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

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

Technology
• lithography (GaAs/AlGaAs heterostructures)
1. optical lithography
AFM-Tip
2. electron beam lithography
AFM-Tip
_
3. direct writing with AFM
Water
Oxide +
2DEG
Heterostructure
5 nm GaAs
5 nm AlGaAs
15 nm AlGaAs:Si
15 nm AlGaAs
• self-organized growth
GaAs Depletion
-
+
I
OX
Oxide
1 µm 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
100
80
60
40
20
0
0 2
ν
= 1
ν
= 2/3
ν
= 2/5
ν
= 1/2
ν = 1/3
60
40
20
4 6
B (T)
8 10 12
0
2
1
0
0.0
0.1
0.2
0.3
T e
(K)
0.4
0.5
0.6
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)
• 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
Zeeman energy
Δ = g
μ
B
B g = - 0.12
spin-polarized current in a magnetic field spin-resolved spectroscopy of the local density of states nanostrukturen uni hannover
Europhys. Lett. 54, 495 (2001)

Anisotropy of Spin Splitting: Spin-Orbit Interaction
GaAs quantum dots disc-like quantum dot spin splitting
B
⊥
B
//
B
⊥
B
//
Phys. Rev. Lett. 94, 226404 (2005)
Bychkov-Rashba (structure, 0,054meV) dominates over Dresselhaus (bulk, 0.012meV) for dots in 10nm quantum well 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
0.025
-140 -120
V
B
(mV)
-100
Kondo
0.000
-80
• 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 ) nanostrukturen uni hannover

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
New J. Phys. 8, 298 (2006) nanostrukturen uni hannover
Ciorga et al. Phys. Rev. B 61 , R16315 (2000)

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

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

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

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

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

E
F
Noise at Fermi Edge Singularity
Θ
E
∝
(
E
F
−
E
D
) − γ
0.6
B = 15 T
T = 0.4 K
E
D
0.4
Θ
E
∝
(
V
−
V th
)
− γ
0.2
PRB 62, 12621 (2000);
PRB, 74, 035329 (2006)
0.0
1.0
α =
Θ
(
Θ
E
E
2
+
+ Θ
C
Θ
C
2
)
2 strong additional noise suppression due to Fermi edge singularity
0.9
0.8
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 nanostrukturen uni hannover
26. ICPS, IOP 171, 233 (2002)
Phys. Rev. Lett. 96, 246803 (2006)

Shot Noise in Transport through Coupled Quantum Dots
Fano factor enhancement
1.4
1.2
1.0
0.8
0.6
-186.5
V (mV)
-187.0
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
150
100
50
0
0
S = α
5
• suppression of randomness
– by driven electron pump
– electrons at well defined times
→ no noise expected
· S
0 f (kH z)
10 nanostrukturen uni hannover

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
U1
• noise suppressed for quantized pumping
3
400 nm
U2
FFT
I/V
2
20
10
0
I = 2.0 ef
1
I = 1.6 ef
0
10
20
10
0
0
20
10
0
-160 -140 -120 -100 -80
U1 (mV) f = 400 MHz
2
Appl. Phys. Lett. 92, 082112 (2008) nanostrukturen uni hannover
4
I = 1.0 ef
6 8 10 12 14 f (kHz)

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

P. Barthold
C. Fühner
J. Könemann
A. Nauen
N. Maire
M. Rogge
F. Hohls
H. W. Schumacher,
B. Kästner nanostrukturen uni hannover
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