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Materials that contain f-electron elements often exhibit complex phase diagrams with different phenomena including nematic electronic states, charge and spin instabilities, the breakdown of Fermi liquid behavior, and unconventional superconductivity. This diversity of behavior is related to the fine balance between several factors including the magnetic exchange, Kondo effect, crystal electric field splitting and strong spin-orbit coupling. As a result, many such systems exhibit intertwined order parameters that are controllable through pressure, magnetic field, and chemical substitution. Here, we report results from chemical substitution studies in three distinct Kondo lattice systems. In each case, we are able to suppress an ordered state towards zero temperature at a possible quantum phase transition and study the resulting behavior. For CeCu$_2$Si$_2$, Si $\rightarrow$ P chemical substitution compresses the unit cell volume while adding $s/p$ electrons. This encourages complex magnetism and drives the system away from a quantum critical point. These results are understood by considering that the electronic hybridization between the f- and conduction electrons in this system is controlled by nearly independent parameters of unit cell volume and s; p; d shell filling, which drive the system's behavior along different axes. For CePd$_2$P$_2$, Pd $\rightarrow$ Ni substitution suppresses the ferromagnetism towards a disordered ferromagnetic QCP at $x_{\rm{cr}}$ = 0.7, where the breakdown of Fermi liquid behavior is observed. We also find that for CePd$_2$P$_2$, a pressure of $P_{\rm{c}}$ = 12 GPa would likely be sufficient to access a quantum phase transition. These results provide a useful experimental testbed for the Belitz-Kirkpatrick-Vojta (BKV) theory. For UCr$_2$Si$_2$, Cr $\rightarrow$ Ru substitution results in filling of the $d$-shell without significantly changing the unit cell volume. This suppresses the antiferromagnetic order $T_{\rm{N}}$ ($T_{\rm{N}}$ $\approx$ 24 K for UCr$_2$Si$_2$) and the structural phase transition $T_{\rm{S}}$ ($T_{\rm{S}}$ $\approx$ 200 K for UCr$_2$Si$_2$) that are seen in the parent compound. $T_{\rm{N}}$ approaches zero temperature near $x_{\rm{c, N}}$ = 0.08 while $T_{\rm{S}}$ reaches a minimum value near $x_{\rm{c, S}}$ = 0.16, after which the structural phase transition disappears for larger $x$. Near this concentration there is evidence for the breakdown of Fermi liquid behavior in the transport and heat capacity measurements, suggesting that this may be a model system for studying a lattice instability at zero temperature, its relationship to a nearby antiferromagnetic quantum critical point, and the resulting impact on electronic properties and lattice modes in a strongly correlated electron metal. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2019. / March 28, 2019. / Chemical Substitution, Quantum Criticality, Strongly Correlated Materials / Includes bibliographical references. / Ryan E. Baumbach, Professor Co-Directing Dissertation; Peng Xiong, Professor Co-Directing Dissertation; Mykhailo Shatruk, University Representative; David Graf, Committee Member; Pedro Schlottmann, Committee Member; Mark Riley, Committee Member.

Topological phases of matter and the phase transitions between them have been the focus of much recent theoretical and experimental interest. In this thesis, we firstly study a type of topological phase transitions between quantum Hall states driven by pairing interactions through Feshbach resonances. Although quantum Hall effects were first discovered in electronic condensed matter systems, this type of phase transitions was proposed to ultra cold atom field for their ability of the control of interactions. In addition, we also investigate the quench dynamics of topological phase transitions based on specifically Haldane model and checkerboard model in the second part. In the study of topological phase transitions between fermionic integer quantum Hall (FIQH) and bosonic fractional quantum Hall (BFQH) phases, we first provide a general picture of this kind of quantum Hall phase transitions. Subsequently, we use exact diagonalization to study the quantum phases and phase transitions when a single species of fermionic atoms at Landau level filling factor vf = 1 in a rotating trap interact through a p-wave Feshbach resonance. We show that under weak pairing interaction, the system undergoes a second order quantum phase transition from vf = 1 fermionic integer quantum Hall (FIQH) state at positive detuning, to vb = ¼ bosonic fractional quantum Hall (BFQH) state at negative detuning. However, when the pairing interaction increases, a new phase between them emerges, corresponding to a fraction of fermionic atoms stay in a coherent superposition of bosonic molecule state and an unbound pair. The phase transition from FIQH phase to the new phase is of second order and that from the new phase to BFQH phase is of first order. Furthermore, we investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via s-wave Feshbach resonance, and are subject to rotation or a synthetic gauge field that puts the fermions at Landau level filling factor vf = 2. We show that the system undergoes a continuous quantum phase transition from a vf = 2 fermionic integer quantum Hall state formed by atoms, to a vf = ½ bosonic fractional quantum Hall state formed by bosonic diatomic molecules. In the disk geometry we use, these two different topological phases are distinguished by their different gapless edge excitation spectra, and the quantum phase transition between them is signaled by the closing of the energy gap in the bulk. Comparisons will be made with field theoretical predictions, and the case of p-wave pairing. In the second part of this thesis, we study the dynamics of systems quenched through topological quantum phase transitions and investigate the behavior of the bulk and edge excitations with various quench rates. Specifically, we consider the Haldane model and checkerboard model in slow quench processes with distinct band-touching structures leading to topology changes. The generation of bulk excitations is found to obey the power-law relation Kibble-Zurek and Landau-Zener theories predict. However, an anti-Kibble-Zurek behavior is observed in the edge excitations. The mechanism of excitation generation on edge states is revealed, which explains the anti-Kibble-Zurek behavior. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2019. / April 12, 2019. / edge excitation, Feshbach resonance, Kibble-Zurek theory, quantum Hall phase transition, quench dynamics, topological phase transition / Includes bibliographical references. / Kun Yang, Professor Directing Dissertation; Theo Siegrist, University Representative; Nicholas E. Bonesteel, Committee Member; Luis Balicas, Committee Member; Lloyd W. Engel, Committee Member; Peng Xiong, Committee Member.

Source: Dissertation Abstracts International, Volume: 40-02, Section: B, page: 0808. / Thesis (Ph.D.)--The Florida State University, 1978.

Source: Dissertation Abstracts International, Volume: 36-08, Section: B, page: 4049. / Thesis (Ph.D.)--The Florida State University, 1975.

Source: Dissertation Abstracts International, Volume: 36-08, Section: B, page: 4051. / Thesis (Ph.D.)--The Florida State University, 1975.

Source: Dissertation Abstracts International, Volume: 37-10, Section: B, page: 5192. / Thesis (Ph.D.)--The Florida State University, 1976.

Source: Dissertation Abstracts International, Volume: 34-07, Section: B, page: 3437. / Thesis (Ph.D.)--The Florida State University, 1973.