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Ordered States of Adatoms in Graphene

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

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Ordered States of Adatoms in Graphene

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  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’ K’ K K K’

  4. Graphene Field Effect Transistor Contacts SiO Resistance Si back gate Gate Voltage Resistance at its maximum is close to h/e2. 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 SiO2) • 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 The position of the impurity Small parameter A 4x4 matrix is defined by the quantum chemistry of the adatom. But not entirely!

  10. An example K K’ K’ K K K’ 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…

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