Weyl semimetals are topological quantum materials whose low energy excitations emerges as massles Weyl Fermions. They have a band touching point near the Fermi level called Weyl node.
What is actually the energy dispersion relation of Weyl Fermions? More specifically, do we have to consider the band as a linear dispersion relation or as a conduction and valence band which takes the shape of two cones?
I came up with this doubt because if we consider the band dispersion relation as linear, then
$$E_k=C\times (k-k_0)$$(For convenience consider 1D. but I know that Weyl semimetals are three dimensional)
then the effective mass is given by $$m*=\frac{\hbar^2}{\frac{\partial^2E_k}{\partial k^2}}$$
that gives
$$m*=\frac{\hbar^2}{0}=\infty$$
Which contradicts the fact that Weyl Fermions are massless.
But If we consider it as the latter one then the derivative is not defined at the Weyl node? Where am I wrong in my calculations and concepts?