In this work, we examine the topological phases of the spring-mass lattices when the spatial inversion symmetry of the system is broken and prove the existence of edge modes when two lattices with different topological phases are glued together. In particular, for the one-dimensional lattice consisting of an infinite array of masses connected by springs, we show that the Zak phase of the lattice is quantized, only taking the value 0 or . We also prove the existence of an edge mode when two semi-infinite lattices with distinct Zak phases are connected. For the two-dimensional honeycomb lattice, we characterize the valley Chern numbers of the lattice when the masses on the lattice vertices are uneven. The existence of edge modes is proved for a joint honeycomb lattice formed by gluing two semi-infinite lattices with opposite valley Chern numbers together.
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Digging for topological property in disordered alloys: the emergence of Weyl semimetal phase and sequential band inversions in PbSe–SnSe alloys
The search for topological systems has recently broadened to include random substitutional alloys, which lack the specific crystalline symmetries that protect topological phases, raising the question of whether topological properties can be preserved, or are modified by disorder. To address this question, we avoid methods that assumed at the outset high (averaged) symmetry, using instead a fully-atomistic, topological description of an alloy. Application to the (PbSe) 1−x (SnSe) x alloy reveals that topology survives in an interesting fashion: (a) spatial randomness removes the valley degeneracy (splitting ≥150 meV), leading to a sequential inversion of the split valley components over a range of compositions; (b) the absence of inversion lifts spin degenerates, leading to a Weyl semimetal phase without the need of an external magnetic field, an unexpected result, given that the alloy constituent compounds are inversion-symmetric. (a) and (b) underpin the topological physics at low symmetry and complete the missing understanding of possible topological phases within the normal-topological insulator transition.
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- Award ID(s):
- 1724791
- PAR ID:
- 10144067
- Date Published:
- Journal Name:
- Materials Horizons
- Volume:
- 6
- Issue:
- 10
- ISSN:
- 2051-6347
- Page Range / eLocation ID:
- 2124 to 2134
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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