What is the physical description and $E$-$k$ plots for Dirac Semimetal, Weyl Semimetal, and Magnetic Weyl Semimetal?

Question

I've been trying to get a physical understanding of these three concepts, and any help would be appreciated. So far this is what I understand:

Dirac semi-metals have relativistic quasi-particles (with or without mass), hence the linear dispersion.

Weyl semi-metals are a special class of Dirac semi-metals with zero mass, and in odd-dimensional space (as such they come in opposite chirality).

Magnetic Weyl semi-metals are Weyl semi-metals with broken time-reversal symmetry.

Is this correct? If so, looking at a $E$-$k$ diagram, how would I distinguish between 1 and 2? I believe for Magnetic Weyl semi-metals, the Weyl nodes appear to two different $k$'s, so that is more easily identified.

mike stone · Accepted Answer

The difference between Dirac and Weyl fermions both in particle physics and in condensed matter is that in the Weyl case there is only one allowed spin direction for a given ${bf k}$ and in the Dirac case there are two. For example
$$
H_{rm Weyl}= kappa {boldsymbol sigma}cdot {bf p}
$$
while
$$
H_{rm Dirac}=kappa left[matrix{{boldsymbol sigma}cdot {bf p}&0cr 0& -{boldsymbol sigma}cdot {bf p}}right].
$$
The Dirac case is like a pair of coincident Weyl nodes, with opposite chirality, at a single point in the Brillouin zone. It can be continuously deformed into a pair of opposite chirality at different points.

What is the physical description and $E$-$k$ plots for Dirac Semimetal, Weyl Semimetal, and Magnetic Weyl Semimetal?

One Answer

Add your own answers!

Ask a Question