PRB.92.075133 Nandini Trivedi

Minimal models for topological Weyl semimetals¶

Phys. Rev. B 95, 075133

Keywords¶

Idea of the paper¶

The theoretical work on topological Weyl semimetals has focused on low-energy effective models of single Weyl nodes. When the chemical potential is shifted slightly away from the nodal energy, the Fermi pockets enclosing the projections of the Weyl nodes are very small. However, in a type II WSM, extended pockets of holes and electrons exist already at the node energy. Doping away from the node energy then results in the surface projections of the Weyl nodes, for typical crystal surfaces, becoming enclosed within large Fermi pockets. Understanding the interplay of these large Fermi pockets and any topological properties associated with the type II nodes can require explicit lattice models, rather than just a low-energy theory.

This paper presents two basic models which can be used for type-II WSM. The hydrogen-like atom model has a single pair of Weyl nodes, which share a single electron pocket and a single hole pocket. This model does not capture some important properties. The Helium-like model is proposed, which has an additional term that splits both the electron pocket and the hole pocket into separate pockets.

Summary¶

TIME-REVERSAL-BREAKING MODEL¶

Let \(\hat{H}(\mathbf{k})\) be the Hamiltonian that hosts Weyl nodes and breaks time-reversal symmetry but preserves inversion symmetry, then we have the following condition to be satisfied,

\[\hat{P}^\dagger\hat{H}(-k)\hat{P} = \hat{H}(k), \ \hat{T}^\dagger{H}(-k)\hat{T} \ne \hat{H}(k)\]

Hydrogen-like atom model

The simplest possible two-node time-reversal-breaking Hamiltonian with type II tilt is written as,