Regular Article

The linear Dirac spectrum and the Weyl states in the Drude-Sommerfeld topological model

¹ Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972 Rio de Janeiro, Brazil
² Instituto de Física “Gleg Wataghin”, Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, São Paulo, Brazil

^a e-mail: mauromdoria@gmail.com

Received: 6 October 2018
Received in final form: 22 January 2019
Published online: 25 March 2019

Abstract

Weyl fermions are shown to exist in a Drude-Sommerfeld topological model (DSTM), that features nearly free carriers in topological protected states under residual collisions. The Weyl fermion features a weak magnetic field around it, produced by its own currents, that dresses it, and is the key to its topological stability. The Weyl fermion state results from a Schroedinger like hamiltonian for particles with spin and magnetic energy which are momentum confined to a layer [M.M. Doria, A. Perali, Europhys. Lett. 119, 21001 (2017)]. The present mechanism for the onset of Weyl fermion breaks the reflection and time symmetries around the layer and displays an energy gap. Much above this gap the spectrum becomes linear (Dirac) and then momentum and spin become orthogonal (zero helicity state, ZHS). The collision time is shown to be renormalized by the inverse of the square of the gap in the linear Dirac spectrum limit. Hence the Weyl fermions are shown to be intrinsically ballistic in this limit. The Weyl fermion own magnetic field, although very weak, cannot be discarded because it yields a non zero Chern-Simons number, which is here calculated in the Dirac limit. The electrical and the thermal conductivities of the Weyl fermions are derived in the framework of a constant relaxation time. The Lorenz number coefficient associated to the Wiedemman-Franz law acquires asymptotic value of 6.5552 times the bulk value of π²∕3.