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. FirsovScience, Vol. 306. pp. 666 – 669 (2004)

Graphene band structure

K

K

K K’

K’

K’

.

Graphene Field Effect Transistor

Gate VoltageR

esis

tanc

e

Contacts

Si back gate

SiO

Resistance at its maximum is close to h/e2. Large on-off ratio is a challenge.

DisorderMobility 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)

The main question.Gapless electron spectrum

Local perturbation of the electronsystem 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 (similarto spin).

Valley mixing matrices (similarto flavor).

Electron-adatom interaction

Small parameterThe position of theimpurity

A 4x4 matrix

is defined by the quantum chemistry of the adatom. But not entirely!

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.

Supperlattice

Three inequivalent positionsof the atom in the lattice

Formal parameterization

Electron-mediated interaction

FM random clock model

Order-disorder phase transition

Visualization

Potential seenby a probe atom

Mosaicordering

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…