Majorana Fermions, Exact Mappings between Classical and Topological Orders

Motivated by the duality between site-centered spin and bond-centered spin in one-dimensional system, which connects two different constructions of fermions from the same set of Majorana fermions, we show that two-dimensional models with topological orders can be constructed from certain well-known models with classical orders characterized by symmetry-breaking. Topology-dependent ground state degeneracy, vanishing two-point correlation functions, and unpaired Majorana fermions on boundaries emerge naturally from such construction. The approach opens a new way to construct and characterize topological orders.Comment: 5 pages, 4 figure

d-Wave Checkerboard Order in Cuprates

We show that the d-wave ordering in particle-hole channels, dubbed d-wave checkerboard order, possesses important physics that can sufficiently explain the scanning tunneling microscopy (STM) results in cuprates. A weak d-wave checkerboard order can effectively suppress the coherence peak in the single-particle spectrum while leaving the spectrum along the nodal direction almost unaffected. Simultaneously, it generates a Fermi arc with little dispersion around the nodal points at finite temperature that is consistent with the results of angle-resolved photoemission spectroscopy (ARPES) experiments in the pseudogap phase. We also show that there is a general complementary connection between the d-wave checkerboard order and the pair-density-wave order. Suppressing superconductivity locally or globally through phase fluctuations should induce both orders in underdoped cuprates and explain the nodal-antinodal dichotomy observed in ARPES and STM experiments

Nature of the Quantum Phase Transition in Quantum Compass Model

In this work, we show that the quantum compass model on an square lattice can be mapped to a fermionic model with local density interaction. We introduce a mean-field approximation where the most important fluctuations, those perpendicular to the ordering direction, are taken into account exactly. It is found that the quantum phase transition point at $J_x=J_z$ marks a first order phase transition. We also show that the mean field result is robust against the remaining fluctuation corrections up to the second order.Comment: 7 pages, 10 fig

Complementary Pair Density Wave and d-wave Checkerboard Order in High Temperature Superconductors

The competing orders in the particle-particle (P-P) channel and the particle-hole (P-H) channel have been proposed separately to explain the pseudogap physics in cuprates. By solving the Bogoliubov-deGennes equation self-consistently, we show that there is a general complementary connection between the d-wave checkerboard order (DWCB) in the particle-hole (P-H) channel and the pair density wave order (PDW) in the particle-particle (P-P) channel. A small pair density localization generates DWCB and PDW orders simultaneously. The result suggests that suppressing superconductivity locally or globally through phase fluctuation should induce both orders in underdoped cuprates. The presence of both DWCB and PDW orders with $4a \times 4a$ periodicity can explain the checkerboard modulation observed in FT-STS from STM and the puzzling dichotomy between the nodal and antinodal regions as well as the characteristic features such as non-dispersive Fermi arc in the pseudogap state

Quasiparticle scattering in two dimensional helical liquid

We study the quasiparticle interference (QPI) patterns caused by scattering off nonmagnetic, magnetic point impurities, and edge impurities, separately, in a two dimensional helical liquid, which describes the surface states of a topological insulator. The unique features associated with hexagonal warping effects are identified in the QPI patterns of charge density with nonmagnetic impurities and spin density with magnetic impurities. The symmetry properties of the QPI patterns can be used to determine the symmetry of microscopic models. The Friedel oscillation is calculated for edge impurities and the decay of the oscillation is not universal, strongly depending on Fermi energy. Some discrepancies between our theoretical results and current experimental observations are discussed.Comment: 12 pages, appendices added. Accepted for publication in Physical Review B (submitted, October 2009

Magnetic Frustration and Iron-Vacancy Ordering in Iron-Chalcogenide

We show that the magnetic and vacancy orders in the 122 $(A_{1-y}Fe_{2-x}Se_2)$ iron-chalcogenides can be naturally derived from the $J_1-J_2-J_3$ model with $J_1$ being the ferromagnetic (FM) nearest neighbor exchange coupling and $J_{2}, J_3$ being the antiferromagnetic (AFM) next and third nearest neighbor ones respectively, previously proposed to describe the magnetism in the 11(FeTe/Se) systems. In the 11 systems, the magnetic exchange couplings are extremely frustrated in the ordered bi-collinear antiferromagnetic state so that the magnetic transition temperature is low. In the 122 systems, the formation of iron vacancy order reduces the magnetic frustration and significantly increases the magnetic transition temperature and the ordered magnetic moment. The pattern of the 245 iron-vacancy order ($\sqrt{5}\times \sqrt{5}$) observed in experiments is correlated to the maximum reduction of magnetic frustration. The nature of the iron-vacancy ordering may hence be electronically driven. We explore other possible vacancy patterns and magnetic orders associated with them. We also calculate the spin wave excitations and their novel features to test our model.Comment: Figures are modified and more discussion is adde

A framework for test topic generation

This study proposes a test topic generation framework through an analysis of existing literature. The framework contains three components, including a list of questions for eliciting users’ information needs, a mechanism for topic generators to interact with the document collection, and a list of criteria to assess the quality of generated test topics. An application of this framework for generating test topics for a collection of library metadata records is presented

d+idd+id chiral superconductivity in a triangular lattice from trigonal bipyramidal complexes

We model the newly predicted high-$T_c$ superconducting candidates constructed by corner-shared trigonal bipyramidal complexes with an effective three-orbital tight-banding Hamiltonian and investigate the pairing symmetry of their superconducting states driven by electron-electron interactions. Our combined weak and strong coupling based calculations consistently identify the chiral $d+id$ superconductivity as the leading pairing symmetry in a wide doping range with realistic interaction parameters. This pairing state has nontrivial topological Chern-number and can host gapless chiral edge modes, and the vortex cores under magnetic field can carry Majorana zero modes.Comment: 8 pages, 9 figure