In recent years, the discovery of topological insulators brought a topological classification of materials and opened a new field in condensed matter physics. Due to the nontrivial topological properties, the topological insulators have insulating bulk and metallic edge/surface relating to some exotic physics such as quantum anomalous Hall effect, quantum spin Hall effect, and magneto-electric effect. Followed realizations of the Z2 topological insulators in two and three dimensions, the quantum anomalous Hall effect was realized in the magnetic-doped topological insulators very recently, which attracts intensive interest. In this thesis, the magnetic topological insulators as a consequence of time-reversal symmetry breaking in the Z2 topological insulators in two or three dimensions are studied. As an introduction, a review of the topological insulators including some relevant theories is given. The approaches involved in this study are also presented. The results can be summarized in two parts. First, the quantum anomalous Hall effect can be found on the two-dimensional decorated lattice with spin-orbit coupling and electron-electron interaction. Without interaction, this model exhibits the quantum spin Hall effect and has at bands in the middle of the spectra. A at-band ferrimagnetism which breaks the time-reversal symmetry and a charge-density wave can be induced by the electron-electron interaction. Altogether they can modulate the Chern number of the system and give rise to the quantum anomalous Hall effect. In the second part, the realization of the quantum anomalous Hall effect in magnetic-doped topological insulator thin films is investigated. With an effective Hamiltonian of the surface states of a topological insulator thin _lm, the condition of the quantum anomalous Hall effect and the behavior of the longitudinal and Hall conductivity is given, which agrees with the experimental results. The effects of the structural inversion asymmetry potential and the particle-hole symmetry breaking term are studied. With a thin _lm model of the three-dimensional topological insulator, it is shown that the lateral surface states account for the non-quantized value of the Hall conductance and the nonzero longitudinal conductance. The quantized Hall conductance restores when the lateral surface state electrons are thoroughly localized by disorder. The quantum anomalous Hall phase in magnetic topological insulator thin film in the present of disorder is also studied. The disorder will shrink the regime of the quantum anomalous Hall effect in a thick film and becomes an obstacle to the realization of the quantum anomalous Hall effect. / published_or_final_version / Physics / Doctoral / Doctor of Philosophy

Thesis (Ph.D.)--Syracuse University, 2008. / "Publication number: AAT 3333585."

Thesis (Ph.D.)--Syracuse University, 2008. / "Publication number: AAT 3323084."

Thesis (Ph. D)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains xvi, 134 p. : ill. (some col.). Includes abstract and vita. Advisor: Arthur J. Epstein, Dept. of Physics. Includes bibliographical references (p. 128-134).

Thesis (PH.D.) -- Syracuse University, 2004. / "Publication number AAT 3160397."

This dissertation focuses on the transport properties of the high-temperature superconductor LSCO in high magnetic fields, particularly the longitudinal magnetoresistance around optimum doping. In this region of the phase diagram the longitudinal magnetoresistance appears to exhibit non-Fermi liquid magnetoresisitance. Additionally, high-field magnetotransport in LBCO is included, which revealed a layered, phase-decoupled superconducting state for x = 0.095. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2015. / April 2, 2015. / Cuprates, Superconductivity / Includes bibliographical references. / Gregory Boebinger, Professor Directing Dissertation; Theo Siegrist, University Representative; Todd Adams, Committee Member; Nick Bonesteel, Committee Member; Scott Riggs, Committee Member.

