WSM with broken T symmetry

Weyl semimetals with broken \(\mathcal{T}\) symmetry¶

The simplest setting to discuss a Weyl semimetal is to assume broken Time reversal symmetry, but to preserve inversion. This allows for the minimal number of Weyl nodesWeyl fermions, i.e., two with opposite Chirality. Inversion symmetry guarantees they are at the same energy and furthermore provides a simple criterion to diagnose the existence of Weyl points based on the parity eigenvalues at the TRIM.

\(H(\textbf{k}) = t_z(2-cosk_xa -cosk_ya+\gamma-cosk_za)\tau_z + t_x(sink_xa)\tau_x + t_y(sink_ya)\tau_y\)

for \(-1 < \gamma <1\), we have a pair of Weyl nodes at location \((0,0,\pm k_0)\), where \(cos k_0 =\gamma\)