Molecular states in a oneelectron double quantum dot Andreas K. - - PowerPoint PPT Presentation

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Molecular states in a one–electron double quantum dot

Andreas K. Hüttel

LS Prof. J. P . Kotthaus, Center for NanoScience, and SFB 631

EP2DS-16, Albuquerque, New Mexico, USA July 14, 2005

Introduction Hybridization of the ground states Hybridization with an excited state Summary

The material system – lateral quantum dots

• GaAs/AlGaAs heterostructure
• two-dimensional electron gas
• SEM lithography
• split–gate technique

GaAs AlGaAs AlGaAs:Si AlGaAs 2DEG GaAs 10nm 60nm 20nm 20nm 10nm z 2DEG E -E

C F

2DES depth z ≃ 120 nm, e− mean free path l ≃ 5 µm, Fermi wavelength λF ≃ 60 nm, e− sheet density n ≃ 1.8 · 1015

1 m2 ,

e− mobility µ ≃ 75 m2

Vs

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Deforming a single quantum dot D S QD gX gL gC gR QPC D S QPC gX gL gC gR

• triangular gate geometry

(M. Ciorga et al., PRB 61, R16315)

• single quantum dot
• N = 1 electrons
• UgC, UgX more negative
• UgL, UgR less negative

− → double well potential

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Measured stability diagram

Side gates used to tune potentials!

U (V)

gR gL

U (V)

IDQD

(nA) 0.001 0.01 0.1 1

• 0.5
• 0.4
• 0.5
• 0.45

gL gR gX gC µL µR

QPC

µS µD

>>0

D +

• S

D +

• S

cond-mat/0501012, to appear in PRB

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Measured stability diagram

Side gates used to tune potentials!

U (V)

gR gL

U (V) 0/0 U (V)

gR gL

U (V)

0/1 1/0 1/1 0/2

gL

dIQPC dU

(a.u.)

• 0.3
• 0.2
• 0.1

0.1

• 0.5
• 0.4
• 0.5
• 0.45

0/0

0/1 1/0 1/1 2/0 0/2

IDQD

(nA) 0.001 0.01 0.1 1

• 0.5
• 0.4
• 0.5
• 0.45

gL gR gX gC µL µR

QPC

µS µD

>>0

D +

• S

D +

• S

cond-mat/0501012, to appear in PRB

Introduction Hybridization of the ground states Hybridization with an excited state Summary

DQD: Finite USD, weak tunnel coupling

• Transport window

µS ≥ µR ≥ µL ≥ µD

• Triplepoints expand to triangles, size ↔ USD
• µR = µL → relaxation required

mD mL mR mS

1/0 N N

L R

/ 0/0 1/1

UgR UgL

• 0/1

TP1 TP2

A.C. Johnson , cond-mat/0410679 et al.

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, strong tunnel coupling — current

I (nA)

0.001 0.01 0.1 1 10

• 0.42
• 0.41
• 0.4
• 0.49
• 0.48

U (V)

gR

U (V)

gL

USD =-0.75mV

+

• D

S L R

• 0.41

I II III

• 0.4

~2t0 ~eUSD U (V)

gL

curved lines ↔ molecular states µ− − µ+ = 2 q ∆2 + t2 ∆ = µR − µL 2

cond-mat/0501012, to appear in PRB

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, strong tunnel coupling — current

I (nA)

0.001 0.01 0.1 1 10

• 0.42
• 0.41
• 0.4
• 0.49
• 0.48

U (V)

gR

U (V)

gL

USD =-0.75mV

• 0.41
• 0.4

U (V)

gL

+

• S

D

• +

~2t0 ~eUSD I II III

curved lines ↔ molecular states µ− − µ+ = 2 q ∆2 + t2 ∆ = µR − µL 2

cond-mat/0501012, to appear in PRB

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, strong tunnel coupling — current

I (nA)

0.001 0.01 0.1 1 10

• 0.42
• 0.41
• 0.4
• 0.49
• 0.48

U (V)

gR

U (V)

gL

USD =-0.75mV

• 0.41
• 0.4

U (V)

gL

+

• S

D

• +

~2t0 ~eUSD I II III

curved lines ↔ molecular states µ− − µ+ = 2 q ∆2 + t2 ∆ = µR − µL 2

cond-mat/0501012, to appear in PRB

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, strong tunnel coupling — current

I (nA)

