Quoted from http://arxiv.org/abs/1301.0330 :

In 3D lattice model, Weyl points always comes in pairs of opposite helicity; this is the fermion doubling theorem.

Explanation from that paper(in my words):

The integral of Berry flux of any sufficient small surface around a Weyl point is $\pm 2\pi$, depending on its chirality (helicity?). However, the total flux in Brillouin zone has to be zero. Therefore Weyl points must comes into pairs if they exist.

So why the integral of Berry flux around Brillouin zone surface is zero?

Quoted from "Beyond Band Insulators: Topology of Semi-metals and Interacting Phases" by Turner and Vishwanath:

In 3D lattice models, Weyl points always come in pairs of opposite helicity; this is the fermion doubling theorem.

Explanation from that paper  (in my words):

The integral of the Berry flux of any sufficient small surface around a Weyl point is $\pm 2\pi$, depending on its chirality (helicity?). However, the total flux in Brillouin zone has to be zero. Therefore Weyl points must comes into pairs if they exist.

So why is the integral of the Berry flux around the Brillouin zone surface zero?

Quoted from http://arxiv.org/abs/1301.0330 :

In 3D lattice model, Weyl points always comes in pairs of opposite helicity; this is the fermion doubling theorem.

Explanation from that paper(in my words):

The integral of Berry flux of any sufficient surface around a Weyl point is $\pm 2\pi$, depending on its chirality (helicity?). However, the total flux in Brillouin zone has to be zero. Therefore Weyl points must comes into pairs if they exist.

So why the integral of Berry flux around Brillouin zone surface is zero?

Quoted from http://arxiv.org/abs/1301.0330 :

In 3D lattice model, Weyl points always comes in pairs of opposite helicity; this is the fermion doubling theorem.

Explanation from that paper(in my words):

The integral of Berry flux of any sufficient small surface around a Weyl point is $\pm 2\pi$, depending on its chirality (helicity?). However, the total flux in Brillouin zone has to be zero. Therefore Weyl points must comes into pairs if they exist.

So why the integral of Berry flux around Brillouin zone surface is zero?