Weyl Chirality and Kitaev Topology through Bargmann Invariants

Abstract:We apply a finite-state geometric formulation based on Bargmann invariants to a two-band Weyl Hamiltonian and the one-dimensional Kitaev model of a p-wave superconductor. For the Weyl system, a symmetry-antisymmetrized third-order Bargmann combination selects the chirality-sensitive component of the local pseudospin geometry and extends to a two-band lattice Weyl model. For the Kitaev chain, a normalized ratio involving a third-order Bargmann invariant and a second-order overlap factor removes the dependence on an intermediate state and reproduces the $Z_2$ distinction between its two gapped phases. We further construct a fourth-order loop connecting localized Majorana edge-mode profiles with finite-energy BdG states and an alternating fourth-order loop involving opposite Weyl pseudospin sectors. These constructions illustrate how suitable Bargmann combinations can probe chirality-sensitive, topological, and higher-order geometric information directly through quantum-state overlaps, providing an alternative state-based route without requiring a continuous description of the underlying state-space geometry.

Superconductivity (cond-mat.supr-con); Other Condensed Matter (cond-mat.other); Quantum Physics (quant-ph)

arXiv:2609.25278 [cond-mat.supr-con]

(or arXiv:2609.25278v1 [cond-mat.supr-con] for this version)

https://doi.org/10.48550/arXiv.2609.25278 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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