Quantized surface magnetism and higher-order topology: Application to the Hopf insulator

Penghao Zhu, Taylor L. Hughes, A. Alexandradinata

Research output: Contribution to journalArticlepeer-review


We identify topological aspects of the subextensive magnetic moment contributed by the surfaces of a three-dimensional crystallite - assumed to be insulating in the bulk as well as on all surface facets, with trivial Chern invariants in the bulk. The geometric component of this subextensive moment is given by its derivative with respect to the chemical potential, at zero temperature and zero field, per unit surface area, and hence corresponds to the surface magnetic compressibility. The sum of the surface compressibilities contributed by two opposite facets of a cube-shaped crystallite is quantized to an integer multiple of the fundamental constant e/hc; this integer is in one-to-one correspondence with the net chirality of hinge modes on the surface of the crystallite, manifesting a link with higher-order topology. The contribution by a single facet to the magnetic compressibility need not be quantized to integers; however, symmetry and/or Hilbert-space constraints can fix the single-facet compressibility to half-integer multiples of e/hc, as will be exemplified by the Hopf insulator.

Original languageEnglish (US)
Article number014417
JournalPhysical Review B
Issue number1
StatePublished - Jan 13 2021
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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