Dynamical nuclear spin polarization induced Theory Results by - - PowerPoint PPT Presentation
Keszthely 2011 C. L opez-Mon s Introduction Dynamical nuclear spin polarization induced Theory Results by electronic current through double Summary quantum dots Carlos L opez-Mon s and Gloria Platero Instituto de Ciencia de
Keszthely 2011
ıs Introduction Theory Results Summary
Carlos L´
ıs and Gloria Platero
Instituto de Ciencia de Materiales de Madrid (CSIC)
June 2011 CLM, et al, NJP (2011).
Keszthely 2011
ıs Introduction Theory Results Summary
Introduction Theory Results Summary
Keszthely 2011
ıs Introduction Theory Results Summary
Keszthely 2011
ıs Introduction Theory Results Summary
S+ T+
_
T
_
S B
Electron Reservoir
µL µR
Electron Reservoir
blocked Current allowed Traffic lights
|S± =
1 2
√ 2 |0, ↑↓
→ Singlets |T+ = | ↑, ↑ |T− = | ↓, ↓ |T0 =
1 √ 2 (| ↑, ↓ + | ↓, ↑)
− → Triplets (SB)
(K. Ono, et al, Science 2002, F. H. L. Koppens, et al, Science 2005)
Keszthely 2011
ıs Introduction Theory Results Summary
S+ T+
_
T
_
S B
Electron Reservoir
µL µR
Electron Reservoir
blocked Current allowed Traffic lights
|S± =
1 2
√ 2 |0, ↑↓
→ Singlets |T+ = | ↑, ↑ |T− = | ↓, ↓ |T0 =
1 √ 2 (| ↑, ↓ + | ↓, ↑)
− → Triplets (SB)
Keszthely 2011
ıs Introduction Theory Results Summary
S+ T+
_
T
_
S B
Electron Reservoir
µL µR
Electron Reservoir
blocked Current allowed Traffic lights
|S± =
1 2
√ 2 |0, ↑↓
→ Singlets |T+ = | ↑, ↑ |T− = | ↓, ↓ |T0 =
1 √ 2 (| ↑, ↓ + | ↓, ↑)
− → Triplets (SB)
Keszthely 2011
ıs Introduction Theory Results Summary
S+ T+
_
T
_
S B
Electron Reservoir
µL µR
Electron Reservoir
blocked Current allowed Traffic lights
|S± =
1 2
√ 2 |0, ↑↓
→ Singlets |T+ = | ↑, ↑ |T− = | ↓, ↓ |T0 =
1 √ 2 (| ↑, ↓ + | ↓, ↑)
− → Triplets (SB)
Keszthely 2011
ıs Introduction Theory Results Summary
S+ T+
_
T
_
S B
Electron Reservoir
µL µR
Electron Reservoir
blocked Current allowed Traffic lights
|S± =
1 2
√ 2 |0, ↑↓
→ Singlets |T+ = | ↑, ↑ |T− = | ↓, ↓ |T0 =
1 √ 2 (| ↑, ↓ + | ↓, ↑)
− → Triplets (SB)
Keszthely 2011
ıs Introduction Theory Results Summary
S+ T+
_
T
_
S B
Electron Reservoir
µL µR
Electron Reservoir
blocked Current allowed Traffic lights
|S± =
1 2
√ 2 |0, ↑↓
→ Singlets |T+ = | ↑, ↑ |T− = | ↓, ↓ |T0 =
1 √ 2 (| ↑, ↓ + | ↓, ↑)
− → Triplets (SB)
Keszthely 2011
ıs Introduction Theory Results Summary
S+ T+
_
T
_
S B
Electron Reservoir
µL µR
Electron Reservoir
blocked Current allowed Traffic lights
|S± =
1 2
√ 2 |0, ↑↓
→ Singlets |T+ = | ↑, ↑ |T− = | ↓, ↓ |T0 =
1 √ 2 (| ↑, ↓ + | ↓, ↑)
− → Triplets (SB)
Keszthely 2011
ıs Introduction Theory Results Summary
Keszthely 2011
ıs Introduction Theory Results Summary
T+
_
T
_
S
Electron Reservoir
µL µR
Electron Reservoir
T0 B
|S± =
1 2
√ 2 |0, ↑↓
→ Singlets |T+ = | ↑, ↑ |T− = | ↓, ↓ |T0 =
1 √ 2 (| ↑, ↓ + | ↓, ↑)
− → Triplets (SB)
Keszthely 2011
ıs Introduction Theory Results Summary
T+
_
T
_
S
Electron Reservoir
µL µR
Electron Reservoir
BL
n
BR
n
TX B
|Tx ≈ |T0 + δ
J |0, ↑↓
− → ST mixing δ = gµB(BL
n − BR n ): Zeeman splitting difference within each dot.
J: exchange energy. |T+ = | ↑, ↑ |T− = | ↓, ↓ − → Triplets (SB)
Keszthely 2011
ıs Introduction Theory Results Summary
T+
_
T
_
S
Electron Reservoir
µL µR
Electron Reservoir
TX B
blocked Current allowed Traffic lights
|Tx ≈ |T0 + δ
J |0, ↑↓
− → ST mixing δ = gµB(BL
n − BR n ): Zeeman splitting difference within each dot.
