Topological continuum charges of acoustic phonons in two dimensions and the Nambu-Goldstone theorem
TLDR
In this paper , the authors analyze the band topology of acoustic phonons in 2D materials by considering the interplay of spatial and internal symmetries with additional constraints that arise from the physical context.Abstract:
We analyze the band topology of acoustic phonons in 2D materials by considering the interplay of spatial and internal symmetries with additional constraints that arise from the physical context. These supplemental constraints trace back to the Nambu-Goldstone theorem and the requirements of structural stability. We show that this interplay can give rise to previously unaddressed non-trivial nodal charges that are associated with the crossing of the acoustic phonon branches at the center ($\Gamma$-point) of the phononic Brillouin zone. We moreover apply our perspective to the concrete context of graphene, where we demonstrate that the phonon spectrum harbors these kinds of non-trivial nodal charges. Apart from its fundamental appeal, this analysis is physically consequential and dictates how the phonon dispersion is affected when graphene is grown on a substrate. Given the generality of our framework, we anticipate that our strategy that thrives on combining physical context with insights from topology should be widely applicable in characterizing systems beyond electronic band theory. read more
Citations
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Edge states of topological acoustic phonons in graphene zigzag nanoribbons
TL;DR: In this paper , the topological acoustic edge states in graphene need to be assessed by the acoustic sum rule (ASR) in phonon systems, which results in edge states of acoustic modes rarely observed in previous works.
Multi-gap topological conversion of Euler class via band-node braiding: minimal models, $PT$-linked nodal rings, and chiral heirs
Adrien Bouhon,Robert-Jan Slager +1 more
TL;DR: In this paper , a universal formulation for Euler phases motivated by their homotopy classification that is related to the Skyrmion-pro�le of a single unit-vector in three-level systems, and that of two unit-vectors in fourlevel systems was presented.
Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
TL;DR: In this paper , anomalous Dirac string topological invariants have been investigated in out-of-equilibrium Floquet settings, leading to a phase characterized by an anomalous Euler class, the prime example of a multi-gap invariant.
Experimental observation of meronic topological acoustic Euler insulators
Bin-hao Jiang,Adrien Bouhon,Shiqiao Wu,Ze-Lin Kong,Zhiping Liu,Robert-Jan Slager,Jian-Hua Jiang +6 more
TL;DR: In this article , the authors report on the experimental observation of a gapped nontrivial Euler topology in an acoustic metamaterial, which is characterized by a meron (half-skyrmion) type topology, in which the cancellation of the orbital Zak phases by Zak phases contributes in forming the characterizing winding number of the acoustic bands.
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Non-Abelian braiding of Weyl nodes via symmetry-constrained phase transitions
TL;DR: In this paper , it was shown that a family of phase transitions characterized by certain symmetry constraints impose that the Weyl nodes have to reorganize by a large amount, shifting from one high-symmetry plane to another.
References
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Journal ArticleDOI
Classification of topological insulators and superconductors in three spatial dimensions
TL;DR: In this paper, the authors systematically studied topological phases of insulators and superconductors in three dimensions and showed that there exist topologically nontrivial (3D) topologically nonsmooth topological insulators in five out of ten symmetry classes introduced in the context of random matrix theory.
Journal ArticleDOI
Classification of topological quantum matter with symmetries
TL;DR: In this article, a review of the classification schemes of both fully gapped and gapless topological materials is presented, and a pedagogical introduction to the field of topological band theory is given.
Journal ArticleDOI
Field Theories with Superconductor Solutions
TL;DR: In this paper, the conditions for the existence of non-perturbative type superconductor solutions of field theories are examined and the symmetry properties of such solutions are examined with the aid of a simple model of self-interacting boson fields.
Journal ArticleDOI
Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
TL;DR: In this article, a detailed study is made of the systems where the phase shift due to Andreev reflection averages to zero along a typical semiclassical single-electron trajectory.
Journal ArticleDOI
Topological crystalline insulators.
TL;DR: A class of three-dimensional "topological crystalline insulators" which have metallic surface states with quadratic band degeneracy on high symmetry crystal surfaces is found.