Coupling, merging, and splitting Dirac points by electron-electron interaction

TL;DR

This paper explores how electron-electron interactions can manipulate Dirac points in various dimensions, enabling topological spectrum changes through interaction tuning rather than band structure engineering.

Contribution

It demonstrates that infinitesimal interactions can cause merging, splitting, or gap opening of Dirac points, providing a new method for topological control in materials.

Findings

Interaction induces gap opening or splitting at Dirac points.

Topological spectrum can be tuned by adjusting electron interactions.

Proposes a Weyl-like Hamiltonian for quadratic band-crossing stability.

Abstract

The manipulation and movement of Dirac points in the Brillouin zone by the electron-electron interaction is considered within leading order perturbation theory. At the merging point, an infinitesimal interaction is shown to cause opening of the gap or splitting of the Dirac points, depending on the inter- or intrasublattice nature of the merging and the sign of the interaction. The topology of the spectrum can therefore be efficiently changed by simply tuning the interaction between particles, as opposed to the usual careful band structure engineering. This is illustrated around the merging transition of one, two, and three dimensional Dirac-Weyl fermions. A simple Weyl-like Hamiltonian that describes the quadratic band-crossing in three dimensions is also proposed, and its stability under interactions is addressed.