arXiv subjects

Barry Bradlyn

Publications and source records attributed to Barry Bradlyn.

At least 73 records · Page 4Linked to original sources

arXiv2020

Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves

In recent theoretical and experimental investigations, researchers have linked the low-energy field theory of a Weyl semimetal gapped with a charge-density wave (CDW) to high-energy theories with axion electrodynamics. However, it remains an open question whether a lattice regularization of the dynamical Weyl-CDW is in fact a single-particle axion insulator (AXI). In this Letter, we use analytic and numerical methods to study both lattice-commensurate and incommensurate minimal (magnetic) Weyl-CDW phases in the mean-field state. We observe that, as previously predicted from field theory, the two inversion- ($\mathcal{I}$-) symmetric Weyl-CDWs with $ϕ= 0,π$ differ by a topological axion angle $δθ_ϕ=π$. However, we crucially discover that $neither$ of the minimal Weyl-CDW phases at $ϕ=0,π$ is individually an AXI; they are instead quantum anomalous Hall (QAH) and "obstructed" QAH insulators that differ by a fractional translation in the modulated cell, analogous to the two phases of the Su-Schrieffer-Heeger model of polyacetylene. Using symmetry indicators of band topology and non-abelian Berry phase, we demonstrate that our results generalize to multi-band systems with only two Weyl fermions, establishing that minimal Weyl-CDWs unavoidably carry nontrivial Chern numbers that prevent the observation of a static magnetoelectric response. We discuss the experimental implications of our findings, and provide models and analysis generalizing our results to nonmagnetic Weyl- and Dirac-CDWs.

cond-mat.mes-hall↗

arXiv2020

Understanding the Use of Fauxtography on Social Media

Despite the influence that image-based communication has on online discourse, the role played by images in disinformation is still not well understood. In this paper, we present the first large-scale study of fauxtography, analyzing the use of manipulated or misleading images in news discussion on online communities. First, we develop a computational pipeline geared to detect fauxtography, and identify over 61k instances of fauxtography discussed on Twitter, 4chan, and Reddit. Then, we study how posting fauxtography affects engagement of posts on social media, finding that posts containing it receive more interactions in the form of re-shares, likes, and comments. Finally, we show that fauxtography images are often turned into memes by Web communities. Our findings show that effective mitigation against disinformation need to take images into account, and highlight a number of challenges in dealing with image-based disinformation.

cs.CY↗

arXiv2020

IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures

We present IrRep - a Python code that calculates the symmetry eigenvalues of electronic Bloch states in crystalline solids and the irreducible representations under which they transform. As input it receives bandstructures computed with state-of-the-art Density Functional Theory codes such as VASP, Quantum Espresso, or Abinit, as well as any other code that has an interface to Wannier90. Our code is applicable to materials in any of the 230 space groups and double groups preserving time-reversal symmetry with or without spin-orbit coupling included, for primitive or conventional unit cells. This makes IrRep a powerful tool to systematically analyze the connectivity and topological classification of bands, as well as to detect insulators with non-trivial topology, following the Topological Quantum Chemistry formalism: IrRep can generate the input files needed to calculate the (physical) elementary band representations and the symmetry-based indicators using the CheckTopologicalMat routine of the Bilbao Crystallographic Server. It is also particularly suitable for interfaces with other plane-waves based codes, due to its flexible structure.

cond-mat.mtrl-sci↗

arXiv2020

On the robustness of topological corner modes in photonic crystals

We analyze the robustness of corner modes in topological photonic crystals, taking a $C_6$-symmetric breathing honeycomb photonic crystal as an example. First, we employ topological quantum chemistry and Wilson loop calculations to demonstrate that the topological properties of the bulk crystal stem from an obstructed atomic limit phase. We then characterize the topological corner modes emerging within the gapped edge modes employing a semi-analytical model, determining the appropriate real space topological invariants. For the first time, we provide a detailed account of the effect of long-range interactions on the topological modes in photonic crystals, and we quantify their robustness to perturbations. We conclude that, while photonic long-range interactions inevitably break chiral symmetry, the corner modes are protected by lattice symmetries.

cond-mat.mes-hall↗

arXiv2020

Observation and control of maximal Chern numbers in a chiral topological semimetal

