Observation of a Higher-Order End Topological Insulator in a Real Projective Lattice

Ce Shang, Shuo Liu, Caigui Jiang, Ruiwen Shao, Xiaoning Zang, Ching Hua Lee*, Ronny Thomale, Aurélien Manchon, Tie Jun Cui*, Udo Schwingenschlögl*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The modern theory of quantized polarization has recently extended from 1D dipole moment to multipole moment, leading to the development from conventional topological insulators (TIs) to higher-order TIs, i.e., from the bulk polarization as primary topological index, to the fractional corner charge as secondary topological index. The authors here extend this development by theoretically discovering a higher-order end TI (HOETI) in a real projective lattice and experimentally verifying the prediction using topolectric circuits. A HOETI realizes a dipole-symmetry-protected phase in a higher-dimensional space (conventionally in one dimension), which manifests as 0D topologically protected end states and a fractional end charge. The discovered bulk-end correspondence reveals that the fractional end charge, which is proportional to the bulk topological invariant, can serve as a generic bulk probe of higher-order topology. The authors identify the HOETI experimentally by the presence of localized end states and a fractional end charge. The results demonstrate the existence of fractional charges in non-Euclidean manifolds and open new avenues for understanding the interplay between topological obstructions in real and momentum space.

Original languageEnglish (US)
Article number2303222
JournalAdvanced Science
Issue number11
StateAccepted/In press - 2024


  • bulk-end correspondence
  • higher-order
  • real projective lattice
  • topolectric circuit
  • topological insulator

ASJC Scopus subject areas

  • Medicine (miscellaneous)
  • General Chemical Engineering
  • General Materials Science
  • Biochemistry, Genetics and Molecular Biology (miscellaneous)
  • General Engineering
  • General Physics and Astronomy


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