# Weyl Semimetal and Dirac semimetal

How to distinguish between a Weyl semimetal and a Dirac semimetal? Which calculations are required to check their existence? Which codes can be used?

Matter Modeling Asked by Shahid Sattar on August 19, 2020

Here are a few thoughts:

### Weyl semimetal

Weyl point. A Weyl point is a point at which 2 bands cross. This places severe constraints on which type of material can host Weyl points, because in materials with both time-reversal and inversion symmetries, bands are already doubly-degenerate (spin up and down have the same energy at every $$mathbf{k}$$-point), so all band crossings will involve 4 (rather than 2) bands and will therefore not be Weyl points. This means that a prerequisite to have a Weyl point is that the material breaks time reversal symmetry (e.g. ferromagnet), or inversion symmetry. The latter futher requires that there is a spin-dependent term in the Hamiltonian to actually split the spin degeneracy of the bands (as inversion symmetry breaking alone is not spin dependent), which can be accomplished with spin-orbit coupling.

Weyl semimetal. A Weyl semimetal is simply a material that has a Weyl point at (or very near) the Fermi energy.

Characterization. A Weyl point is a source or sink (monopole) of Berry curvature, so you can characterize a Weyl point by constructing a surface in $$mathbf{k}$$-space that encloses the Weyl point, and then calculating the Chern number over that surface. It will be $$+1$$ or $$-1$$ for Weyl points, and the sign is called the chirality of the Weyl point.

Codes. Most codes that allow you to calculate topological properties can be used to characterize Weyl points. For example, Z2Pack or WannierTools, both of which have interfaces with some of the major DFT codes.

### Dirac semimetal

A Dirac semimetal is similar to a Weyl semimetal, but now the crossing involves four bands rather than two. This means that the symmetry breaking conditions are not as severe, and a well-known example of a material that hosts Dirac points is graphene. In fact, the very presence of Dirac points in graphene is protected by time-reversal and inversion symmetry (see here).

Answered by ProfM on August 19, 2020

## Related Questions

### Supercell band structure unfolding advantages

2  Asked on December 23, 2020 by tristan-maxson

### How do I predict the structure of a nanoparticle with Calypso and Quantum ESPRESSO?

0  Asked on December 11, 2020

### How many GB of RAM would be needed for VASP to evaluate optical properties of a material?

1  Asked on December 5, 2020 by anibal-bezerra

### Promising functionals for transition metal chemistry

0  Asked on October 21, 2020 by andrew-rosen

### Atom legend in VESTA

1  Asked on September 26, 2020 by achintha-ihalage

### Weyl Semimetal and Dirac semimetal

1  Asked on August 19, 2020 by shahid-sattar

### Great computer graphics for matter modelling

1  Asked on August 11, 2020 by user14717

### I wrote a Python code to do MD for a Lennard-Jones fluid but the VACF is wrong: What might be the problem?

0  Asked on July 22, 2020 by user207526