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Chapter 4
Correlated electrons on the
honeycomb lattice
4.1 Outline
We investigate the ground state of the t–J model on the honeycomb lattice as
a function of doping by variational Monte Carlo calculations. d x 2 −y 2 + id xy superconductivity
is observed in the range of doping δ =]0, 1 [, disappearing at the
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doping which corresponds to the van Hove singularity of the free electron density
of states. Néel order and superconductivity coexist in the range [0, 0.07]. The van
Hove singularity stabilizes a spin density wave for δ =[ 1 , 0.22]. When the spin
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density wave phase disappears, the system is polarized progressively, reaching full
ferromagnetic polarization at δ =0.5. The work done in this chapter is resulting
from a collaboration with Thomas Gloor and Andreas Martin Läuchli. In particular,
the mean-field calculations and the Quantum Monte-Carlo calculations
in this chapter were done by Thomas Gloor (a former PhD student of Professor
Frederic Mila) and by Andreas Martin Läuchli.
4.2 Introduction
The observation of superconductivity in alkali-metal graphite intercalation compounds
(GIC’s) was reported years ago by Hannay et al. [95]. They are formed
by inserting foreign atoms or molecules between the hexagonal two-dimensional
sheets of graphite, forming a honeycomb layer geometry, leading to ordered structures.
Since graphite is a semi-metal, the electrons accepted or donated by the
intercalant (i.e. there is a charge transfer from the intercalate layer to the host
carbon layer) modify the electronic properties of graphite, resulting in a metallic
behavior in the final material.
Intensive research work in this area was ensued and many GIC’s were subsequently
found to exhibit superconductivity. An interesting property of the
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