scholarly journals Symmetry-enriched phases obtained via pseudo anyon condensation

2014 ◽  
Vol 28 (24) ◽  
pp. 1450172 ◽  
Author(s):  
Ling-Yan Hung ◽  
Yidun Wan
Keyword(s):  
Physical Properties ◽  
Complete Classification ◽  
Topological Phases ◽  
Topological Order ◽  
Edge States ◽  
Symmetric Phase ◽  
Internal Symmetries

We propose a framework to describe topological phases with global internal symmetries. This involves embedding the phase of interest into an intrinsic topological-order. Such an embedding is related to the physics of anyon condensation, although no physical condensation actually occurs here. Crucial physical properties of the symmetric phase, such as edge states and global charges of anyons are easily recovered from the embedding. The framework naturally reproduces all phases that are currently known in 2+1 d, and potentially provides a complete classification of symmetric topological phases in 2+1 d. We illustrate our idea with simple examples.

scholarly journals Tri- and Tetrahyperbolic Isofrequency Topologies Complete Classification of Bianisotropic Materials

2020 ◽  
Vol 10 (3) ◽  
pp. 763 ◽  
Author(s):  
Maxim Durach ◽  
Robert Williamson ◽  
Morgan Laballe ◽  
Thomas Mulkey
Keyword(s):  
Phase Transitions ◽  
Optical Materials ◽  
Complete Classification ◽  
Topological Phases ◽  
Longitudinal Polarization ◽  
Polarization Impedance ◽  
High K ◽  
All Optical ◽  
Zero Group

We describe novel topological phases of isofrequency k-space surfaces in bianisotropic optical materials—tri- and tetrahyperbolic materials—which are induced by the introduction of chirality. This completes the classification of isofrequency topologies for bianisotropic materials, as we showed that all optical materials belong to one of the following topological classes—tetra-, tri-, bi-, mono-, or nonhyperbolic. We showed that phase transitions between these classes occur in the k-space directions with zero group velocity at high k-vectors. This classification is based on the sets of high-k polaritons (HKPs), supported by materials. We obtained the equation describing these sets and characterized the longitudinal polarization-impedance of HKPs.

scholarly journals Classification of topological phases with finite internal symmetries in all dimensions

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Liang Kong ◽  
Tian Lan ◽  
Xiao-Gang Wen ◽  
Zhi-Hao Zhang ◽  
Hao Zheng
Keyword(s):  
Mathematical Description ◽  
Mathematical Theory ◽  
Special Care ◽  
Topological Phases ◽  
Topological Excitations ◽  
Symmetry Protected ◽  
Internal Symmetries

Abstract We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first approach is to gauge the symmetry in the same dimension by adding topological excitations as it was done in the 2d case, in which the gauging process is mathematically described by the minimal modular extensions of unitary braided fusion 1-categories. This 2d result immediately generalizes to all dimensions except in 1d, which is treated with special care. The second approach is to use the 1-dimensional higher bulk of the SPT/SET order and the boundary-bulk relation. This approach also leads us to a precise mathematical description and a classification of SPT/SET orders in all dimensions. The equivalence of these two approaches, together with known physical results, provides us with many precise mathematical predictions.

scholarly journals Topological gaps by twisting

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Matheus I. N. Rosa ◽  
Massimo Ruzzene ◽  
Emil Prodan
Keyword(s):  
Magnetic Field ◽  
Quantum Hall Effect ◽  
Twist Angle ◽  
Quantum Hall ◽  
Topological Phases ◽  
Edge States ◽  
Layered Systems ◽  
Virtual Laboratories ◽  
Higher Dimensional ◽  
Chern Numbers

AbstractTwisted bilayered systems such as bilayered graphene exhibit remarkable properties such as superconductivity at magic angles and topological insulating phases. For generic twist angles, the bilayers are truly quasiperiodic, a fact that is often overlooked and that has consequences which are largely unexplored. Herein, we uncover that twisted n-layers host intrinsic higher dimensional topological phases, and that those characterized by second Chern numbers can be found in twisted bi-layers. We employ phononic lattices with interactions modulated by a second twisted lattice and reveal Hofstadter-like spectral butterflies in terms of the twist angle, which acts as a pseudo magnetic field. The phason provided by the sliding of the layers lives on 2n-tori and can be used to access and manipulate the edge states. Our work demonstrates how multi-layered systems are virtual laboratories for studying the physics of higher dimensional quantum Hall effect, and can be employed to engineer topological pumps via simple twisting and sliding.

