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arXiv · 2605.03459

Cubic edge dispersion in a semi-Dirac Chern insulator

Marta García Olmos·David Martín Tejedor·Mario Amado·Yuriko Baba·Rafael A. Molina
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Abstract

Topological edge states in Chern insulators are typically characterized by a linear dispersion relation inherited from the Dirac structure of the bulk Hamiltonian. Here we show that this paradigm can be fundamentally altered in systems with anisotropic semi-Dirac band structures. We introduce a minimal two-band lattice model realizing a semi-Dirac Chern insulator and determine its topological phase diagram analytically. Using a mass-domain-wall approach in a semi-infinite geometry, we derive an explicit expression for the chiral edge states and find that their low-energy dispersion scales cubically with momentum, $E(k)\propto k^3$. Numerical diagonalization of the corresponding tight-binding ribbon confirms the analytical prediction. Our results demonstrate that unconventional bulk band structures can produce qualitatively different boundary excitations, providing a route to engineering nonstandard chiral edge dynamics in topological materials and synthetic quantum systems.

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Marta García Olmos, David Martín Tejedor, Mario Amado, Yuriko Baba, Rafael A. Molina. 2026-05-05. Cubic edge dispersion in a semi-Dirac Chern insulator. https://arxiv.org/abs/2605.03459

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