Aspectos de modelos eletrônicos bidimensionais fortemente correlacionados: aplicações em cupratos supercondutores
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2016-06-06
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Universidade Federal de Goiás
Resumo
We investigate here the low-energy properties of two strongly correlated electronic models in two
spatial dimensions. The first one consists in a version of the Hubbard model in which are
considered just the degrees of freedom of the system in the neighborhood of the so-called hot
spots, which are defined as the intersection of the Fermi surface of the model with the
antiferromagnetic zone. Initially, we set our theory up by linearizing the dispersion model in hot
spots and consider all the interacting processes between these regions that conserve momentum
within a reciprocal-lattice wave vector. In order to access the physics of the model, we then turn to
the renormalization group method of quantum field theory and derive the flow equations for the
couplings in the two-loop approximation. As a result, we obtain that the Fermi surface is strongly
renormalized in hot spots as the renormalized couplings flow to a non-trivial fixed point in the
low-energy limit. Then we suggest that this system can be viewed as an example of a non-Fermi
liquid in two spatial dimensions, due to the lack of well defined quasiparticle fermionic excitations
in the region close to hot spots. Moreover, we solve the Callan-Symanzik equation for the oneparticle
Green function up to two-loop order, calculate the density of states in the hot spots, and
derive the renormalization group equations for the order parameters of the potential instabilities
which may eventually occur in the system at lower energies. We verify that the system can be
characterized, in this regime, in terms of an emergent pseudospin symmetry [SU(2)]4, which leads
to the appearance of entangled orders in the region close to the non-trivial fixed point of the model.
We also show that the fermionic excitations in the adjacent regions to the hot spots get a gap in
both charge a spin excitation spectra. Because of this, we argue that the Fermi surface of the model
can be reconstructed, leading therefore to the formation of either Fermi arcs or electronic pockets.
The second model analyzed in this thesis was the three-band Emery model, which describes all the
interacting processes between fermionic excitations localized in both copper (Cu) and oxygen (O)
orbitals in the CuO2 unit cell. By making use of a Hubbard-Stratonovich transformation, we
introduce two order parameters in the system: one for the so-called ΘII-loop-current order, which
violates Z2 time-reversal symmetry, and another one for the entangled phase with dx
2
-y
2 symmetry
involving the singlet superconducting instability and the quadrupole density wave order, whose
wave vector points in the direction of the Brillouin zone diagonal. Minimizing the free energy of
the model, we derive the self-consistent mean-field equations for these order parameters. The
solution of these equations for the zero temperature regime shows that the two phases compete
with themselves for the same region of the phase space and, consequently, the system tends not to
display coexistence between them. We argue that this effect could be the main reason for the fact
that the quadrupole density wave order has never been observed in experiments performed on the
cuprate superconductors. Next, we analyze the competition between the ΘII-loop-current order,
which is experimentally observed, and charge order with dx
2
-y
2 symmetry and wave vectors in the
direction of the main axes of the Brillouin zone. As a result, we obtain that the system only exhibits
coexistence between the ΘII-loop-current phase and the bidirectional charge order. Due to the
existence of a pseudospin symmetry in this model, we also confirm that the ΘII-loop-current phase
coexists with the bidirectional pair density wave order. Finally, we discuss the implications of these
results for the pseudogap phase of the cuprate superconductors, which appears in the underdoped
regime in these systems.
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CARVALHO, V. S. Aspectos de modelos eletrônicos bidimensionais fortemente correlacionados: aplicações em cupratos supercondutores. 2016. 132 f. Tese (Doutorado em Física) - Universidade Federal de Goiás, Goiânia, 2016.