0.001 0.01 0.1 1 10

• 0.42
• 0.41
• 0.4
• 0.49
• 0.48

U (V)

gR

U (V)

gL

USD =-0.75mV

• 0.41
• 0.4

U (V)

gL

+

• S

L R D ~2t0 ~eUSD I II III

curved lines ↔ molecular states µ− − µ+ = 2 q ∆2 + t2 ∆ = µR − µL 2

cond-mat/0501012, to appear in PRB

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, strong tunnel coupling — current

I (nA)

0.001 0.01 0.1 1 10

• 0.42
• 0.41
• 0.4
• 0.49
• 0.48

U (V)

gR

U (V)

gL

USD =-0.75mV

• 0.41
• 0.4

U (V)

gL

+

• S

D ~2t0 ~eUSD I II III

curved lines ↔ molecular states µ− − µ+ = 2 q ∆2 + t2 ∆ = µR − µL 2

cond-mat/0501012, to appear in PRB

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, strong tunnel coupling — current

I (nA)

0.001 0.01 0.1 1 10

• 0.42
• 0.41
• 0.4
• 0.49
• 0.48

U (V)

gR

U (V)

gL

USD =-0.75mV

• 0.41
• 0.4

U (V)

gL

+

• S

D

Coulombblockade =1 N

~2t0 ~eUSD I II III

curved lines ↔ molecular states µ− − µ+ = 2 q ∆2 + t2 ∆ = µR − µL 2

cond-mat/0501012, to appear in PRB

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, strong tunnel coupling — conductance

0.001 0.01 0.1 1

G (e/h)

2

• 0.42
• 0.41
• 0.4
• 0.49
• 0.48

U (V)

gR

U (V)

gL

USD =-0.75mV

• 0.41
• 0.4

U (V)

gL

+

• S

D

Coulombblockade =1 N

~2t0 ~eUSD I II III

curved lines ↔ molecular states µ− − µ+ = 2 q ∆2 + t2 ∆ = µR − µL 2

cond-mat/0501012, to appear in PRB

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Tuning the tunnel coupling

1 2 B (T) UgC =-1.47V chargingenergy E2 tunnelsplitting2t0 0.01 0.1 1 10

• 1.6
• 1.5
• 1.4

Energy(meV) UgC (V) B =0T modelcurve

UgC shifts the dots apart, B⊥ compresses the dot states model ↔ WKB approximation

cond-mat/0501012, to appear in PRB

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Effect of B⊥ on the level structure

• 0.42
• 0.41
• 0.4
• 0.49
• 0.48

0.001 0.01 0.1

G(e²/h)

U (V)

gL

U (V)

gR

B=0.5T B=1T B=1.4T

• 0.41
• 0.4 U (V)

gL

• 0.41
• 0.4 U (V)

gL

• 0.41
• 0.4 U (V)
• overall G decreases, tunnel coupling at ∆ = 0 decreases
• tip of triangle splits, additional line ↔ excited state

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, B⊥ = 1.4 T: second level anticrossing

• 0.49

USD= -0.75mV

• 0.48

0.001 0.01 B= 1.4T G (e²/h)

U (V)

gR

• 0.41
• 0.4

U (V)

gL

• 0.41
• 0.4

~ II I I* III U (V)

gL

+

• D

S L

• R
• ground state – ground state coupling very small

2t0 ≃ 0.06 meV

• finite asymmetry ∆ −

→ excited state of left dot couples to ground state of right dot 2t∗

0 ≃ 0.2 meV cond-mat/0507101

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, B⊥ = 1.4 T: second level anticrossing

• 0.49

USD= -0.75mV

• 0.48

0.001 0.01 B= 1.4T G (e²/h)

U (V)

gR

• 0.41
• 0.4

U (V)

gL

• 0.41
• 0.4

~ II I I* III U (V)

gL

+ D S L

• R
• ground state – ground state coupling very small

2t0 ≃ 0.06 meV

• finite asymmetry ∆ −

→ excited state of left dot couples to ground state of right dot 2t∗

0 ≃ 0.2 meV cond-mat/0507101

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, B⊥ = 1.4 T: second level anticrossing

• 0.49

USD= -0.75mV

• 0.48

0.001 0.01 B= 1.4T G (e²/h)

U (V)

gR

• 0.41
• 0.4

U (V)

gL

• 0.41
• 0.4

~ II I I* III U (V)

gL

+ D S R L

• ground state – ground state coupling very small

2t0 ≃ 0.06 meV

• finite asymmetry ∆ −

→ excited state of left dot couples to ground state of right dot 2t∗

0 ≃ 0.2 meV cond-mat/0507101

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, B⊥ = 1.4 T: second level anticrossing