Organic conductors are interesting to study due to their low dimensionality that leads to a number of competing low temperature ground states. Comprised of a number of different molecules that can be varied by the substitution of one atom for another, organic systems also provide a large number of similar compounds that lend themselves to comparison studies. Two such low-dimensional organic conductors, Per2[Pt(mnt)2] and (TMTSF)2ClO4, which are members of large families of compounds, are the topic of this dissertation. Both materials are considered quasi-one-dimensional and have a number of low temperature transitions, some of which can be studied via changes in the magnetic properties of the systems. The Per2[M(mnt)2] family of compounds provides a system for exploring the similarities and differences of the system's properties when the metal M has a localized spin (M = Pt, Ni, and Fe) versus when the metal is diamagnetic (M = Au, Cu, and Co). In the case of Per2[Pt(mnt)2] - one of the compounds of focus in this dissertation - the metallic perylene chains undergo a metal- insulator transition due to the formation of a charge density wave at Tc ~ 8 K, which also occurs in Per2[Au(mnt)2] at 12 K. However, unlike in the M = Au compound, an additional transition occurs in the M = Pt compound due to the localized Pt spins (S = 1/2) on the insulating Pt(mnt)2 chains - the spin chains of Per2[Pt(mnt)2] undergo a spin-Peierls transition at 8 K. One focus of the experimental work of this dissertation focuses on the magnetic properties of the spin chains in Per2[Pt(mnt)2], via inductive susceptibility measurements at temperatures down to 0.5 K and fields up to 60 T. The experimental results show a coupling of the spin-Peierls and charge density wave states below 8 K and 20 T, above which both states are suppressed. Further measurements show a second spin state transition occurs above 20 T that coincides with a field induced insulating state in the perylene chains. These results support a strong coupling between the charge density wave and spin-Peierls state even at high magnetic fields, which are discussed in the context of other experimental results and theories. Additionally, a simple model is developed to explore the possible mechanisms behind the coupling of the two segregated chains. The other experimental part of this dissertation focuses on one member of the (TMTSF)2X family of compounds, where the anion molecule (X) can have an octahedral symmetry (X = PF6, SbF6, AsF6) or a tetrahedral symmetry (X = ClO4, ReO4, BF4). All of these compounds undergo metal-insulator transitions with the formation of a spin density wave, which can be suppressed and replaced by a transition to a superconducting state with the application of pressure in all but the X = ClO4 compound. In (TMTSF)2ClO4, which is the other compound of focus in this dissertation, both the spin density wave state and the superconducting state can be realized at ambient pressure; however, the determination of the state is dependent on the rate at which the material is cooled through an anion ordering temperature. If the sample is cooled too quickly it remains disordered and the sample enters the spin density wave state; on the other hand, if it cools slowly and the anions are allowed to order, superconductivity is realized at 1.2 K. This superconducting state has been experimentally studied with a wide variety of experimental techniques and much is known about its properties. However, nanoparticles of (TMTSF)2ClO4 have recently been realized, which opens up a new avenue of research on this compound, since the bulk properties of a material are often modified when its size approaches the length scale of the ground state order parameter. As such, the experimental work on (TMTSF)2ClO4 in this dissertation focuses on the critical temperature and fields of the superconducting state of the nanoparticles using the same inductive susceptibility technique mentioned above. The experiments on an assembly of (TMTSF)2ClO4 nanoparticles show that the nanoparticles exhibit bulk-like properties similar to those of randomly oriented crystals of the parent compound; possible explanations for this observation and future plans are discussed in this context. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2015. / February 25, 2015. / High Magnetic Fields, One-Dimensional Instabilities, Organic Conductors / Includes bibliographical references. / Stephen Hill, Professor Co-Directing Dissertation; David Graf, Professor Co-Directing Dissertation; Susan Latturner, University Representative; Pedro Schlottmann, Committee Member; Jorge Piekarewicz, Committee Member.

At low temperature (T) and weak magnetic field (B), two dimensional electron systems (2DES) can exhibit strong 1/B-periodic resistance oscillations on application of sufficiently strong microwave radiation. These oscillations are known as microwave induced resistance oscillations (MIROs), MIROs appearing near cyclotron resonance (CR) and its harmonics involve single photon processes and are called integer MIROs while the oscillations near CR subharmonics require multiphoton processes and are called fractional MIROs. Similar strong 1/B periodic resistance oscillations can occur due to strong dc current, and are known as Hall-field resistance oscillations (HIROs). Oscillations also occur for a combination of microwave radiation and strong dc current. In one prominent theory of MIROs, known as the displacement model , electrons make impurity-assisted transitions into higher or lower Landau levels by absorbing or emitting one or more (N) photons. In the presence of combined strong dc current and microwave radiation, electrons make transitions between Landau levels by absorbing or emitting photons followed by a space transition along the applied dc bias. The object of the dissertation is to explore how the different resistance oscillations are affected by strong microwave radiation when multiphoton processes are relevant. We used a coplanar waveguide (CPW) structure deposited on the sample, as opposed to simply placing the sample near the termination of a waveguide as is more the usual practice in this field. The CPW allows us to estimate the AC electric field (E_{AC}) at the sample. In much of the work presented in this thesis we find that higher $N$ processes supersede the competing lower N processes as microwave power is increased. We show this in the presence and in the absence of a strong dc electric field. Finally, we look at the temperature evolution of fractional MIROs to compare the origin of the fractional MIROs with that of integer MIROs. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester, 2014. / November 13, 2014. / Includes bibliographical references. / Lloyd Engel, Professor Co-Directing Dissertation; Irinel Chiorescu, Professor Co-Directing Dissertation; Naresh Dalal, University Representative; Jianming Cao, Committee Member; Nicholas Bonesteel, Committee Member; Alexander Volya, Committee Member.

