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 pp. 666 – 669 (2004)

Graphene band structure K K KK’.

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.

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)

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.

The Dirac Hamiltonian

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

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!

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

Supperlattice Three inequivalent positions of the atom in the lattice

Formal parameterization

Electron-mediated interaction

FM random clock model

Order-disorder phase transition

Visualization Potential seen by a probe atom Mosaic ordering

Mean field gap

Generalizations

Classification of W matrices irrep

Complete order parameters

Epoxy-bond adatom

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…