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

scholarly journals Non-Hermitian route to higher-order topology in an acoustic crystal

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
He Gao ◽  
Haoran Xue ◽  
Zhongming Gu ◽  
Tuo Liu ◽  
Jie Zhu ◽  
...  
Keyword(s):  
Higher Order ◽  
Order Topology ◽  
Topological Phases ◽  
Edge States ◽  
Experimental Realization ◽  
Artificial Materials ◽  
Intrinsic Loss ◽  
Topological Phases Of Matter ◽  
Hierarchical Features ◽  
Nontrivial Topology

AbstractTopological phases of matter are classified based on their Hermitian Hamiltonians, whose real-valued dispersions together with orthogonal eigenstates form nontrivial topology. In the recently discovered higher-order topological insulators (TIs), the bulk topology can even exhibit hierarchical features, leading to topological corner states, as demonstrated in many photonic and acoustic artificial materials. Naturally, the intrinsic loss in these artificial materials has been omitted in the topology definition, due to its non-Hermitian nature; in practice, the presence of loss is generally considered harmful to the topological corner states. Here, we report the experimental realization of a higher-order TI in an acoustic crystal, whose nontrivial topology is induced by deliberately introduced losses. With local acoustic measurements, we identify a topological bulk bandgap that is populated with gapped edge states and in-gap corner states, as the hallmark signatures of hierarchical higher-order topology. Our work establishes the non-Hermitian route to higher-order topology, and paves the way to exploring various exotic non-Hermiticity-induced topological phases.

The Classification of Parauapebas Meteorite: Petrological, Mineralogical and Elemental Compositions and Physical Properties

2021 ◽  
pp. 105250
Author(s):  
Amanda A. Tosi ◽  
Maria Elizabeth Zucolotto ◽  
Wania Wolff ◽  
Julio C. Mendes ◽  
Sergio Suárez ◽  
...  
Keyword(s):  
Physical Properties ◽  
Elemental Compositions

scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

scholarly journals Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sungmin Kim ◽  
Johannes Schwenk ◽  
Daniel Walkup ◽  
Yihang Zeng ◽  
Fereshte Ghahari ◽  
...  
Keyword(s):  
Atomic Force Microscopy ◽  
Chemical Potential ◽  
Quantum Hall ◽  
Broken Symmetry ◽  
Topological Order ◽  
Edge States ◽  
Force Microscopy ◽  
Atomic Force ◽  
Intimate Relation ◽  
Boundary Measurements

AbstractThe quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the “bulk” topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of $${{\nu }}={{0}},\pm {{1}}$$ ν = 0 , ± 1 across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.

scholarly journals Topological electronics

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Matthew J. Gilbert
Keyword(s):  
Information Processing ◽  
Physical Properties ◽  
Materials Science ◽  
Electronic Device ◽  
Condensed Matter ◽  
Topological Phases ◽  
Applied Physics ◽  
New Paradigm ◽  
Topological Materials ◽  
Device Applications

AbstractWithin the broad and deep field of topological materials, there are an ever-increasing number of materials that harbor topological phases. While condensed matter physics continues to probe the exotic physical properties resulting from the existence of topological phases in new materials, there exists a suite of “well-known” topological materials in which the physical properties are well-characterized, such as Bi2Se3 and Bi2Te3. In this context, it is then appropriate to ask if the unique properties of well-explored topological materials may have a role to play in applications that form the basis of a new paradigm in information processing devices and architectures. To accomplish such a transition from physical novelty to application based material, the potential of topological materials must be disseminated beyond the reach of condensed matter to engender interest in diverse areas such as: electrical engineering, materials science, and applied physics. Accordingly, in this review, we assess the state of current electronic device applications and contemplate the future prospects of topological materials from an applied perspective. More specifically, we will review the application of topological materials to the general areas of electronic and magnetic device technologies with the goal of elucidating the potential utility of well-characterized topological materials in future information processing applications.

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