Topological Weyl Semimetals: Symmetry, Z2 Invariants, and Fermi Arcs — E8 Intelligence Research

FINDING: Weyl semimetals exhibit topologically protected band crossings (Weyl nodes) that require time-reversal symmetry breaking for stabilization, with the Z2 invariant governing surface Fermi arcs. | MATH: Weyl node dispersion \( E(k) = ± v_F |k - k_0| \) (linear, chiral); Chern number \( C = 1/2π∮ B(k) · dS \) per node; Z2 invariant \( ν = 1/2π∮∂ BZ A · dk 2 \); time-reversal operator \( T^2 = -1 \) forces Kramers degeneracy at TRIM points. | CONNECTION: Weyl nodes come in pairs of opposite chirality — the net Chern number sums to zero, mirroring the root system \( A_1 \) (two opposite roots) of SU(2). The three-fold degeneracy mentioned (Vergniory) at \( p \) and \( -p \) under time-reversal suggests a \( Z_3 \) structure, echoing the triality of \( D_4 \) root lattice (24 roots, 3-fold symmetry axes). The lattic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com