Symmetry Breaking on the Three-Dimensional Hyperkagome Lattice of Na_4Ir_3O_8

We study the antiferromagnetic spin-1/2 Heisenberg model on the highly frustrated, three-dimensional, hyperkagome lattice of Na_4Ir_3O_8 using a series expansion method. We propose a valence bond crystal with a 72 site unit cell as a ground state that supports many, very low lying, singlet excitations. Low energy spinons and triplons are confined to emergent lower-dimensional motifs. Here, and for analogous kagome and pyrochlore states, we suggest finite temperature signatures, including an Ising transition, in the magnetic specific heat due to a multistep breaking of discrete symmetries.Comment: 4 pages, 3 figure

Hierarchy wave functions--from conformal correlators to Tao-Thouless states

Laughlin's wave functions, describing the fractional quantum Hall effect at filling factors $\nu=1/(2k+1)$, can be obtained as correlation functions in conformal field theory, and recently this construction was extended to Jain's composite fermion wave functions at filling factors $\nu=n/(2kn+1)$. Here we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multi-hole states, make the connection to Wen's general classification of abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally we discuss to what extent our wave functions can be described in the language of composite fermions.Comment: 9 page

Topology and Interactions in a Frustrated Slab: Tuning from Weyl Semimetals to C > 1 Fractional Chern Insulators

We show that, quite generically, a [111] slab of spin-orbit coupled pyrochlore lattice exhibits surface states whose constant energy curves take the shape of Fermi arcs, localized to different surfaces depending on their quasimomentum. Remarkably, these persist independently of the existence of Weyl points in the bulk. Considering interacting electrons in slabs of finite thickness, we find a plethora of known fractional Chern insulating phases, to which we add the discovery of a new higher Chern number state which is likely a generalization of the Moore-Read fermionic fractional quantum Hall state. By contrast, in the three-dimensional limit, we argue for the absence of gapped states of the flat surface band due to a topologically protected coupling of the surface to gapless states in the bulk. We comment on generalizations as well as experimental perspectives in thin slabs of pyrochlore iridates.Comment: Published. 6+4 page

Hierarchy of fractional Chern insulators and competing compressible states

We study the phase diagram of interacting electrons in a dispersionless Chern band as a function of their filling. We find hierarchy multiplets of incompressible states at fillings \nu=1/3, 2/5, 3/7, 4/9, 5/9, 4/7, 3/5 as well as \nu=1/5,2/7. These are accounted for by an analogy to Haldane pseudopotentials extracted from an analysis of the two-particle problem. Important distinctions to standard fractional quantum Hall physics are striking: absent particle-hole symmetry in a single band, an interaction-induced single-hole dispersion appears, which perturbs and eventually destabilizes incompressible states as \nu increases. For this reason the nature of the state at \nu=2/3 is hard to pin down, while \nu=5/7,4/5 do not seem to be incompressible in our system.Comment: 5 pages with 4 figures, plus 6 pages and 8 figures of supplementary materia

One-Dimensional Theory of the Quantum Hall System

We consider the lowest Landau level on a torus as a function of its circumference $L_1$. When $L_1\to 0$, the ground state at general rational filling fraction is a crystal with a gap--a Tao-Thouless state. For filling fractions $\nu=p/(2pm+1)$, these states are the limits of Laughlin's or Jain's wave functions describing the gapped quantum Hall states when $L_1\to \infty$. For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral dipoles, or rather to a Luttinger liquid modification thereof, at $L_1\sim5$ magnetic lengths. This state is a version of the Rezayi-Read state, and develops continuously into the state that is believed to describe the observed metallic phase as $L_1\to \infty$. Furthermore, the effective Landau level structure that emerges within the lowest Landau level follows from the magnetic symmetries.Comment: 4 pages, 1 figur

Tuning from Weyl Semimetals to C>1 Fractional Chern Insulators

We show that, quite generically, a [111] slab of spin-orbit coupled pyrochlore lattice exhibits surface states whose constant energy curves take the shape of Fermi arcs, localized to different surfaces depending on their quasimomentum. Remarkably, these persist independently of the existence of Weyl points in the bulk. Considering interacting electrons in slabs of finite thickness, we find a plethora of known fractional Chern insulating phases, to which we add the discovery of a new higher Chern number state which is likely a generalization of the Moore-Read fermionic fractional quantum Hall state. By contrast, in the three-dimensional limit, we argue for the absence of gapped states of the flat surface band due to a topologically protected coupling of the surface to gapless states in the bulk. We comment on generalizations as well as experimental perspectives in thin slabs of pyrochlore iridates

