Weyl states mean magnetic protectorates (Vol. 49, No. 1)

Electrons in conductors are basically free particles subject to residual collisions, a picture first proposed by Paul Drude in 1900 and later developed by Arnold Sommerfeld in 1927 with quantum concepts. The Drude-Sommerfeld assumption that in between any two collisions the electrons move freely is only approximate since electrons transport charge. While in motion they give rise to an electric current that creates a magnetic field able to influence each other’s trajectories. In the Drude-Sommerfeld scenario this small magnetic field interaction among electrons is simply discarded. However this magnetic field can lead to topologically protected states in case the electrons move in a layer no matter its strength assuming residual collisions. The magnetic field streamlines, created by the electronic motion, form loops that pierce the layer twice. These magnetic field loops are a consequence that electrons occupy Weyl states and yet live in the parabolic band of the Drude-Sommerfeld scenario. Indeed this residual magnetic interaction brings these Weyl states to a higher energy since they acquire magnetic energy. Nevertheless they fall in magnetic protectorates forbid to decay into a lower energy state.

M. M. Doria and A. Perali, Weyl states and Fermi arcs in parabolic bands, EPL 119, 21001 (2017)
[Abstract]