Title:
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Excitonic condensation in two-layer graphene
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We consider two parallel separately controlled graphene monolayers
in which external gates induce a finite density of electrons in one layer
and holes in another layer. In this thesis the theory of the excitonic
insulator in such systems is developed.
We analyze the symmetry of the excitonic state in the system, classify
all possible phases, and build a phase diagram that takes into account
the effect of the symmetry breaking due to the external electric
and magnetic fields.
The large-N approximation is used, where N = 8 is a number of
electron's species in the system. Taking into account leading and sub-leading
orders in 1/N expansion of the dynamically screened Coulomb
interaction in the system, for the most energetically stable phase in
absence of magnetic field we find a gap in the single-particle excitation
spectrum at zero temperature. The result for the gap is found up
to the first sub-leading order in 1/N. We determined the leading 1/N
contribution to the exponential pre-factor in the expression for the gap
Δ=Cexp[-2N]EF .
Also we consider the simplified interaction, which reflects two most
important features of the dynamically screened interaction: 1 )the interaction
between charge carriers on Fermi surface, which is the most
important for the excitonic condensation, and 2)the undamped plasmon.
In such a case, in contrast to the suggested by other authors
Ref.[59] enhancement of transition temperature Tc by plasmon pole in
the dynamically screened interaction, we find no enhancement of Tc and
arrive at Tc≈10-7EF, which is comparable to the result Tc≈10-7EF
which was obtained using a statically screened interaction [42, 43].
Moreover, we found the presence of Goldstone modes with linear
spectrum, therefore fluctuations of the order parameter suppress the
transition into the excitonic insulator state even further.
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