Spectral localization for semimetals and Callias operators

Schulz-Baldes H, Stoiber T (2023)

Publication Type: Journal article

Publication year: 2023


Book Volume: 64

Article Number: 081901

Journal Issue: 8

DOI: 10.1063/5.0093983


A semiclassical argument is used to show that the low-lying spectrum of a self-adjoint operator, the so-called spectral localizer, determines the number of Dirac or Weyl points of an ideal semimetal. Apart from the ion-mobility spectrometer localization procedure, an explicit computation for the local toy models given by a Dirac or Weyl point is the key element of proof. The argument has numerous similarities to Witten’s reasoning leading to the strong Morse inequalities. The same techniques allow to prove a spectral localization for Callias operators associated with potentials with isolated gap-closing points.

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How to cite


Schulz-Baldes, H., & Stoiber, T. (2023). Spectral localization for semimetals and Callias operators. Journal of Mathematical Physics, 64(8). https://dx.doi.org/10.1063/5.0093983


Schulz-Baldes, Hermann, and Tom Stoiber. "Spectral localization for semimetals and Callias operators." Journal of Mathematical Physics 64.8 (2023).

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