RKKY Interactions on Dirac Surfaces by Herbert A Fertig

Explore RKKY interactions on Dirac surfaces in this comprehensive lecture from the ICTS Discussion Meeting on Edge Dynamics in Topological Phases. Delve into effective spin-spin interactions, perturbation theory approaches, and RKKY interactions in graphene as a paradigm for Dirac surfaces. Examine helical electron wavefunctions, spin impurity locations, and strong local antiferromagnetic correlations. Investigate methods to induce ferromagnetism in graphene through symmetry breaking and strain. Analyze the breakdown of second-order perturbation theory and explore mean-field theory for RKKY interactions in strained graphene. Conclude with insights on Dirac surfaces in topological insulators and topological crystalline insulators, followed by a summary and Q&A session.

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