Cubic edge dispersion in a semi-Dirac Chern insulator

TL;DR

This paper introduces a semi-Dirac Chern insulator model where edge states exhibit a cubic dispersion relation, challenging the typical linear behavior in topological insulators.

Contribution

It presents a minimal lattice model with an analytical phase diagram and explicit edge state expressions showing cubic dispersion, supported by numerical validation.

Findings

Edge states have a cubic dispersion relation, E(k) ∝ k^3.

Analytical and numerical methods confirm the unconventional edge behavior.

The model demonstrates how anisotropic band structures affect boundary excitations.

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.