Charge Density Waves and Electronic Nematicity in the Three Band Model of Cuprate Superconductors
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Cuprate superconductors exhibit very high critical temperatures, $T_c$, compared to those in the conventional superconductors. The doping at which $T_c$ is maximized is called optimal doping. Below this level, in the underdoped region, cuprate superconductors exhibit not only high $T_c$ superconductivity, but also the celebrated pseudogap phase, a theory of which is still not established. In the pseudogap region cuprates exhibit incommensurate charge orders and electronic nematicity, which are the focus of this thesis. Borrowed from the liquid crystal terminology, nematicity refers to the breaking of rotational symmetry in the electron degree of freedom where charge densities are re-arranged within the unit cell. The aim of this thesis is to establish the microscopic origin of charge orders in cuprates, and provide an explanation for some of the anomalous properties in the pseudogap region. Established by experiments, electronic nematicity originates from the inequivalency of the two oxygen orbitals in the cuprate unit-cell. Using this hint, the instability towards nematic charge orders was studied in the three-band model of cuprate superconductors, which explicitly takes into account the oxygen orbitals. Using the generalized random phase approximation, the nematic charge susceptibility was calculated, and it was found that the three-band model has nematic instabilities driven by the Coulomb repulsion between densities at oxygen orbitals. In the experimentally relevant doping range, the leading charge instability occurs as electronic nematicity with a modulation in space whose periodicity incommensurate with the underlying lattice. Such density modulations cause Fermi surface reconstructions, giving so-called Fermi arcs and small Fermi surface pockets. These findings, as well as the doping dependence of the modulation wavevector, are consistent with experiments. There is some disagreement with experiments as well: the modulation wavevector points along the diagonal of the Brillouin zone as opposed to the zone axes, and its magnitude is about half of that measured experimentally. Further improvement to the model is necessary to better match the experimental findings. A thorough understanding of electronic nematicity and its interplay with other phases is necessary to establish the theory of the pseudogap phase as well as that of the cuprate high-temperature superconductivity.