004)
  • Phys. Rev. B (2008)
  • Phys. Rev. Lett. 93, 196801 (2004)
  • Phys. Rev. Lett. 92, 156401 (2004)
  • Phys. Rev. Lett. 93, 026801 (2004)
  • Phys. Rev. B 74, 165325 (2006)
  • Phys. Rev. B 74, 195324 (2006)
  • Phys. Rev. B 76, 153311 (2007)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 1 2

C/r0 (nJ/K) Te (K) 2 4 6 8 10 12 20 40 60 80 100 20 40 60 Rxy (kΩ) B (T)

ν = 1 ν = 1/2 Rxx (kΩ) ν = 1/3 ν = 2/5 ν = 2/3

Other Fields of Research

  • quantum Hall effect and fractional quantum Hall effect
  • transport in quantum rings
  • transport through double and triple dots
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Spin-Resolved Tunneling through Quantum Dots

  • Europhys. Lett. 54, 495 (2001)

B g

B

μ = Δ

Zeeman energy spin-resolved spectroscopy

  • f the local density of states

spin-polarized current in a magnetic field

g = - 0.12

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Anisotropy of Spin Splitting: Spin-Orbit Interaction

⊥

B

//

B

⊥

B

//

B

disc-like quantum dot

  • Phys. Rev. Lett. 94, 226404 (2005)

Bychkov-Rashba (structure, 0,054meV) dominates over Dresselhaus (bulk, 0.012meV) for dots in 10nm quantum well

spin splitting

GaAs quantum dots extreme anisotropy: holes in SiGe/Ge structure

  • Phys. Rev. Lett. 96, 086403 (2006)

g=6.2 0

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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

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Many Electrons in Magnetic Field

Keller, PRB 64 (2001) Stopa PRL 88. 256804 (2003)

  • Phys. Rev. B 66, 161305(R) (2002)

single-electron tunneling conductance within Coulomb blockade vanishes for large T

regular tiles – chequer board periodicity of one flux quantum

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Spin-Spin Interaction: Kondo Effect

  • spin ½ on dot forms singlet with

spins in leads

  • transport via virtual state at Fermi

energy involving spin flips

  • finite conductance in Coulomb

valley

Kondo, Prog. Theor. Phys. 32, 37 (1964) Glazman and Raikh, JETP Lett. 47, 452 (1988) 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)

  • 140
  • 120
  • 100
  • 80

0.000 0.025 0.050

G (e²/h) VB (mV)

Kondo

  • Phys. Rev. Lett. 90, 196601 (2003)
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Spin Polarization in High Magnetic Fields

dot: 2 Landau levels edge/core leads: spin polarized edge channels spin down: strong amplitude spin up: weak amplitude

Ciorga et al. Phys. Rev. B 61, R16315 (2000)

New J. Phys. 8, 298 (2006)

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Spin Blockade versus Kondo Effect

spin blockade Kondo effect spin polarized leads necessary both spins in the leads necessary

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  • with increasing B:

spin blockade increases, Kondo effect decreases

  • rigin: spin polarization of edge
  • intermediate regime: both effects visible

spin structure

Transition between Spin Blockade and Kondo Effect in Dots with Many Electrons

  • Phys. Rev. Lett. 96, 046802 (2006)

Kondo spin blockade

  • Phys. Rev. Lett. 96, 176801 (2006)

shell structure

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B (T) 1.7 1.9 2.1 2.3 2.5

  • 0.4
  • 0.5
  • 0.6
  • 0.7
  • 0.8
  • 0.9
  • 1.0
  • 1.1
  • 1.2

V (mV)

G

Source Drain

VG

1 µm

x20 x1

  • Phys. Rev. Lett. 96, 176801 (2006)

Spin Structures

100 electrons different spin configurations

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Shot Noise

  • electrical current

barrier

DC DC + AC

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Shot Noise

DC DC + AC

SPoisson = 2eI (single barrier) correlations can suppress noise

eI S 2 α =

Fano factor

Ugo Fano

  • U. Fano, Phys. Rev. 72, 26 (1947)
  • W. Schottky,

Annalen der Physik, 57, 541 (1918)