• 0.49

USD= -0.75mV

• 0.48

0.001 0.01 B= 1.4T G (e²/h)

U (V)

gR

• 0.41
• 0.4

U (V)

gL

• 0.41
• 0.4

~ II I I* III U (V)

gL

+ D S L R

• ground state – ground state coupling very small

2t0 ≃ 0.06 meV

• finite asymmetry ∆ −

→ excited state of left dot couples to ground state of right dot 2t∗

0 ≃ 0.2 meV cond-mat/0507101

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, B⊥ = 1.4 T: second level anticrossing

• 0.49

USD= -0.75mV

• 0.48

0.001 0.01 B= 1.4T G (e²/h)

U (V)

gR

• 0.41
• 0.4

U (V)

gL

• 0.41
• 0.4

~ II I I* III U (V)

gL

+ D S L R

• ground state – ground state coupling very small

2t0 ≃ 0.06 meV

• finite asymmetry ∆ −

→ excited state of left dot couples to ground state of right dot 2t∗

0 ≃ 0.2 meV cond-mat/0507101

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Finite USD, B⊥ = 1.4 T: second level anticrossing

• 0.49

USD= -0.75mV

• 0.48

0.001 0.01 B= 1.4T G (e²/h)

U (V)

gR

• 0.41
• 0.4

U (V)

gL

0.01 0.1 USD= -0.75mV B= 1.5T I (nA)

• 0.41
• 0.4

U (V)

gL

• ground state – ground state coupling very small

2t0 ≃ 0.06 meV

• finite asymmetry ∆ −

→ excited state of left dot couples to ground state of right dot 2t∗

0 ≃ 0.2 meV cond-mat/0507101

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Summary

• One-electron double quantum dot, strong tunnel coupling
• Tunnel splitting is directly visible as anticrossing in nonlinear transport

and can be measured

• Tunnel splitting can be controlled by gate voltages or magnetic field
• At finite B⊥ and finite asymmetry, a hybridization of the ground state of
• ne quantum dot with an excited state of the other quantum dot causes

a second level anticrossing

Introduction Hybridization of the ground states Hybridization with an excited state Summary

Thanks

Jörg P . Kotthaus Stefan Ludwig & Karl Eberl, Robert H. Blick, Jan von Delft & coworkers, ...

Publications

• ‘Direct control of the tunnel splitting in a one–electron double quantum dot’
• A. K. Hüttel, S. Ludwig, H. Lorenz, K. Eberl, and J. P

. Kotthaus, accepted for publication by Phys. Rev. B (Rapid Comm.); cond-mat/0501012

• ‘Molecular states in a one–electron double quantum dot’
• A. K. Hüttel, S. Ludwig, H. Lorenz, K. Eberl, and J. P

. Kotthaus EP2DS conference contribution; cond-mat/0507101

DQD: Linear response, weak tunnel coupling

D

dotL drain UgL I dotR UgR

S

source USD

NL NR

• hexagons of stable

charge configuration

• tunnel current only at

triplepoints

• 0/1

1/0 2/0 N /N 0/0

L R

2/1 2/2 1/1 1/2 0/2 UgR UgL

D L R S

back

DQD: Linear response, strong tunnel coupling

Hybridized, molecular electron states

2t0 EC

fromR.H.Blick , PRL ,4032 (1998) etal. 80

D S S D=0 EC

UgR UgL

D>>0 D=0

mD m+ m- mS mD m+ m- mS

hexagons rounded, µ− − µ+ = 2 q ∆2 + t2

back

Tunnel coupling and the WKB–approximation

2t0 ≃ 2E0 π exp − p 2m∗φ d 2 ! − → log (2t0) ∝ d In a magnetic field B⊥, LFD = r

• ωcm∗

1

4

r 1 +

4ω2 ω2

c

, ωc = eB m∗ − → d(B) = d∞ − LFD(B)

d d LFD

• back

Finite USD, strong tunnel coupling — dIQPC

dUgL

• QPC detects charging:
• left of dark line, N ≈ 0
• right of dark line, N ≈ 1
• Information on tunnel rates!
• ‘Jump’ at finite asymmetry
• Line III not visible

(in triplepoint region)

− → Drain–side tunnel rate smaller

• 1

1 2

• 0.42
• 0.41
• 0.4
• 0.49

N=0 N=1

• 0.48

U (V)

gL

U (V)

gR

GT,QPC (a.u.) USD =-0.75mV

I II III

back