R. Sánchez 1 , E. Cota 2 , R. Aguado 1 and G. Platero 1

1. 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

2. .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

3. 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

4. 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.

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

6. Allowed and forbidden transitions in artificial hydrogen and helium atoms: Electrical pump and probe experiments. T. Fujisawa et al., Nature 2002 T=100mK

7. The relaxation time does not involve spin-flip (10 ns) Orbital relaxation Average number of tunneling electrons per pulse:

8. The relaxation time involves spin-flip

9. Our System:

10. Hamiltonian one level in left dot one level in right dot Tunnelling between dots Zeeman splitting

11. 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)

12. 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.

13. : 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

14. 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

15. 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 :

16. 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)

17. Hamiltonian two levels in the right dot:

18. Including intradot triplet state in the right dot: As a consequence of Hund’s rule the intradot exchange J is ferromagnetic: J<0

19. spin filter b) Spin down current c) Spin up current current peaks also at Absorption of N photons

20. 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

21. 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

22. 1-photon triplet

24. 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)

25. 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:

26. For For for FW is linear with : FW=2 . Measuring FW at we obtain the decoherence timefor the closed system:

27. Including PAT through the contact barriers UnitaryTransformation

28. 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

29. Comparison of I versus VAC including (non including) PAT through the contacts.

31. Tuning the AC parameters pure spin current (not charge current) could be achieved

32. 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.

33. 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.

34. T1=2.58 ms at B=0.02T