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AC-driven double quantum dots as spin pumps and spin filters. R. Sánchez 1 , E. Cota 2 , R. Aguado 1 and G. Platero 1 1 Instituto de Ciencia de Materiales de Madrid – CSIC, Cantoblanco, Madrid 28049, Spain 2 Centro de Ciencias de la Materia Condensada-UNAM, Ensenada, México.

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slide1

AC-driven double quantum dots as spin pumps and spin filters

R. Sánchez1, E. Cota2 , R. Aguado1 and G. Platero1

1Instituto de Ciencia de Materiales de Madrid – CSIC, Cantoblanco, Madrid 28049, Spain

2Centro de Ciencias de la Materia Condensada-UNAM, Ensenada, México

“Nanoscale Dynamics and Quantum Coherence”

Catania october 2005

slide2

.One of the most important requirements for any spin-based electronics devices is the ability to generate spin polarized currents.Control of spin dynamics of electrons spintronicsProposals for generating spin-polarized currents: spin injection by ferromagnetic metals or DMS.Semiconducting quantum dots can be used as spin filters or spin pumps: We propose a system for realizing both spin filtering and spin pumping with unpolarized leads, by using an ac-driven double QD connectedin series in thepresence of a uniform magnetic field.

Motivation

slide3

Current Rectification by Pauli Exclusion in a Weakly Coupled Double Quantum Dot System

K. Ono , D.G. Austing, Y. Tokura and S. Tarucha, Science, vol 297 (02)

Spin Blockade

slide4

K. Ono , D.G. Austing, Y. Tokura and S. Tarucha, Science, 297 (02)

J.Iñarrea et al.

two main peaks I/V in a double QD. The spin blockade region

is the plateau between the peaks.

slide5

K. Ono , D.G.

Austing, Y. Tokura

and S. Tarucha,

Science, 297 (02)

slide6

Allowed and forbidden transitions in artificial hydrogen

and helium atoms:

Electrical pump and probe experiments.

T. Fujisawa et al.,

Nature 2002

T=100mK

slide7

The relaxation time does not involve spin-flip (10 ns)

Orbital relaxation

Average number of tunneling

electrons per pulse:

hamiltonian
Hamiltonian

one level in left dot

one level in right dot

Tunnelling between dots

Zeeman splitting

slide11

Master equation for the reduced density matrix:

Blum K., 1981,

Density Matrix:

Theory and Applications,

(Plenum)

From Liouville equation

reversible dynamics:

coherent effects

irreversible dynamics

relaxation

decoherence

: Occupation probability of the level s

:Coherence and phase of superpositions of dot levels s,s’

its real part is responsible for the time decay of the off-diagonal DM elements (coherences)

slide12

transition rates due to tunnelling through the contacts

Transition amplitude

Electrons coming onto left dot from the left lead

Electrons leaving from left dot onto the left lead

We consider that the AC does not affect the transition probability through the contact barriers

We include spin-flip processes:

Electronic dot states are affected by intrinsic degrees of freedom: hyperfine coupling, S-O interaction: spin relaxation and decoherence.

slide13

: Spin relaxation time:includes processes where the electron spin is flipped

The spin relaxation rates

At low T:

:Spin decoherence time(decay of the off-diagonal elements of the DM) it destroys the information about the relative phase in a superposition of and

it accounts as well for the intrinsic spin decoherence which is present even with no coupling to the leads

Open system

Closed system

Coherent manipulations of electron spins:

gate operations for quantum computation

must be performed faster than T2

slide14

The current through the drain contact barrier:

Where s states are such that the right dot is occupied and

s’ are states with one electron less

slide15

Results:

Open system

UR=1.3, UL=1

a)

Appearance of interdot triplet

blocks pumping: spin blockade

unpolarized contacts

NO!

Too high in

energy!

Spin down polarized contacts

b)

  • Pumping of spins is realized for fully spin down polarized injection from left lead :
slide16

Pauli principle is used for filtering the electronic spin in a QD

NO!!

E =0

E =0

E (=Dz)

E =Dz

-Dz

-Dz

U2

U2

m=

= < mR

Spin pump follows the next sequence

m=

= U2 >mR

E =U2

E (=U2) -

E (=U2) -

E =U1

Spintronics in quantum dots

An AC gate voltage acts as spin pump in

a DQD with unpolarized leads

mL

mR

Spin-polarized pumping in a double quantum dot,

E. Cota, R. Aguado, C. E. Creffield and G. Platero, Nanotechnology 14, 152 (2003)

hamiltonian1
Hamiltonian

two levels in the right dot:

slide18

Including intradot triplet state in the right dot:

As a consequence of Hund’s rule

the intradot exchange J is

ferromagnetic: J<0

slide19

spin filter

b)

Spin

down

current

c)

Spin

up

current

current peaks also at

Absorption of N photons

slide20

An external B breaks the degeneracy for one and two-electron states, but there is a degeneracy in the three electron sector for

spin up current

spin down current

The degeneracy is broken as

for

slide21

The width of the peaks changes in a non trivial way

as a function of

J=-.2

tLR=5

1-photon

UL=1., UR=1.3

The width of

the peaks is

determined by

if and

it is determined

by for:

2-photons

3-photons

slide24

Excited states

Spin-up current sensitive to

relaxation processes if

Pumped current near resonance: =0.6 for different relaxation rates. Inset: FWHM of I as a function of the relaxation rate for strong ( black dots) and weak (red squares) field intensity.

E. Cota et al., PRL, 107202 (2005)

slide25

Rabi frequency

High field

Low field

Black dots: low VAC Red squares: high VAC

Measuring the width of the current peak as a function of one gets direct information on the spin decoherence time:

slide26

For

For

for FW is linear with : FW=2 . Measuring FW at

we obtain the decoherence timefor the closed system:

pumped current as a function of frequency
Pumped Current as a function of frequency

UR=1.3, UL=1.

2-photons

1-photon

Current through

double occupied

singlet S0 in the

right dot

Spin down current

Spin up current through PAT at the leads

slide31

Tuning the AC parameters pure spin current

(not charge current) could be achieved

slide32

CONCLUSIONS

  • We propose a new scheme for realizing both spin filtering and spin pumping using ac-driven double quantum dots coupled to unpolarized leads.
  • Spin polarization of the current can be manipulated (including fully reversing) by tuning the frequency of the ac field.
  • The width in frequency of spin-up pumped current gives information on the relaxation and decoherence times.
  • PAT through the contacts limits the spin filter effect only at high VAC.
slide33

Future work

Cotunnel including PAT in the contacts

Analysis of the relaxation and

decoherence times T1 and T2 at finite T.

EARLY STAGE RESEARCHER MC RTN POSITION

Applications are encouraged for a two-year position as an “early stage researcher” in the Madrid node of this Marie Curie Research and Training Network (RTNNANO). The successful candidate will initiate his/her contract shortly before completion of Ph. D., afterwards continuing in Madrid as a postdoc.

Starting date: between January 1 and (ideally) April 1, 2006.

Research interests in the Madrid node include electron entanglement and decoherence, spintronics, electron and heat AC transport, and NS transport.

Interested applicants should contact one of the following:

Francisco Guinea (ICMM-CSIC)

Gloria Platero (ICMM-CSIC)

Fernando Sols (Universidad Complutense de Madrid) (contractor)

Closing date: November 30, 2005.

slide34

T1=2.58 ms

at B=0.02T

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