1. Ordered States of Adatoms in Graphene V. Cheianov, O. Syljuasen, V. Fal’ko, and B. Altshuler

2. Graphene graphite graphene FET K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov Science, Vol. 306. pp. 666 – 669 (2004)

3. Graphene band structure K K KK’.

4. Graphene Field Effect Transistor Gate Voltage Resistance Contacts Si back gate SiO Resistance at its maximum is close to h/e 2. Large on-off ratio is a challenge.

5. Disorder Mobility is controlled by disorder scattering. Types of disorder: Long-range Coulomb scatterers (charged traps in SiO 2 ) Lattice defects Surface adsorbants The latter can stick to the surface naturally or be deposited artificially (STM images from NIST)

6. The main question. Gapless electron spectrum Local perturbation of the electron system propagates over a large distance (e.g. as Friedel oscillations) Long-range interactions between impurity atoms (RKKY). Q: How will electron mediated interaction affect relative positions of mobile (non-magnetic) adatoms and what feedback will these correlations have on the electron system.

7. The Dirac Hamiltonian

8. Pseudo-spin and pseudo-flavor Sublattice mixing matrices (similar to spin). Valley mixing matrices (similar to flavor).

9. Electron-adatom interaction Small parameter The position of the impurity A 4x4 matrix is defined by the quantum chemistry of the adatom. But not entirely!

10. An example K K KK’ Intervalley scattering = momentum transfer K-K' There are 3 inequivalent positions of the adatom in the lattice.

11. Supperlattice Three inequivalent positions of the atom in the lattice

12. Formal parameterization

13. Electron-mediated interaction

14. FM random clock model

15. Order-disorder phase transition

16. Visualization Potential seen by a probe atom Mosaic ordering

17. Mean field gap

18. Generalizations

19. Classification of W matrices irrep

20. Complete order parameters

21. Epoxy-bond adatom

22. Conclusions and open questions Electron-mediated interactions may lead to correlations in the positions of adatoms The transition to ordered states is accompanied by a gap opening in the electron spectrum Outstanding: competition between order and disorder contributions, glassy states, domains, quantum chemistry, experiment…