1. Enhancement of Kondo effect through Rashba spin-orbit interactions. Nancy Sandler Dept. of Physics and Astronomy Ohio University In collaboration with: Sergio Ulloa Mehdi Zarea

2. Why Kondo and Rashba? Kondo effect on surfaces Manoharan et al Nature Feb 2000 Kondo Switch V. Iancu, A. Deshpande, S.-W. Hla, Nano Lett. 6 (2006) 820-823.

3. More recently: graphene… Chen et al arXiv:1004.3373 HOPG with defects Graphene on SiC with Co Mattos et al, unpublished

4. Rashba spin-orbit interaction Time reversal symmetry: preserved Semiconductor physics: Electric fields drive spins. E. I. Rashba Nature Physics 2, (2006).

5. Anderson impurity model: Kondo Spin-scattering Many-body effect Virtual many-body bound state Kondo temperature Schrieffer-Wolff TransformationKondo model

6. What does Rashba do to Kondo? Many answers since 1969… Gainon and Heeger, PRL 22 (1969) Everts, Z. Phys. 251 (1972) Wingreen and Meir PRB 50 (1994) Malecki, J. Stat. Phys. 129 (2007)

7. Anderson model with RSO Bath Coupling to impurity spin: select channels in the bath S=1/2 L = 0 One-channel Kondo model

8. Anderson model with RSO II In 2d: polar symmetry In the presence of RSO, the hybridization term couples the impurity to more than one mode in the bath: Natural (chiral) basis: 2-channel Anderson model:

9. Anderson model with RSO II Total Hamiltonian describes a two- channel Anderson model SU(2) Spin-symmetry: broken Two-bands: J1J1 J2J2

10. Anderson model with RSO III How do you solve it in the Kondo regime? Introduce chiral basis (helicity basis) Do proper Schrieffer-Wolff transformation (SWT) Bode et al, Nature 447 (2007) (Mn on W)

11. Kondo regime with RSO Renormalization group: Anti-ferro: J > 0  J 1  strong coupling  J 2  vanishes Ferro: J < 0  J 1  antiferromagnet (even from J = 0!!!)  J 2  ferromagnet Exponential increase of T K

12. Kondo in graphene with Rashba SymmetricOn top or substitutional No evidence of two-channel Kondo regime. Increase of Kondo temperature

13. Conclusions Anderson impurity model with Rashba bath: 2-channel Kondo Ferro and anti-ferromagnetic Kondo couplings. Flow of Kondo coupling constants to strong coupling (antiferro) Graphene: excellent substrate to test effect of Rashba in Kondo

14. What about Rashba? Dedkov et al, PRL 100 (2008) Dresden Graphene/Ni (111) Rader et al, PRL 102 (2009) Berlin Graphene/Ni (111) Graphene/Co (0001) Graphene/Au/Ni (111) Varykhalov et al, PRL 102 (2009) Berlin λ R ~ 225meV λ R ~ 0 meV λ R ~ 20 meV

15. What about experiments? II λ R up to 200meV Graphene on SiC(0001) Gierz et al arXiv (2010) Stuttgart

16. Spintronics with graphene Graphene: interesting material for electron (charge) transport and magnetotransport Electronic spin transport and spin precession in single graphene layers at room temperature. Tombros et al., Nature 448 (2007) Spin field effect transistor with a graphene channel. Semenov et al., App. Phys. Letts. 91 (2007)