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Remaining Landau levels handled by perturbation theory:
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RKKY Interactions on Dirac Surfaces by Herbert A Fertig
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- 1 RKKY Interactions on Dirac Surfaces
- 2 Outline
- 3 Effective spin-spin interaction
- 4 Another completely equivalent approach: second order perturbation theory
- 5 RKKY Interactions in Graphene: A Paradigms for Dirac Surfaces
- 6 3. Electron wavefunctions are helical
- 7 4. Different possible locations for spin impurities: sd exchange coupling to multiple sites possible
- 8 So AA response is different than AB response
- 9 Strong local antiferromagnetic correlations from single particle physics
- 10 Numerical check: graphene sheet with periodic boundary conditions nanotube
- 11 Can we induce ferromagnetism in graphene? Need to break symmetry between sublattices. One way: use strain!
- 12 Problem: Breakdown of second order perturbations theory
- 13 Hilbert Space of states in LLL: M angular momentum states
- 14 Relative angle
- 15 Remaining Landau levels handled by perturbation theory:
- 16 Mean-field theory for RKKY interactions in strained graphene: Pairwise RKKY interaction = LLL nonperturbative part + 2nd order perturbative part
- 17 Net Moment
- 18 Dirac Surfaces on Topological Insulators
- 19 Topological crystalline insulators TCI
- 20 In topological regime....For 1 11 surface: Dirac points present at I and M 3 of these points
- 21 Slab geometry:total free energy computed for different orientations
- 22 Many thanks to ....
- 23 Summary
- 24 Q&A
