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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Mattos et al, unpublished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)