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Shot Noise Measurement

  • direct measurement of current noise

spectrum ( PRB 66, 161303R (2002) )

  • reduction of shot noise due to

Coulomb blockade

  • S = α·2eI with

measurement resolution: ΔS ~10-30 A2/Hz 1 kΩ resistor @ 300 K: S = 1.6 ·10-23 A2/Hz

x x

E E

Θ = 1 τ

C C

Θ = 1 τ

T = 1.5 K

( )

2

2 1

C E C E

Θ + Θ Θ Θ − = α

2 4 6 8 10 20 40 60 20 40 60 80 100 120 50 100 150 200

Vsd = 131 mV 120 mV

S ( 10

  • 30A

2/Hz)

f (kHz)

100 mV

I (pA) VSD (mV)

ED

S=2eI

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( )

2 2 2 C E C E

Θ + Θ Θ + Θ = α

236 238 240 242 0.6 0.7 0.8 0.9 1.0 0.0 0.2 0.4 0.6 Fano factor α

VSD (mV)

I (nA)

Noise at Fermi Edge Singularity

B = 15 T T = 0.4 K

  • Phys. Rev. B 75, 233304 (2007)

strong additional noise suppression due to Fermi edge singularity

( )

γ −

− ∝ Θ

th E

V V

EF

PRB 62, 12621 (2000); PRB, 74, 035329 (2006)

( )

γ −

− ∝ Θ

D F E

E E

ED

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Transport through Coupled Quantum Dots

  • Phys. Rev. Lett. 96, 246803 (2006)

stacks of InAs dots

  • 26. ICPS, IOP 171, 233 (2002)
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Shot Noise in Transport through Coupled Quantum Dots

  • Phys. Rev. Lett. 96, 246803 (2006)

Fano factor

enhancement

  • 186.5
  • 187.0

0.6 0.8 1.0 1.2 1.4 V (mV) Fano Factor α

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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

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EL < ER

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 EL = ER

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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)
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  • shot noise caused by randomness of tunneling events
  • suppression of randomness

– by driven electron pump – electrons at well defined times → no noise expected

Putting Electrons on a String

5 10 50 100 150 200

S(f) (fA

2/Hz)

f (kHz)

S = α·S0

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400 nm FFT

~

U1 U2

I/V

E

Noise Suppression in an Electron Pump

  • electrons pumped by actively driven barriers

(Blumenthal et al, Nat. Phys. 2007, Kaestner et al, arXiv:0707.0993)

  • quantized current plateaus I = nef

– n electrons per cycle; repetition frequency f

  • noise suppressed for quantized pumping

10 20 10 20 2 4 6 8 10 12 14 10 20 I = 1.0 ef I = 1.6 ef I = 2.0 ef S (fA

2 / Hz)

f (kHz)

1 2 3

  • 160
  • 140
  • 120
  • 100
  • 80

10 I / ef U1 (mV) S (fA

2/ Hz)

  • Appl. Phys. Lett. 92, 082112 (2008)

f = 400 MHz

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Shot Noise and Electron Counting in Quantum Dots

ε (mV) ε (mV) 0.0

  • 0.1
  • 0.2
  • 0.3

2.7 K 1.4 K

I (nA)

  • 186.5
  • 187.0

0.5 1.0 1.5 V

SD (mV)

1.4 K 2.7 K

Fano Factor α

  • Phys. Rev. B 66,161303 (2002)
  • Phys. Rev. B 69, 113316 (2004)
  • Phys. Rev. B 70, 033305 (2004)
  • Phys. Rev. B 75, 233304 (2007)
  • Phys. Rev. Lett. 96, 246803 (2006)
  • Phys. Rev. Lett. 99, 206602 (2007)

single dots coupled dots

  • Phys. Rev. B 76, 155307 (2007)
  • Appl. Phys. Lett. 92, 082112 (2008)

noise in electron pump bimodal counting statistics

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