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Abstract:
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The two -dimensional electronic systems (2DESs ) have kept surprising physicists for the last few decades . Examples include the integer and fractional quantum Hall effects , cuprate superconductivity , and graphene . This thesis is intended to develop suitable theoretical tools which can be generalized to study new types of 2DESs with strong correlation feature . The first part of this thesis describes the investigation of heterostructures made by Mott insulators . This work is mostly motivated by the significant improvement of techniques for layer -by -layer growth of transition metal oxides in the last few years . We construct a toy model based on generalized Hubbard model complemented with long -ranged Coulomb interaction , and we study it by Hartree -Fock theory , dynamical mean -field theory , and Thomas -Fermi theory . We argue that interesting 2D strongly correlated electronic systems can be created in such heterostructures under several conditions . Since these 2D systems are formed entirely due to the gap generated by electron -electron interaction , they are not addiabatically connected to a noninteracting electron states . This feature makes these 2D systems distinguish from the ones created in semiconductor heterostructures , and they may be potential systems having non -Fermi liquid behaviors . The second part of this thesis is devoted to the study of collective excitations in high -temperature superconductors . One important achievement in this work is to develop a time -dependent mean -field theory for t -U -J -V model , an effective low energy model for cuprates . The time -dependent mean -field theory is proven to be identical to the generalized random -phase approximation (GRPA ) which includes both the bubble and ladder diagrams . We propose that the famous 41 meV magnetic resonance mode observed in the inelastic neutron scattering measurements is a collective mode arising from a conjugation relation , which has been overlooked in previous work , between the antiferromagnetic fluctuation and the phase fluctuation of the d -wave superconducting order parameter near momentum ([pi , pi] ) . Furthermore , we find that this collective mode signals the strength of the antiferromagnetic fluctuations which are responsible for the suppression of the superfluid density in the underdoped cuprates even at zero temperature . Finally , we perform a complete analysis on an effective model with parameters fitted by experimental data of Bi2212 within the GRPA scheme and conclude that the short -range antiferromagnetic interactions which are a remnant of the parent Mott -insulator are more likely the pairing mechanism of the High -T[subscript c] cuprates . |