Raman scattering and anomalous current algebra in Mott insulators

We present a theory of large shift Raman scattering in Mott insulators and show that inelastic light scattering provides information about electronic current algebra. We argue that the recent experiment where a new excitation below the optical absorption threshold was observed in crossed polarizations gives evidence of anomalous terms in the current alegebra. We show that it suggests there exists an exciton bound state with a topological magnetic excitation with odd parity with respect to a spatial reflection

Raman Scattering and Anomalous Current Algebra: Observation of Chiral Bound State in Mott Insulators

Recent experiments on inelastic light scattering in a number of insulating cuprates [1] revealed a new excitation appearing in the case of crossed polarizations just below the optical absorption threshold. This observation suggests that there exists a local exciton-like state with an odd parity with respect to a spatial reflection. We present the theory of high energy large shift Raman scattering in Mott insulators and interpret the experiment [1] as an evidence of a chiral bound state of a hole and a doubly occupied site with a topological magnetic excitation. A formation of these composites is a crucial feature of various topological mechanisms of superconductivity. We show that inelastic light scattering provides an instrument for direct measurements of a local chirality and anomalous terms in the electronic current algebra.Comment: 18 pages, TeX, C Version 3.

An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators

We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize the majority of phases in the periodic table of topological insulators.Comment: 24 pages, 6 figure

Optical and dc transport properties of a strongly correlated charge density wave system: exact solution in the ordered phase of the spinless Falicov-Kimball model with dynamical mean-field theory

We derive the dynamical mean-field theory equations for transport in an ordered charge-density-wave phase on a bipartite lattice. The formalism is applied to the spinless Falicov-Kimball model on a hypercubic lattice at half filling. We determine the many-body density of states, the dc charge and heat conductivities, and the optical conductivity. Vertex corrections continue to vanish within the ordered phase, but the density of states and the transport coefficients show anomalous behavior due to the rapid development of thermally activated subgap states. We also examine the optical sum rule and sum rules for the first three moments of the Green's functions within the ordered phase and see that the total optical spectral weight in the ordered phase either decreases or increases depending on the strength of the interactions.Comment: 14 pages, 14 figures, submitted to Phys. Rev.

Topological Phases of Matter: Classification, Realization and Application.

The recent discovery of topological insulators has led to a tremendous interest in the exploration of topological phases of matter which do not fit into Landau's symmetry breaking paradigm. Numerous exotic topological materials are theoretically predicted. Some of them have been experimentally reported, but many remain not. In this thesis, we explore topological phases of matter from three aspects: their classification, realization and application. We first review some basic classification theories, which provide us a "big picture" and lay the foundation for the rest of the thesis. We then move on to propose a systematic method based on quaternion algebra to construct toy tight-binding Hamiltonians for all the exotic phases in a recently developed periodic table for topological insulators and superconductors. We also introduce two peculiar families of topological phases that are beyond the table---the Hopf and four-dimensional topological insulators without time reversal symmetry. Prototypical Hamiltonians are constructed and their topological properties, such as robust edge states, are numerically studied. Motivated by rapid experimental progress in engineering spin-orbit coupling and artificial gauge field for cold atoms, we continue the thesis by proposing a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice. To unambiguously probe topological phases, we also bring forth systematic and generic methods to measure the characteristic topological invariants, for both free and strongly interacting systems. Moreover, we demonstrate that a kaleidoscope of knot and link structures is encoded in the spin texture of Hopf insulators and show how to observe different knots and links in cold atoms via time-of-flight images. The last part of the thesis is about the application of topological materials. After a demonstration of how to create, braid and detect Majorana fermions with cold atoms, we put forward a proposal to construct a self-test quantum random number generator by using Majorana fermions. Majorana random number generators are able to generate certifiable true random numbers with unconditional security. They offer a new perspective to the utilization of topological materials and may have vital applications in cryptography and related areas.PhDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111397/1/dldeng_1.pd

Edge magnetization and spin transport in an SU(2)-symmetric Kitaev spin liquid

FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOMEC - MINISTÉRIO DA EDUCAÇÃOMCTIC - MINISTÉRIO DA CIÊNCIA, TECNOLOGIA, INOVAÇÕES E COMUNICAÇÕESCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOWe investigate the edge magnetism and the spin transport properties of an SU(2)-symmetric Kitaev spin liquid (KSL) model put forward by Yao and Lee [Phys. Rev. Lett. 107, 087205 (2011)] on the honeycomb lattice. In this model, the spin degrees of freedom fractionalize into a Z(2) static gauge field and three species of either gapless (Dirac) or gapped (chiral) Majorana fermionic excitations. We find that, when a magnetic field is applied on a zigzag edge, the Dirac KSL exhibits a nonlocal magnetization associated with the existence of zero-energy edge modes. The application of a spin bias V = mu(up arrow) - mu(down arrow) y at the interface of the spin system with a normal metal produces a spin current into the KSL, which depends as a power law on V, in the zero-temperature limit, for both Dirac and chiral KSLs, but with different exponents. Lastly, we study the longitudinal spin Seebeck effect, in which a spin current is driven by the combined action of a magnetic field perpendicular to the plane of the honeycomb lattice and a thermal gradient at the interface of the KSL with a metal. Our results suggest that edge magnetization and spin transport can be used to probe the existence of charge-neutral edge states in quantum spin liquids.9815112FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOMEC - MINISTÉRIO DA EDUCAÇÃOMCTIC - MINISTÉRIO DA CIÊNCIA, TECNOLOGIA, INOVAÇÕES E COMUNICAÇÕESCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOMEC - MINISTÉRIO DA EDUCAÇÃOMCTIC - MINISTÉRIO DA CIÊNCIA, TECNOLOGIA, INOVAÇÕES E COMUNICAÇÕESCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO2016/05069-7sem informaçãosem informação405584/2016-

Multicomponent strongly correlated fermions in optical lattices

The present thesis is devoted to the study of physical phenomena emerging from strong correlations in strongly interacting quantum many-body systems with several components. Hubbard models are widely used as minimal models which take into account the interactions between particles and they have been studied in relation to phenomena such as Mott localization, unconventional superconductivity, quantum magnetism and many others. All of these striking phenomena share their origin from the strong correlations among fermions induced by their mutual interactions. Furthermore, condensed matter models are usually realized only in an approximate fashion in actual solid-state systems, making the situation all the more puzzling and hard to be treated analytically or numerically. Therefore, a great effort has been performed to simulate Hubbard models in a system of atoms cooled down to ultra low temperatures and trapped in optical lattices. The most peculiar feature of cold atoms experiments consists in the possibility of tuning relevant physical parameters of the systems, as the density or the interactions among atoms, using laser and/or magnetic fields. This paved the way to the observation of fundamental quantum states of matter as the weakly interacting Bose-Einstein condensate, the super fluid to Mott insulator transition, the super fluid BEC-BCS crossover, the Mott transition in systems of composite fermions and so on. Hence, it is considered of great interest establishing connections between the quantum simulations cold atomic toolbox and systems realized in solid-state physics..