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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Nonsymmorphic 1D four-band models with Kramers degeneracy support Z2 and Z4 invariants computed via extended open-path winding numbers, realized in topolectric circuits whose impedance reproduces phase boundaries and zero-energy modes that remain pinned under minimal disorder.
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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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One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
Nonsymmorphic 1D four-band models with Kramers degeneracy support Z2 and Z4 invariants computed via extended open-path winding numbers, realized in topolectric circuits whose impedance reproduces phase boundaries and zero-energy modes that remain pinned under minimal disorder.