Transition metal oxides and chalcogenides have been the major focus of studies in condensed matter physics. The complexity of the system, involving spin and orbital effects, as well as lattice degree of freedom, makes them intriguing subjects not only because of these individual effects, but also the effects due to the interaction among them. In AB2X4 materials (A = Mn2+, Co2+, Fe2+; B = V3+, Cr3+; X = O2-, S2-) which crystallize in spinel structure (space group F d -3 m), these effects and their interactions manifest in their transport properties, magnetic ordering, itinerant electron magnetism, structural distortion, and geometrical frustration effect due to the antiferromagnetically coupled B-sites. These effects are dependent on the distance between the interacting cations, which can be varied by chemical substitution or pressure. The main objective of this dissertation is to study the physical properties of Mott-insulator spinels in approaching their critical inter-cationic distances where an insulator-metal transition occurs. Studying the insulator-metal transition in Mott insulators is important in advancing our understanding, especially in the field of fundamental physics and materials engineering, on the intricate relationships between the transport and magnetic properties and the emergence of new behaviors that arise from such properties in these materials. In this dissertation, the behavior of the physical properties of Mn1-xCoxV2O4, AV2O4 (A = Cd, Mg, Zn), and the transport properties of FeCr2S4 in approaching the insulator-metal transition are reported. Mn1-xCoxV2O4, AV2O4, and FeCr2S4 are chosen for this study due to their dominant V-V or Cr-Cr interactions, which are responsible for their transport properties. In Mn1-xCoxV2O4, the vanadium-vanadium distance is varied by means of chemical pressure (chemical substitution) to bring the system closer to the itinerant electron limit given by the critical V-V distance of 2.94 Å. In Mn1-xCoxV2O4, the structural distortion temperature and transport activation energy decreases with decreasing V-V distance, while the magnetic ordering temperature increases. The results of the transport and structural studies are in agreement with the critical V-V distance scenario of electronic delocalization. Next, a comparative structural study on AV2O4 with non-magnetic A-site ions (A = Cd, Mg, Zn) and Mn1-xCoxV2O4 is also reported. The study indicates that while the V-V interactions are dominant, the A-site ions and their magnetism produce a considerable effect on the passage from the localized to delocalized electron limit. This is proven by the two paths that emerge in the V-V distance dependence of the transport and structural properties where one path includes only the AV2O4, whereas the other includes only Mn1-xCoxV2O4. The transport property of FeCr2S4 under high pressure was also studied. Due to the t2g electronic configuration of Cr3+, the Cr-Cr interaction is also dominant. A high pressure measurement using a cubic anvil press up to 8 GPa was performed to induce an insulator-metal transition. The decrease in the Cr-Cr distance with increasing hydrostatic pressure was confirmed by x-ray diffraction measurements. The Bloch parameter of FeCr2S4 was found to be -2.4, which suggests that FeCr2S4 lies in the localized regime. The high pressure transport measurement on FeCr2S4 shows a decrease in the activation energy and an increase in the magnetic transition temperature with increasing hydrostatic pressure. An insulator to metal transition was observed at a pressure of 7.5 GPa with a possible onset at 7 GPa, at which the Cr-Cr distance is 3.44 Å. In the case of Cr-oxides, it was predicted that the critical Cr-Cr distance is 2.84 Å, but it should be higher for a less electronegative anion. Therefore, the difference in the anion species is responsible for the difference of 0.6 Å between the critical Cr-Cr distance in oxides and the actual Cr-Cr distance where the insulator-metal transition occurs. The insulator-metal transition is followed by a structural transformation at P = 8 GPa. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester, 2014. / November 3, 2014. / Includes bibliographical references. / Haidong Zhou, Professor Co-Directing Dissertation; Vladimir Dobrosavljević, Professor Co-Directing Dissertation; Theo M. Siegrist, University Representative; Christianne Beekman, Committee Member; Volker Credé, Committee Member.

Despite over thirty years of research, the origin of high-temperature superconductivity remains unsolved. In these thirty years, the phase diagram for the rst-discovered high-temperature superconductors, the cuprates, has been found to be rather complex and exhibits many different phases such as antiferromagnetism, charge density waves, spin density waves, nematicity, the pseudogap, and of course, superconductivity. Furthermore, several structural instabilities can manifest that affect the stability of these phases. In the La-214 cuprates, for example, it is known the concomitant charge and spin orders (or stripe order) are stabilized by a low-temperature tetragonal structure. The stripe order coincides with a suppression of the superconducting critical temperature, leading the conclusion that these phases either compete or are intertwined. Since the stability of the low-temperature tetragonal structure, and therefore stripes, can be controlled by various dopants, the La-214 cuprates can be used to investigate how these orders intertwine. In this thesis, both striped and unstriped La-214 compounds have been investigated to understand the interplay of these various orders: superconductivity, stripes, and structure. In three distinct studies, using various charge transport techniques, the interplay between these orders is shown to lead to interesting and unexpected behavior. The first study reveals static charge order is in fact a fluctuating order pinned by the structure. The second study shows the two-dimensional nature of the superconductivity in the absence of stripe order, which is speculated to decouple CuO2 planes. Finally, the third study reveals the existence of a hidden order of Cooper pairs in the T=0 field-driven superconducting-normal-state transition when stripes are present. The culmination of these distinct studies lead to a better understanding of the physics of cuprates through the interplay of their various orders, and thus the general phase diagram of high-temperature superconductivity. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2018. / April 19, 2018. / Charge Transport, Cuprates, High-Temperature Superconductivity, Intertwined Orders / Includes bibliographical references. / Dragana Popovic, Professor Co-Directing Dissertation; Vladimir Dobrosavljevic, Professor Co-Directing Dissertation; Vincent Salters, University Representative; Jorge Piekarewicz, Committee Member; Irinel Chiorescu, Committee Member.