Coexistence of zero-, one- and two-dimensional degeneracy in tetragonal SnO${}_2$ phonons

Abstract

Based on the dimension of degeneracy, topological electronic systems can roughly be divided into three parts: nodal point, line and surface materials corresponding to zero-, one- and two-dimensional degeneracy, respectively. In parallel to electronic systems, the concept of topology was extended to phonons, promoting the birth of topological phonons. Till date, few nodal point, line and surface phonons candidates have been predicted in solid-state materials. In this study, based on symmetry analysis and first-principles calculation, for the first time, we prove that zero-, one- and two-dimensional degeneracy co-exist in the phonon dispersion of one single realistic solid-state material SnO${}_2$ with \textit{P}4${}_2$/\textit{mnm} structure. In contrast to the previously reported electronic systems, the topological phonons observed in SnO${}_2$ are not restricted by the Pauli exclusion principle, and they experience negligible spin-orbit coupling effect. Hence, SnO${}_2$ with multiple dimensions of degeneracy phonons is a good platform for studying the entanglement among nodal point, line and surface phonons. Moreover, obvious phonon surface states are visible, which is beneficial for experimental detection.

References in corpus (41)

• WannierTools: An open-source software package for novel topological materials
• Topological nodal semimetals
• Topological quantum chemistry
• Phononics: Manipulating heat flow with electronic analogs and beyond
• The (High Quality) Topological Materials In The World
• Topological nodal line semimetals with and without spin-orbital coupling
• Catalogue of Topological Electronic Materials
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Topological nodal line semimetals
• Dirac Semimetals in Two Dimensions
• Topological Semimetals
• Topological classification of crystalline insulators through band structure combinatorics
• Nodal surface semimetals: Theory and material realization
• Quantitative mappings between symmetry and topology in solids
• 3D Dirac semimetals: current materials, design principles and predictions of new materials
• Topological Semimetals from first-principles
• Chemical Principles of Topological Semimetals
• Observation of Double Weyl Phonons in Parity-Breaking FeSi
• Type-II nodal loops: theory and material realization
• Computation and data driven discovery of topological phononic materials
• Symmetry-Protected Topological Triangular Weyl Complex
• Phononic Helical Nodal Lines with $\mathcal{P}\mathcal{T}$ Protection in MoB${}_2$
• Topological Thermoelectricity in Metals
• Diagnosis for topological semimetals in the absence of spin-orbital coupling
• Unsupervised Manifold Clustering of Topological Phononics
• Hybrid Nodal Loop Metal: Unconventional Magnetoresponse and Material Realization
• Three-dimensional Dirac Phonons with Inversion Symmetry
• Symmetry-Enforced Weyl Phonons
• Recipe for Dirac Phonon States with Quantized Valley Berry Phase in Two Dimensional Hexagonal Lattices
• Hybrid Dirac Semimetal in CaAgBi Materials Family
• Quadratic contact point semimetal: Theory and material realization
• Berry Phase and Topological Effects of Phonons
• Ideal Intersecting Nodal Ring Phonons in a Body-Centered Cubic C${}_8$
• Ideal type-II Weyl phonons in wurtzite CuI
• Vibrational surface EELS probes confined Fuchs-Kliewer modes
• Hourglass Weyl loops in two dimensions: Theory and material realization in monolayer GaTeI family
• SpaceGroupIrep: A package for irreducible representations of space group
• Symmetry-enforced ideal lantern-like phonons in ternary nitride Li${}_6$WN${}_4$
• Topological gimbal phonons in T-carbon
• Topology of Triple-Point Metals

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