Topological semimetals feature protected nodal band degeneracies characterized by a topological invariant known as the Chern number (C). Nodal band crossings with linear dispersion are expected to have at most |C|=4, which sets an upper limit to the magnitude of many topological phenomena in these materials. Here we show that the chiral crystal PdGa displays multifold band crossings, which are connected by exactly four surface Fermi-arcs, thus proving that they carry the maximal Chern number magnitude of 4. By comparing two enantiomers, we observe a reversal of their Fermi-arc velocities, which demonstrates that the handedness of chiral crystals can be used to control the sign of their Chern numbers.

cond-mat.mes-hall↗

arXiv2020

Pairing Obstructions in Topological Superconductors

The modern understanding of topological insulators is based on Wannier obstructions in position space. Motivated by this insight, we study topological superconductors from a position-space perspective. For a one-dimensional superconductor, we show that the wave function of an individual Cooper pair decays exponentially with separation in the trivial phase and polynomially in the topological phase. For the position-space Majorana representation, we show that the topological phase is characterized by a nonzero Majorana polarization, which captures an irremovable and quantized separation of Majorana Wannier centers from the atomic positions. We apply our results to diagnose second-order topological superconducting phases in two dimensions. Our work establishes a vantage point for the generalization of Topological Quantum Chemistry to superconductivity.

cond-mat.supr-con↗

arXiv2020

Band Representations and Topological Quantum Chemistry

In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space. Next, we introduce the concept of a band representation, which quantifies the symmetry of topologically trivial band structures. By combining band representations with symmetry constraints on the connectivity of bands in momentum space, we show how topologically nontrivial bands can be catalogued and classified. We present several examples of new topological phases discovered using this paradigm, and conclude with an outlook towards future developments.

cond-mat.mes-hall↗

arXiv2020

Chiral Topological Semimetal with Multifold Band Crossings and Long Fermi arcs

Topological semimetals in crystals with a chiral structure (which possess a handedness due to a lack of mirror and inversion symmetries) are expected to display numerous exotic physical phenomena, including fermionic excitations with large topological charge [1], long Fermi arc surface states [2,3], unusual magnetotransport [4] and lattice dynamics [5], as well as a quantized response to circularly polarized light [6]. To date, all experimentally confirmed topological semimetals exist in crystals that contain mirror operations, meaning that these properties do not appear. Here, we show that AlPt is a structurally chiral topological semimetal that hosts new fourfold and sixfold fermions, which can be viewed as a higher spin eneralization of Weyl fermions without equivalence in elementary particle physics. These multifold fermions are located at high symmetry points and have Chern numbers larger than those in Weyl semimetals, thus resulting in multiple Fermi arcs that span the full diagonal of the surface Brillouin zone. By imaging these long Fermi arcs, we experimentally determine the magnitude and sign of their Chern number, allowing us to relate their dispersion to the handedness of their host crystal.

cond-mat.mes-hall↗

arXiv2020

Hall viscosity in quantum systems with discrete symmetry: point group and lattice anisotropy

Inspired by recent experiments on graphene, we examine the non-dissipative viscoelastic response of anisotropic two-dimensional quantum systems. We pay particular attention to electron fluids with point group symmetries, and those with discrete translational symmetry. We start by extending the Kubo formalism for viscosity to systems with internal degrees of freedom and discrete translational symmetry, highlighting the importance of properly considering the role of internal angular momentum. We analyze the Hall components of the viscoelastic response tensor in systems with discrete point group symmetry, focusing on the hydrodynamic implications of the resulting forces. We show that though there are generally six Hall viscosities, there are only three independent contributions to the viscous force density in the bulk. To compute these coefficients, we develop a framework to consistently write down the long-wavelength stress tensor and viscosity for multi-component lattice systems. We apply our formalism to lattice and continuum models, including a lattice Chern insulator and anisotropic superfluid.

cond-mat.mes-hall↗

arXiv2019

Tutorial: Computing topological invariants in two-dimensional photonic crystals

The field of topological photonics emerged as one of the most promising areas for applications in transformative technologies: possible applications are in topological lasers or quantum optics interfaces. Nevertheless, efficient and simple methods for diagnosing the topology of optical systems remain elusive for an important part of the community. In this tutorial, we provide a summary of numerical methods to calculate topological invariants emerging from the propagation of light in photonic crystals. We first describe the fundamental properties of wave propagation in lattices with a space-dependent periodic electric permittivity. Next, we provide an introduction to topological invariants; proposing an optimal strategy to calculate them through the numerical evaluation of Maxwell's equation in a discretized reciprocal space. Finally, we will complement the tutorial with a few practical examples of photonic crystal systems showing different topological properties, such as photonic valley-Chern insulators, photonic crystals presenting an "obstructed atomic limit", photonic systems supporting fragile topology and finally photonic Chern insulators, where we also periodically modulated the magnetic permeability.

