Enhancement of Kondo effect through Rashba spin-orbit interactions.Nancy Sandler Dept. of Physics and AstronomyOhio University

In collaboration with:

Sergio UlloaMehdi Zarea

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.

More recently: graphene…

Chen et al arXiv:1004.3373

HOPG with defects Graphene on SiC with Co

Mattos et al, unpublished

Rashba spin-orbit interaction

Time reversal symmetry: preserved

Semiconductor physics: Electric fields drive spins.E. I. Rashba Nature Physics 2, (2006).

Anderson impurity model: Kondo

• Spin-scattering

• Many-body effect

• Virtual many-body bound state

Kondo temperature

Schrieffer-Wolff Transformation

Kondo model

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)

Anderson model with RSO

Bath

Coupling to impurity spin: select channels in the bath

S=1/2L = 0

One-channel Kondo model

Anderson model with RSO II

In 2d: polar symmetry

In the presence of RSO, the hybridization term couples theimpurity to more than one mode in the bath:

Natural (chiral) basis: 2-channel Anderson model:

Anderson model with RSO II

Total Hamiltonian describes a two-channel Anderson model

SU(2) Spin-symmetry: broken

Two-bands:

J1 J2

Anderson model with RSO IIIHow 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)

Kondo regime with RSO

Renormalization group:

• Anti-ferro: J > 0 J1 strong coupling J2 vanishes

• Ferro: J < 0 J1 antiferromagnet (even from J = 0!!!) J2 ferromagnet

Exponential increase of TK

Kondo in graphene with Rashba

Symmetric

On top or substitutional

No evidence of two-channel Kondo regime.

Increase of Kondo temperature

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

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

λR ~ 225meV

λR ~ 0 meV

λR ~ 20 meV

What about experiments? II

λR up to 200meV

Graphene on SiC(0001)

Gierz et al arXiv (2010) Stuttgart

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)