Magnetism and Mott Transition: A Slave-rotor Study

Motivated by the debate of spin-density-wave (SDW) versus local-moment (LM) picture in the iron-based superconducting (FeSC) materials, we consider a two-band orbital-symmetric Hubbard model in which there is robust Fermi surface nesting at $(\pi,0)$. We obtain the phase diagram of such system by a mean-field slave-rotor approach, in which the Fermi surface nesting and the SDW order are explicitly taken into account via a natural separation of scale between the Hund's coupling and the Coulomb interaction. We find that for a sizable range of Hund's coupling the Mott transition acquires a strong first-order character, but there also exists a small range of stronger Hund's coupling in which an enhancement of magnetization can be observed on the SDW side. We interpret the former scenario as one in which a sharp distinction can be drawn between LM and the SDW picture, and the latter scenario as one in which signs of LM physics begin to develop in the metallic phase. It is tempting to suggest that some FeSC materials are in the vicinity of the latter scenario.Comment: 7 pages, 5 figures; v2: Added discussions on anisotropy in renormalized hopping, clarifications and discussions with regard to orbital order, new inset in Fig. 3(d), expanded and revised bibliography, plus other minor revisions. Accepted to PR

Proposal for detecting spin-chirality terms in Mott insulators via resonant inelastic x-ray scattering

We consider the question of whether resonant inelastic x-ray scattering (RIXS) can be used to detect many-body excitations that are coupled to the spin-chirality terms S_i . (S_j x S_k) in a Mott insulator. We find that while the spin-chirality terms are in general absent in the usual experimental setups of RIXS, there are prospects of realizing such terms if one considers instead the scattering near a pre-edge. We then perform detailed analyses for the square and the kagome lattices, and brief analyses for the triangular and the honeycomb lattices, in which we show that the spin-chirality terms are indeed present in all the above lattices, but that they occur at a higher order in our expansion for the kagome and the honeycomb lattices. The merit of using RIXS in addition to Raman spectroscopy to detect excitations that are coupled to the spin-chirality terms is also briefly discussed in the context of the emergent gauge boson in the U(1) Dirac spin liquid.Comment: 9 pages, 9 figures; v2: minor revisions, concurrent with the published versio

Novel magnetic and superconducting states in spin-1/2 kagome lattice and its doped variant

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 121-128).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.by Wing-Ho Ko.Ph.D

Raman signature of the U(1) Dirac spin-liquid state in spin-1/2 kagome system

We followed the Shastry--Shraiman formulation of Raman scattering in Hubbard systems and considered the Raman intensity profile in the spin-1/2 "perfect" kagome lattice herbertsmithite ZnCu_3(OH)_6Cl_2, assuming the ground state is well-described by the U(1) Dirac spin-liquid state. In the derivation of the Raman T-matrix, we found that the spin chirality term appears in the A_{2g} channel in the kagome lattice at the t^4/(\omega_i-U)^3 order, but (contrary to the claims by Shastry and Shraiman) vanishes in the square lattice to that order. In the ensuing calculations on the spin-1/2 kagome lattice, we found that the Raman intensity profile in the E_g channel is invariant under an arbitrary rotation in the kagome plane, and that in all (A_{1g}, E_g, and A_{2g}) symmetry channels the Raman intensity profile contains broad continua that display power-law behaviors at low energy, with exponent approximately equal to 1 in the A_{2g} channel and exponent approximately equal to 3 in the E_g and the A_{1g} channels. For the A_{2g} channel, the Raman profile also contains a characteristic 1/\omega singularity, which arose in our model from an excitation of the emergent U(1) gauge field.Comment: 17 pages, 19 figures; Minor revisions, updated to be consistent with the published versio

Spontaneous spin ordering of Dirac spin liquid in a magnetic field

The Dirac spin liquid was proposed to be the ground state of the spin-1/2 Kagome antiferromagnets. In a magnetic field $B$, we show that the state with Fermi pocket is unstable to the Landau level (LL) state. The LL state breaks the spin rotation around the axis of the magnetic field. We find that the LL state has an in-plane 120$^{\circ}$ $q=0$ magnetization $M$ which scales with the external field $M\sim B^{\alpha}$, where $\alpha$ is an intrinsic calculable universal number of the Dirac spin liquid. We discuss the related experimental implications which can be used to detect the possible Dirac spin liquid phase in Herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$.Comment: rewritten for clarit

Addressing quality, access and equity in the school direct subsidy scheme in Hong Kong : a study of government strategies and tools

published_or_final_versionPolitics and Public AdministrationMasterMaster of Public Administratio

Doped Kagome System as Exotic Superconductor

A Chern--Simons theory for the doped spin-1/2 kagom\'e system is constructed, from which it is shown that the system is an exotic superconductor that breaks time-reversal symmetry. It is also shown that the system carries minimal vortices of flux $hc/4e$ (as opposed to the usual $hc/2e$ in conventional superconductors) and contains fractional quasiparticles (including fermionic quasiparticles with \emph{semionic} mutual statistics and spin-1/2 quasiparticles with \emph{bosonic} self-statistics) in addition to the usual spin-1/2 fermionic Bougoliubov quasiparticle. Two Chern--Simons theories--one with an auxiliary gauge field kept and one with the auxiliary field and a redundant matter field directly eliminated--are presented and shown to be consistent with each other.Comment: 13 pages, 7 figures and 1 table; Extensive revision and expansion, including a new section on classifying the quasiparticles and a new section on an alternative Chern--Simons Lagrangia

Associations between child maltreatment and adolescents’ health-related quality of life and emotional and social problems in low-income families, and the moderating role of social support

This study aimed to examine the associations between different types of child maltreatment and health-related quality of life (HRQoL) and emotional and social problems in adolescents, and to examine the moderating effect of social support on those associations. A cross-sectional survey was conducted between January and June 2016 in Hong Kong. The sample comprised 351 parent and adolescent dyads from low-income families. The parents reported on child maltreatment (physical abuse, psychological aggression, and neglect), and the adolescents reported on their HRQoL, emotional problems, and social problems. The adolescents’ perceived social support was included as a potential moderator. Results of the study show that child physical abuse was strongly associated with emotional and social problems (B = 0.91-1.45, p < .05). Lower overall HRQoL was associated with psychological aggression (B = −3.96, p < .05) and neglect (B = −4.14, p < .05). Physical functioning was affected by psychological aggression (B = −3.16, p < .05), and emotional functioning was affected by neglect (B = −4.82, p < .05). Social functioning was impacted by all three types of maltreatment (B = −9.16 to −5.26, p < .05). This study extends previous literature by showing the varying effects of different types of child maltreatment on children’s health in the context of low-income families. The findings of this study also support that peer social support may buffer the effects of child physical abuse on adolescents’ emotional and social problems