Topological Monomodes in non-Hermitian Systems

Topological monomodes have been for long as elusive as magnetic monopoles. The latter was experimentally shown to emerge in effective descriptions of condensed-matter systems, while the experimental exploration of the former has largely been hindered by the complexity of the conceived setups. Here, we present a remarkably simple model and the experimental observation of topological monomodes generated dynamically. By focusing on non-Hermitian one-dimensional (1D) and 2D Su-Schrieffer-Heeger (SSH) models, we theoretically unveil the minimal configuration to realize a topological monomode upon engineering losses and breaking of lattice symmetries. Furthermore, we classify the systems in terms of the (non-Hermitian) symmetries that are present and calculate the corresponding topological invariants. To corroborate the theory, we present experiments in photonic lattices, in which a monomode is observed in the non-Hermitian 1D and 2D SSH models, thus breaking the paradigm that topological corner states should appear in pairs. Our findings might have profound implications for photonics and quantum optics because topological monomodes increase the robustness of corner states by preventing recombination.Comment: 30 (13+17) pages, 17 (4+13) figures, comments are welcom

Quantum Hall system in Tao-Thouless limit

We consider spin-polarized electrons in a single Landau level on a torus. The quantum Hall problem is mapped onto a one-dimensional lattice model with lattice constant $2\pi/L_1$, where $L_1$ is a circumference of the torus (in units of the magnetic length). In the Tao-Thouless limit, $L_1\to 0$, the interacting many-electron problem is exactly diagonalized at any rational filling factor $\nu=p/q\le 1$. For odd $q$, the ground state has the same qualitative properties as a bulk ($L_1 \to \infty$) quantum Hall hierarchy state and the lowest energy quasiparticle exitations have the same fractional charges as in the bulk. These states are the $L_1 \to 0$ limits of the Laughlin/Jain wave functions for filling fractions where these exist. We argue that the exact solutions generically, for odd $q$, are continuously connected to the two-dimensional bulk quantum Hall hierarchy states, {\it ie} that there is no phase transition as $L_1 \to \infty$ for filling factors where such states can be observed. For even denominator fractions, a phase transition occurs as $L_1$ increases. For $\nu=1/2$ this leads to the system being mapped onto a Luttinger liquid of neutral particles at small but finite $L_1$, this then develops continuously into the composite fermion wave function that is believed to describe the bulk $\nu=1/2$ system. The analysis generalizes to non-abelian quantum Hall states.Comment: 25 pages, 9 figure

Topological Monomodes in non-Hermitian Systems

Topological monomodes have been for long as elusive as magnetic monopoles. The latter was experimentally shown to emerge in effective descriptions of condensed-matter systems, while the experimental exploration of the former has largely been hindered by the complexity of the conceived setups. Here, we present a remarkably simple model and the experimental observation of topological monomodes generated dynamically. By focusing on non-Hermitian one-dimensional (1D) and 2D Su-Schrieffer-Heeger (SSH) models, we theoretically unveil the minimal configuration to realize a topological monomode upon engineering losses and breaking of lattice symmetries. Furthermore, we classify the systems in terms of the (non-Hermitian) symmetries that are present and calculate the corresponding topological invariants. To corroborate the theory, we present experiments in photonic lattices, in which a monomode is observed in the non-Hermitian 1D and 2D SSH models, thus breaking the paradigm that topological corner states should appear in pairs. Our findings might have profound implications for photonics and quantum optics because topological monomodes increase the robustness of corner states by preventing recombination

The Mitochondrial Genome and Transcriptome of the Basal Dinoflagellate Hematodinium sp.: Character Evolution within the Highly Derived Mitochondrial Genomes of Dinoflagellates

The sister phyla dinoflagellates and apicomplexans inherited a drastically reduced mitochondrial genome (mitochondrial DNA, mtDNA) containing only three protein-coding (cob, cox1, and cox3) genes and two ribosomal RNA (rRNA) genes. In apicomplexans, single copies of these genes are encoded on the smallest known mtDNA chromosome (6 kb). In dinoflagellates, however, the genome has undergone further substantial modifications, including massive genome amplification and recombination resulting in multiple copies of each gene and gene fragments linked in numerous combinations. Furthermore, protein-encoding genes have lost standard stop codons, trans-splicing of messenger RNAs (mRNAs) is required to generate complete cox3 transcripts, and extensive RNA editing recodes most genes. From taxa investigated to date, it is unclear when many of these unusual dinoflagellate mtDNA characters evolved. To address this question, we investigated the mitochondrial genome and transcriptome character states of the deep branching dinoflagellate Hematodinium sp. Genomic data show that like later-branching dinoflagellates Hematodinium sp. also contains an inflated, heavily recombined genome of multicopy genes and gene fragments. Although stop codons are also lacking for cox1 and cob, cox3 still encodes a conventional stop codon. Extensive editing of mRNAs also occurs in Hematodinium sp. The mtDNA of basal dinoflagellate Hematodinium sp. indicates that much of the mtDNA modification in dinoflagellates occurred early in this lineage, including genome amplification and recombination, and decreased use of standard stop codons. Trans-splicing, on the other hand, occurred after Hematodinium sp. diverged. Only RNA editing presents a nonlinear pattern of evolution in dinoflagellates as this process occurs in Hematodinium sp. but is absent in some later-branching taxa indicating that this process was either lost in some lineages or developed more than once during the evolution of the highly unusual dinoflagellate mtDNA