2020
DOI: 10.1073/pnas.2007384117
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Topological Weaire–Thorpe models of amorphous matter

Abstract: Amorphous solids remain outside of the classification and systematic discovery of new topological materials, partially due to the lack of realistic models that are analytically tractable. Here we introduce the topological Weaire–Thorpe class of models, which are defined on amorphous lattices with fixed coordination number, a realistic feature of covalently bonded amorphous solids. Their short-range properties allow us to analytically predict spectral gaps. Their symmetry under permutation of orbitals allows us… Show more

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Cited by 54 publications
(33 citation statements)
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“…Pfaffians are calculated using Pfapack [46]. The numerical density of states, momentum-resolved spectral function, and effective Hamiltonian calculations are performed using the kernel polynomial method [17,23,47,48].…”
Section: B Numerical Methodsmentioning
confidence: 99%
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“…Pfaffians are calculated using Pfapack [46]. The numerical density of states, momentum-resolved spectral function, and effective Hamiltonian calculations are performed using the kernel polynomial method [17,23,47,48].…”
Section: B Numerical Methodsmentioning
confidence: 99%
“…The spectrum of H eff (k) closely follows the peaks of the spectral function, especially near the gap closing points. The key properties of H eff are that it transforms the same way under symmetries as continuum Hamiltonians discussed before, its gap only closes when the gap in the bulkĤ closes [23], and it is properly regularized in the k → ∞ limit [17]. Hence, the bulk invariants defined for continuum systems are directly applicable to detecting topological phase transitions in amorphous systems.…”
Section: Effective Hamiltonian Of Amorphous Modelsmentioning
confidence: 95%
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“…The methods usually applied to calculate the topological properties have been mainly developed for crystalline cases. However, in some situations, there is no such thing as a crystal lattice [ 34 , 35 ], and the bulk-boundary correspondence—a cornerstone in topological insulators—is not straightforward to follow. For these cases, a local probe of the symmetries giving rise to the topological order could be useful, especially one that provides chemical intuition.…”
Section: Introductionmentioning
confidence: 99%