Higher-order topological phases can be protected solely by the bulk gap, fundamental symmetries, and the global topology of the system shape via its genus, independent of crystalline symmetries.
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Rounded hard squares confined in a circle transition from a cross-shaped tetratic domain with four +1/4 disclinations to a six-domain partition with six +1/4 disclinations and one central -1/2 disclination as roundness increases.
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Genus-protected higher-order topological phases
Higher-order topological phases can be protected solely by the bulk gap, fundamental symmetries, and the global topology of the system shape via its genus, independent of crystalline symmetries.
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Rounded hard squares confined in a circle
Rounded hard squares confined in a circle transition from a cross-shaped tetratic domain with four +1/4 disclinations to a six-domain partition with six +1/4 disclinations and one central -1/2 disclination as roundness increases.