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Cohomology of Knotted Semimetals in Three Dimensions by Celeste, Joshua is a scholarly article available to read on EtoBox.

What is Cohomology of Knotted Semimetals in Three Dimensions about?

We extend the topological classification scheme of Weyl semimetals via cohomology and the Mayer-Vietoris sequence to account for nodal line semimetals with space-time inversion symmetry. These are semimetals where bands meet generally in 1-dimensional submanifolds, which can generally be knots in $\T^3$. These nodal loops have two charges, the quantized Berry phase and the $\Z_2$-monopole charge, the second related to linking numbers of nodal knots between bands. We provide a manifestly topological proof of the Weyl charge cancellation condition for the $\Z_2$ monopole charge, which is known to be the second Stiefel-Whitney class of a tubular neighbourhood surrounding a Weyl submanifold via the Mayer-Vietoris sequence.

Author

Celeste, Joshua

Published

2023

Language

EN