J: exchange energy. |T+ = | ↑, ↑ |T− = | ↓, ↓ − → Triplets (SB)
Keszthely 2011
ıs Introduction Theory Results Summary
T+
_
T
_
S
Electron Reservoir
µL µR
Electron Reservoir
TX B
Keszthely 2011
ıs Introduction Theory Results Summary
T+
_
T
_
S
Electron Reservoir
µL µR
Electron Reservoir
TX B
◮ Electron tunnelling induces a dynamical nuclei spin
polarization P = (N↑ − N↓)/N,
◮ (gµB)/(gnµn) ∼ 103 −
→ Hyperfine mediated spin-flip transitions do not conserve energy, and
◮ at low temperatures (∼ 100mK) emission processes
dominate over absorption processes.
Fujisawa, et al, Science (1998)
Keszthely 2011
ıs Introduction Theory Results Summary
T+
_
T
_
S
Electron Reservoir
µL µR
Electron Reservoir
TX B
◮ Electron tunnelling induces a dynamical nuclei spin
polarization P = (N↑ − N↓)/N,
◮ (gµB)/(gnµn) ∼ 103 −
→ Hyperfine mediated spin-flip transitions do not conserve energy, and
◮ at low temperatures (∼ 100mK) emission processes
dominate over absorption processes.
Keszthely 2011
ıs Introduction Theory Results Summary
Keszthely 2011
ıs Introduction Theory Results Summary
Model
◮ Anderson model for the quantum dots.
Keszthely 2011
ıs Introduction Theory Results Summary
Model
◮ Anderson model for the quantum dots. ◮ Hyperfine coupling
ˆ VHF =
Al N
N
ˆ Sxˆ Iix + ˆ Syˆ Iiy
+
Al N
N
ˆ Slzˆ Iiz
ˆ VHF = ˆ Vxy + ∆ 2
SLz + ˆ SRz
2
SLz − ˆ SRz
n + BR n ), δ = gµB(BL n − BR n ) ∝ P.
Keszthely 2011
ıs Introduction Theory Results Summary
Model
◮ Anderson model for the quantum dots. ◮ Hyperfine coupling
ˆ VHF =
Al N
N
ˆ Sxˆ Iix + ˆ Syˆ Iiy
+
Al N
N
ˆ Slzˆ Iiz
ˆ VHF = ˆ Vxy + ∆ 2
SLz + ˆ SRz
2
SLz − ˆ SRz
n + BR n ), δ = gµB(BL n − BR n ) ∝ P. ◮ Tunnelling rates through the contact barriers are computed
using Fermi’s Golden Rule (e.g. Γ(0,↑);Tx ∝ P2).
Keszthely 2011
ıs Introduction Theory Results Summary
Rate equations
◮ For computing the time evolution of the population of the
DQD states and for the nuclei spin polarization.
Keszthely 2011
ıs Introduction Theory Results Summary
Rate equations
◮ For computing the time evolution of the population of the
DQD states and for the nuclei spin polarization.
◮ Tunnelling rates and spin-flip rates are functions of the
nuclei spin polarization → nonlinear rate equations.
Current Nuclei spin polarization
Keszthely 2011
ıs Introduction Theory Results Summary
Keszthely 2011
ıs Introduction Theory Results Summary
5 10 15 20 1.0 0.5 0.0 0.5 1.0
kBT Μ eV P S+ T+ T0 T− S_ J µB
n
g B ◮ A critical temprature TC exists.
Keszthely 2011
ıs Introduction Theory Results Summary
5 10 15 20 1.0 0.5 0.0 0.5 1.0
kBT Μ eV P S+ T+ T0 T− S_ J µB
n
g B ◮ A critical temprature TC exists. ◮ Above TC P = 0 → δ = 0 so
|Tx ≈ |T0 + δ J |0, ↑↓ ⇒ |Tx = |T0 and no ST-mixing.
Keszthely 2011
ıs Introduction Theory Results Summary
5 10 15 20 1.0 0.5 0.0 0.5 1.0
kBT Μ eV P S+ T+ T0 T− S_ J µB
n
g B ◮ A critical temprature TC exists. ◮ Above TC P = 0 → δ = 0 so
|Tx ≈ |T0 + δ J |0, ↑↓ ⇒ |Tx = |T0 and no ST-mixing.
◮ Below TC → bifurcation → δ = 0 → the current induced
nuclei spin polarization (kBTC ∝ AL + AR).
Keszthely 2011
ıs Introduction Theory Results Summary
Current dip to current peak transition
0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.00 0.05 0.10 0.15
Bext T I pA T TC
0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.06 0.08 0.10 0.12 0.14 0.16
Bext T I pA T TC
Signature of the induced finite nuclei spin polarization.
Keszthely 2011
ıs Introduction Theory Results Summary
Hysteresis
0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.3 0.2 0.1 0.0 0.1 0.2 0.3
Bext T P T TC
0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.4 0.2 0.0 0.2 0.4
Bext T P T TC
Keszthely 2011
ıs Introduction Theory Results Summary
◮ Electron current through a double quantum dot in the spin
blockade regime induces a finite nuclei spin polarization below a critical temperature.
◮ The phase transition is observable in the current versus the
external magnetic field in a transition from a current dip to a current peak.
◮ By measuring the critical temperature it is possible to
estimate the hyperfine coupling constant of the material.
Keszthely 2011
ıs Introduction Theory Results Summary
[S ;(0,1)] µ [T ;(0,1)]
x
µ
−
[S ;(0,1)] µ
+
[S ;(1,0)] µ [T;(1,0)] µ
−
[S ;(1,0)] µ