Numerical and experimental studies of high-temperature superconducting systems

McNiven, Brad (2024) Numerical and experimental studies of high-temperature superconducting systems. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

The objective of this thesis is to study the correlated behaviour of electron and lattice dynamics in the high-temperature cuprate superconductors. In particular, we are interested in the lattice (i.e., structural and phonon) and electronic dynamics in these systems and how they may influence the driving mechanisms of high-Tc superconductivity. We do this through two methods: numerical calculations on the two-dimensional Hubbard model and inelastic light scattering experiments. For the numerical component of this work, we compute the static and dynamical longitudinal charge and spin susceptibilities as functions of real frequency on a twodimensional square lattice with weak-coupling for the t − t' − U Hubbard model via a perturbative, diagrammatic approach. In the static case, the spin susceptibility is dominated by q = (π, π) spin fluctuations that are largest near half-filling, while the charge susceptibility has a clear multi-peak structure with a minimum located at the van Hove singularity of the non-interacting dispersion, a feature not observed in the commonly employed random-phase approximation. For dynamical charge and spin susceptibilities, we plot the dispersion for each respective collective electronic excitation on the real frequency axis. These excitations were found to split into separate modes surrounding the van Hove singularity, only to merge again in the longwavelength limit. From an experimental standpoint, these results will prove useful for those studying electronic excitations as our calculations indicate that electron doped cuprates should be probed at higher energies in order to detect spin and charge excitations in comparison to the hole doped cuprates. For the experimental aspect of this work, we study the single-crystal Bi₂Sr₂CaCu₂O₈₊δ (Bi-2212) cuprate by Brillouin light scattering spectroscopy at room-temperature. We study the acoustic phonon behaviour in the normal state and gain further information on the structural dynamics which currently remain unresolved. From spectra ii collected with an excitation source of 532 nm, we identify the Rayleigh surface mode, a longitudinal resonance mode, and six bulk acoustic modes (four quasi-transverse and two quasi-longitudinal), contrary to the typically expected three. From bulk spectral peaks, the extracted frequency shift and linewidth were used to determine the optical extinction coefficient-to-refractive index ratios. These ratios were subsequently used to obtain the extinction coefficient, penetration depth, optical absorption coefficient, and complex dielectric function, and were found to be 5 − 7 times larger than those obtained from optical interference measurements. The number of bulk modes observed in the Brillouin data suggests Bi-2212 is an incommensurate composite crystal consisting of two weakly interacting sublattices. Further analysis of the Brillouin data allows us to assign the two independent sublattices as Bi₂Sr₂O₄ and CaCu₂O₄, calculate the hypersound velocity of the observed surface and bulk acoustic phonon modes, and derive an expression relating the bulk crystals longitudinal acoustic phonon velocity to the bulk longitudinal acoustic phonon velocities corresponding to the two sublattices. Finally, we determined the elastic constants C₁₁, C₂₂, C₃₃, C₄₄, C₅₅, C₁₂, and C₂₃ and related sublattice elastic constants. Overall, the utility of the experimental work presented in this thesis is multi-fold. Firstly, it has refined the acoustic phonon velocities, and subsequently the elastic constants, of Bi-2212 which have received little attention. Secondly, our derived expression relating the bulk and sublattice longitudinal velocities will aid in expanding upon the model of incommensurate composite crystals and the study incommensurate crystallography in general. Lastly, and most importantly, our experimental verification that Bi-2212 is comprised of two interacting sublattices alludes to a highly non-trivial optic phonon structure and the existence of low-lying optic phonon modes. Identification of such modes may play an important role in understanding the driving mechanisms surrounding high-Tc superconductivity.

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