 10147 J.B. Bru, W. de Siqueira Pedra, and A.S. D mel
 A microscopic twoband model for the electronhole asymmetry in high$T_c$ superconductors and reentering behavior
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Sep 16, 10

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Abstract. To our knowledge there is no rigorously analyzed microscopic model explaining the electronhole asymmetry of the
critical temperature seen in high$T_{c}$ cuprate superconductors  at least no model not breaking artificially this symmetry.
We present here a microscopic twoband model based on the structure of energetic levels of holes in
$\mathrm{CuO}_{2}$ conducting layers of cuprates. In particular,
our Hamiltonian does not contain \emph{ad hoc} terms implying  explicitly  different masses for electrons and holes.
We prove that two energe\tically nearlying interacting bands can explain
the electronhole asymmetry.
Indeed, we rigorously
analyze the phase diagram of the model and show that
the critical temperatures
for fermion densities below halffilling can manifest a very different behavior as compared to the case of densities above halffilling. This fact results from the interband interaction
and intraband Coulomb repulsion in interplay with thermal fluctuations between two energetic levels. So, if the energy difference between
bands is too big (as compared to the energy scale defined by the critical temperatures of
superconductivity) then the asymmetry disappears.
Moreover, the critical temperature turns out to be a nonmonotonic function
of the fermion density and the phase diagram of our model shows
``superconducting domes'' as in high$T_{c}$ cuprate
superconductors. This explains why
the maximal critical temperature is attained at donor densities away from the
maximal one. Outside the superconducting phase and for fermion densities
near halffilling the thermodynamics
governed by our Hamiltonian corresponds, as in real high$T_c$ materials,
to a Mottinsulating phase.
The nature of the interband interaction can be
electrostatic (screened Coulomb interaction), magnetic
(for instance some Heisenbergtype onesite spinspin interaction),
or a mixture of both.
If the interband interaction is predominately
magnetic then  additionally to the electronhole asymmetry  we observe a reentering behavior meaning that the superconducting phase can only occur in a finite interval
of temperatures. This phenomenon is rather rare, but has also been observed in the socalled magnetic superconductors.
The mathematical results here
are direct consequences of [J.B. Bru, W. de Siqueira Pedra, Rev.
Math. Phys. 22, 233303 (2010)] which is reviewed in the introduction.
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