Abstract
Higher-order topological (HOT) phases feature boundary (such as corner and hinge) modes of codimension $d_c>1$. We here identify an \emph{antiunitary} operator that ensures the spectral symmetry of a two-dimensional HOT insulator and the existence of cornered localized states ($d_c=2$) at precise zero energy. Such an antiunitary symmetry allows us to construct a generalized HOT insulator that continues to host corner modes even in the presence of a \emph{weak} anomalous Hall insulator and a spin-orbital density wave orderings, and is characterized by a quantized quadrupolar moment $Q_{xy}=0.5$. Similar conclusions can be drawn for the time-reversal symmetry breaking HOT $p+id$ superconductor and the corner localized Majorana zero modes survive even in the presence of weak Zeeman coupling and $s$-wave pairing. Such HOT insulators also serve as the building blocks of three-dimensional second-order Weyl semimetals, supporting one-dimensional hinge modes.
Highlights
The hallmark of topological phases of matter is the presence of gapless modes at the boundary, protected by the nontrivial bulk topological invariant
While the bulk topological invariant assures the existence of boundary modes, often the localized topological modes get pinned at precise zero energy due to the spectral symmetry, which we exploit here to propose the most general setup for a two-dimensional higher-order topological (HOT) insulator, characterized by a quantized quadrupolar moment Qxy = 0.5 and supports four corner localized zero-energy modes
Before leaving the territory of charged fermions, we demonstrate the applicability of the above construction of generalized higherorder topological insulator (GHOTI) in the context of the original model of the twodimensional HOT insulator introduced in Ref. [8], the Belancazar-Bernevig-Hughes (BBH) model
Summary
We here identify an antiunitary operator that ensures the spectral symmetry of a two-dimensional HOT insulator and the existence of cornered localized states (dc = 2) at precise zero energy. Similar conclusions can be drawn for the time-reversal symmetry breaking HOT p + id superconductor and the corner localized Majorana zero modes survive even in the presence of weak Zeeman coupling and s-wave pairing. Such HOT insulators serve as the building blocks of threedimensional second-order Weyl semimetals, supporting one-dimensional hinge modes
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