cond-mat.mes-hall↗

arXiv2019

A Quantitative Approach to Understanding Online Antisemitism

A new wave of growing antisemitism, driven by fringe Web communities, is an increasingly worrying presence in the socio-political realm. The ubiquitous and global nature of the Web has provided tools used by these groups to spread their ideology to the rest of the Internet. Although the study of antisemitism and hate is not new, the scale and rate of change of online data has impacted the efficacy of traditional approaches to measure and understand these troubling trends. In this paper, we present a large-scale, quantitative study of online antisemitism. We collect hundreds of million posts and images from alt-right Web communities like 4chan's Politically Incorrect board (/pol/) and Gab. Using scientifically grounded methods, we quantify the escalation and spread of antisemitic memes and rhetoric across the Web. We find the frequency of antisemitic content greatly increases (in some cases more than doubling) after major political events such as the 2016 US Presidential Election and the "Unite the Right" rally in Charlottesville. We extract semantic embeddings from our corpus of posts and demonstrate how automated techniques can discover and categorize the use of antisemitic terminology. We additionally examine the prevalence and spread of the antisemitic "Happy Merchant" meme, and in particular how these fringe communities influence its propagation to more mainstream communities like Twitter and Reddit. Taken together, our results provide a data-driven, quantitative framework for understanding online antisemitism. Our methods serve as a framework to augment current qualitative efforts by anti-hate groups, providing new insights into the growth and spread of hate online.

cs.CY↗

arXiv2019

Characterizing the Use of Images in State-Sponsored Information Warfare Operations by Russian Trolls on Twitter

State-sponsored organizations are increasingly linked to efforts aimed to exploit social media for information warfare and manipulating public opinion. Typically, their activities rely on a number of social network accounts they control, aka trolls, that post and interact with other users disguised as "regular" users. These accounts often use images and memes, along with textual content, in order to increase the engagement and the credibility of their posts. In this paper, we present the first study of images shared by state-sponsored accounts by analyzing a ground truth dataset of 1.8M images posted to Twitter by accounts controlled by the Russian Internet Research Agency. First, we analyze the content of the images as well as their posting activity. Then, using Hawkes Processes, we quantify their influence on popular Web communities like Twitter, Reddit, 4chan's Politically Incorrect board (/pol/), and Gab, with respect to the dissemination of images. We find that the extensive image posting activity of Russian trolls coincides with real-world events (e.g., the Unite the Right rally in Charlottesville), and shed light on their targets as well as the content disseminated via images. Finally, we show that the trolls were more effective in disseminating politics-related imagery than other images.

cs.SI↗

arXiv2019

Multifold nodal points in magnetic materials

We describe the symmetry protected nodal points that can exist in magnetic space groups and show that only 3-, 6-, and 8-fold degeneracies are possible (in addition to the 2- and 4-fold degeneracies that have already been studied.) The 3- and 6-fold degeneracies are derived from "spin-1" Weyl fermions. The 8-fold degeneracies come in different flavors. In particular, we distinguish between 8-fold fermions that realize non-chiral "Rarita-Schwinger fermions" and those that can be described as four degenerate Weyl fermions. We list the (magnetic and non-magnetic) space groups where these exotic fermions can be found. We further show that in several cases, a magnetic translation symmetry pins the Hamiltonian of the multifold fermion to an idealized exactly solvable point that is not achievable in non-magnetic crystals without fine-tuning. Finally, we present known compounds that may host these fermions and methods for systematically finding more candidate materials.

cond-mat.mes-hall↗

arXiv2019

Quasinormal Modes and Hawking-Unruh effect in Quantum Hall Systems: Lessons from Black Hole Phenomena

