| dc.description.abstract | Quantum spin liquids, which are quantum ground states of interacting spin systems that break no symmetries, have long been a fascination among the theoretical condensed matter community. After years of experimental searches, several promising candidates finally emerged, including herbertsinithite ZnCu3 (OH)6 Cl2 , which can be modeled as a spin-1/2 kagome lattice. Theoretically, the U(1) Dirac spin liquid (U(1) DSL) state is shown to be a plausible description of the system, and previous works have indicate that this particular quantum spin liquid state may enjoy a host of interesting properties, such as the power-law decay of correlation functions, the existence of spin-1/2 excitations known as the spinon, and the existence of an emergent U(1) gauge field. In this thesis, after the relevant motivation and background information are discussed, I shall present my work on the spin-1/2 kagome lattice that built upon the U(1) DSL state. First, I shall present the theoretical study of Raman scattering in the U(1) DSL state, which shows that in all symmetry channels the Raman intensity profiles contain broad continua that display power-law behaviors at low energy, which can be attributed to the excitations of spinon-antispinon pairs. In, addition, for the A2g channel, the Raman profile also contains a characteristic 1/o singularity, which arise from an excitation of the emergent U(1) gauge field. The possibility of more clearly observing the signature of this U(1) emergent gauge field in resonant inelastic X-ray scattering (RIXS) is also discussed. Next, I shall consider the case when the spin-1/2 kagome lattice is subjected to an external magnetic field, in which a state with an additional uniform amount of gauge flux of top of the U(1) DSL ansatz, which results in the formation of Landau levels in the spinon spectrum, is shown to be energetically favorable. Unlike the usual quantum Hall system, the Landau level state is shown to contain a gapless S2 density mode, which in turns indicate that system is XY ordered in the plane perpendicular to the applied magnetic field. Third, I shall consider the case in which the spin-1/2 kagome lattice is hole-doped. Similar to the B-field case, a Landau-level state is shown to be energetically favorable, in which a gapless charge density mode is shown to exists, and which through the Anderson-Higgs mechanism causes the system to become a superconductor. This resulting superconductor is then shown to be exotic, in the sense that it contains minimal vortices having a flux of hc/4e, as well as bosonic quasiparticles that have semionic mutual statistics. The thesis concludes with a short summary and outlook. | en_US |
