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


.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


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


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.


K. Ono , D.G. 297 (02)

Austing, Y. Tokura

and S. Tarucha,

Science, 297 (02)


Allowed and forbidden transitions in artificial hydrogen 297 (02)

and helium atoms:

Electrical pump and probe experiments.

T. Fujisawa et al.,

Nature 2002

T=100mK


The relaxation time does not involve spin-flip (10 ns) 297 (02)

Orbital relaxation

Average number of tunneling

electrons per pulse:



Our System 297 (02):


Hamiltonian
Hamiltonian 297 (02)

one level in left dot

one level in right dot

Tunnelling between dots

Zeeman splitting


Master equation for the reduced density matrix: 297 (02)

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)


transition rates due to tunnelling through the contacts 297 (02)

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.


: 297 (02)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


The current through the drain contact barrier: 297 (02)

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

s’ are states with one electron less


Results: 297 (02)

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 :


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 in a QD

two levels in the right dot:


Including intradot triplet state in the right dot: in a QD

As a consequence of Hund’s rule

the intradot exchange J is

ferromagnetic: J<0


spin filter in a QD

b)

Spin

down

current

c)

Spin

up

current

current peaks also at

Absorption of N photons


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


The width of the peaks changes in a non trivial way states, but there is a degeneracy in the three electron sector for

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


1-photon triplet states, but there is a degeneracy in the three electron sector for


Excited states states, but there is a degeneracy in the three electron sector for

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)


Rabi frequency states, but there is a degeneracy in the three electron sector for

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:


For states, but there is a degeneracy in the three electron sector for

For

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

we obtain the decoherence timefor the closed system:


Including PAT through the contact barriers states, but there is a degeneracy in the three electron sector for

UnitaryTransformation


Pumped current as a function of frequency
Pumped Current as a function of frequency states, but there is a degeneracy in the three electron sector for

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


Comparison of I versus V states, but there is a degeneracy in the three electron sector forAC including (non including) PAT through the contacts.


Tuning the AC parameters pure spin current states, but there is a degeneracy in the three electron sector for

(not charge current) could be achieved


CONCLUSIONS states, but there is a degeneracy in the three electron sector for

  • 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.


Future work states, but there is a degeneracy in the three electron sector for

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.


T states, but there is a degeneracy in the three electron sector for1=2.58 ms

at B=0.02T


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