In this work, we propose the quantum Hall system as a platform for exploring black hole phenomena. By exhibiting deep rooted commonalities between lowest Landau level and spacetime symmetries, we show that features of both quantum Hall and gravitational systems can be elegantly captured by a simple quantum mechanical model, the inverted harmonic oscillator. Through this correspondence, we argue that radiation phenomena in gravitational situations, such as presented by W. G. Unruh and S. Hawking, bears a parallel with saddle-potential scattering of quantum Hall quasiparticles. We also find that scattering by the quantum Hall saddle potential can mimic the signature quasinormal modes in black holes, such as theoretically demonstrated through Gaussian scattering off a Schwarzschild black hole by C. V. Vishveshwara. We propose a realistic quantum Hall point contact setup for probing these temporally decaying modes in quasiparticle tunneling, offering a new mesoscopic parallel for black hole ringdown.

cond-mat.mes-hall↗

arXiv2019

Engineering Fragile Topology in Photonic Crystals: Topological Quantum Chemistry of Light

In recent years, there have been rapid advances in the parallel fields of electronic and photonic topological crystals. Topological photonic crystals in particular show promise for coherent transport of light and quantum information at macroscopic scales. In this work, we apply for the first time the recently developed theory of "Topological quantum chemistry" to the study of band structures in photonic crystals. This method allows us to design and diagnose topological photonic band structures using only group theory and linear algebra. As an example, we focus on a family of crystals formed by elliptical rods in a triangular lattice. We show that the symmetry of Bloch states in the Brillouin zone can determine the position of the localized photonic wave packets describing groups of bands. By modifying the crystal structure and inverting bands, we show how the centers of these wave packets can be moved between different positions in the unit cell. Finally, we show that for shapes of dielectric rods, there exist isolated topological bands which do not admit a well-localized description, representing the first physical instance of "fragile" topology in a truly noninteracting system. Our work demonstrates how photonic crystals are the natural platform for the future experimental investigation of fragile topological bands.

cond-mat.mes-hall↗

arXiv2019

Evidence for an axionic charge density wave in the Weyl semimetal (TaSe4)2I

An axion insulator is a correlated topological phase, predicted to arise from the formation of a charge density wave in a Weyl semimetal. The accompanying sliding mode in the charge density wave phase, the phason, is an axion. It is expected to cause anomalous magneto-electric transport effects. However, this axionic charge density wave has so far eluded experimental detection. In this paper, we report the observation of a large, positive contribution to the magneto-conductance in the sliding mode of the charge density wave Weyl semimetal (TaSe4)2I for collinear electric and magnetic fields (E||B). The positive contribution to the magneto-conductance originates from the anomalous axionic contribution of the chiral anomaly to the phason current, and is locked to the parallel alignment of E and B. By rotating B, we show that the angular dependence of the magneto-conductance is consistent with the anomalous transport of an axionic charge density wave.

cond-mat.mes-hall↗

arXiv2019

Revisiting (higher order and crystalline) topology in old models of lead telluride

In this work, we revisit the model of PbTe presented in [E. Fradkin, E. Dagotto, and D. Boyanovsky, Phys. Rev. Lett. 57, 2967 (1986)]. We show that the low energy theory of this model corresponds to a (higher-order) topological crystalline insulator in space group $Fm\bar{3}m1'$, diagnosable by symmetry indicators. We show that the gapless fermions found on antiphase domain walls are the topological boundary modes of the system, due to a nonvanishing mirror Chern number. Furthermore, we show that any symmetric completion of the model must be in this same topological phase. Finally, we comment on the relationship of this model to realistic PbTe, which has recently been predicted to have a phase which realizes same bulk symmetry indicators.

cond-mat.mes-hall↗

arXiv2019

Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice

In this work, we examine the topological phases that can arise in triangular lattices with disconnected elementary band representations. We show that, although these phases may be "fragile" with respect to the addition of extra bands, their topological properties are manifest in certain nontrivial holonomies (Wilson loops) in the space of nontrivial bands. We introduce an eigenvalue index for fragile topology, and we show how a nontrivial value of this index manifests as the winding of a hexagonal Wilson loop; this remains true even in the absence of time-reversal or sixfold rotational symmetry. Additionally, when time-reversal and twofold rotational symmetry are present, we show directly that there is a protected nontrivial winding in more conventional Wilson loops. Crucially, we emphasize that these Wilson loops cannot change without closing a gap to the nontrivial bands. By studying the entanglement spectrum for the fragile bands, we comment on the relationship between fragile topology and the "obstructed atomic limit" of B. Bradlyn et al., Nature 547, 298--305 (2017). We conclude with some perspectives on topological matter beyond the K-theory classification.

cond-mat.mes-hall↗