Genus-protected higher-order topological phases
Shahroze Shahab, Hui Liu, Daniel Varjas, Ion Cosma Fulga
TLDR
This paper introduces a new class of higher-order topological phases protected by the system's global topology (genus), independent of lattice symmetries.
Key contributions
- Proposes novel higher-order topological phases (HOTPs) protected by global system topology (genus).
- These HOTPs are independent of crystalline lattice symmetries, relying on bulk gap and fundamental symmetries.
- Resulting boundary modes are robust against purely-surface perturbations.
Why it matters
The paper redefines how topological phases are protected, shifting from lattice symmetries to global topology. This fundamental change broadens the scope of topological material design and deepens our understanding of topological matter.
Original Abstract
Higher-order topological phases (HOTPs) feature protected gapless modes on boundaries of higher codimension, such as the corners or hinges of a crystal. They are understood as being protected by lattice symmetries: If the latter are broken, it becomes possible to remove the boundary modes without closing the bulk gap. In this work, we present construction schemes for HOTPs protected solely by the bulk gap, by fundamental symmetries, and by the global topology of the system shape (its genus, or number of holes), independent of any crystalline symmetries. As long as the fundamental local symmetries are preserved, the resulting boundary states cannot be removed by any purely-surface perturbation.
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