Projected topological branes

Archisman, Panigrahi,; Juričić, Vladimir; Roy, Bitan

doi:10.1038/s42005-022-01006-x

Cited by 12 publications

(6 citation statements)

References 64 publications

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“…To construct the PTB, we employ the method based on the Schur complement 22 . Consider a lattice tight-binding model defined in d -dimensions for a system of lattice sites, which we refer to as the parent system.…”

Section: Projected Topological Branesmentioning

confidence: 99%

“…Consider a lattice tight-binding model defined in d -dimensions for a system of lattice sites, which we refer to as the parent system. The real-space Hamiltonian for the parent system can be written in the block form as The Hamiltonian for the PTB then takes the form 22 , where corresponds to the real-space Hamiltonian of lattice sites on the -dimensional brane. By contrast, is the real-space Hamiltonian for the remaining subsystem formed by lattice sites which do not constitute the -dimensional brane.…”

Section: Projected Topological Branesmentioning

confidence: 99%

“…In Ref. 22 , projected topological branes (PTBs) were introduced as a robust pathway to performing dimensional reduction of a lattice tight-binding model while preserving the bulk topology. This construction was exemplified on one- and two-dimensional PTBs obtained from two-dimensional Chern insulators and three-dimensional (3D) Weyl semimetals, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional $${\mathbb {Z}}$$ topological insulators without reflection symmetry

Tyner,

Juričić

2024

Sci Rep

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In recent decades, the Altland-Zirnabuer (AZ) table has proven incredibly powerful in delineating constraints for topological classification of a given band-insulator based on dimension and (nonspatial) symmetry class, and has also been expanded by considering additional crystalline symmetries. Nevertheless, realizing a three-dimensional (3D), time-reversal symmetric (class AII) topological insulator (TI) in the absence of reflection symmetries, with a classification beyond the $${\mathbb {Z}}_{2}$$ Z 2 paradigm remains an open problem. In this work we present a general procedure for constructing such systems within the framework of projected topological branes (PTBs). In particular, a 3D projected brane from a “parent” four-dimensional topological insulator exhibits a $${\mathbb {Z}}$$ Z topological classification, corroborated through its response to the inserted bulk monopole loop. More generally, PTBs have been demonstrated to be an effective route to performing dimensional reduction and embedding the topology of a $$(d+1)$$ ( d + 1 ) -dimensional “parent” Hamiltonian in d dimensions, yielding lower-dimensional topological phases beyond the AZ classification without additional symmetries. Our findings should be relevant for the metamaterial platforms, such as photonic and phononic crystals, topolectric circuits, and designer systems.

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Section: Projected Topological Branesmentioning

confidence: 99%

Section: Projected Topological Branesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Three-dimensional $${\mathbb {Z}}$$ topological insulators without reflection symmetry

Tyner,

Juričić

2024

Sci Rep

Self Cite

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“…A question is naturally remarked whether the bulk band topology can be revealed by these internal 'boundaries'. One positive answer is provided by topological defects [457][458][459][460][461][462][463][464][465][466][467][468][469][470][471][472], which include, for example, dislocations (see figures 32(a) and (b)) and disclinations (see figure 32(c)).…”

Section: Topological Defects and Bulk-defect Correspondencesmentioning

confidence: 99%

Topological phononic metamaterials

Zhu,

Deng,

Liu

et al. 2023

Rep. Prog. Phys.

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The concept of topological energy bands and their manifestations have been demonstrated in condensed matter systems as a fantastic paradigm toward unprecedented physical phenomena and properties that are robust against disorders. Recent years, this paradigm was extended to phononic metamaterials (including mechanical and acoustic metamaterials), giving rise to the discovery of remarkable phenomena that were not observed elsewhere thanks to the extraordinary controllability and tunability of phononic metamaterials as well as versatile measuring techniques. These phenomena include, but not limited to, topological negative refraction, topological `sasers' (i.e., the phononic analog of lasers), higher-order topological insulating states, non-Abelian topological phases, higher-order Weyl semimetal phases, Majorana-like modes in Dirac vortex structures and fragile topological phases with spectral flows. Here we review the developments in the field of topological phononic metamaterials from both theoretical and experimental perspectives with emphasis on the underlying physics principles. To give a broad view of topological phononics, we also discuss the synergy with non-Hermitian effects and cover topics including synthetic dimensions, artificial gauge fields, Floquet topological acoustics, bulk topological transport, topological pumping, and topological active matters as well as potential applications, materials fabrications and measurements of topological phononic metamaterials. Finally, we discuss the challenges, opportunities and future developments in this intriguing field and its potential impact on physics and materials science.

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“…Those highly unusual properties (sketched in Fig. 1b) have inspired a myriad of recent theoretical works on 2D Weyl semimetals [42,[46][47][48][49]. So far, however, experimental realization of topological 2D Weyl semimetals has remained elusive.…”

Section: Introductionmentioning

confidence: 99%

Observation of 2D Weyl Fermion States in Epitaxial Bismuthene

Lu¹,

Reddy²,

Jeon³

et al. 2023

Preprint

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A two-dimensional (2D) Weyl semimetal featuring a spin-polarized linear band dispersion and a nodal Fermi surface is a new topological phase of matter. It is a solidstate realization of Weyl fermions in an intrinsic 2D system. The nontrivial topology of 2D Weyl cones guarantees the existence of a new form of topologically protected boundary states, Fermi string edge states. In this work, we report the realization of a 2D Weyl semimetal in monolayer-thick epitaxial bismuthene grown on SnS(Se) substrate. The intrinsic band gap of bismuthene is eliminated by the space-inversionsymmetry-breaking substrate perturbations, resulting in a gapless spin-polarized Weyl band dispersion. The linear dispersion and spin polarization of the Weyl fermion states are observed in our spin and angle-resolved photoemission measurements. In addition, the scanning tunneling microscopy/spectroscopy reveals pronounced local density of states at the edge, suggesting the existence of Fermi string edge states. These results open the door for the experimental exploration of the exotic properties of Weyl fermion states in reduced dimensions.

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Projected topological branes

Cited by 12 publications

References 64 publications

Three-dimensional $${\mathbb {Z}}$$ topological insulators without reflection symmetry

Three-dimensional $${\mathbb {Z}}$$ topological insulators without reflection symmetry

Topological phononic metamaterials

Observation of 2D Weyl Fermion States in Epitaxial Bismuthene

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