Speaker
Description
Whether the nodal point of a three-dimensional Weyl semimetal survives weak short-range disorder has been genuinely contested: instanton calculations including fluctuations have claimed that the zero-energy density of states ρ(0) vanishes identically, while exact numerics find it finite. I will show how the question is settled within a controlled saddle-point calculation. In a supersymmetric formulation, the saddle obeys a nonlinear Weyl equation, which I solve in its exact hedgehog j = 1/2 form, and then carry out the fluctuation integral about it in full: every zero mode is accounted for — six bosonic against four fermionic — and the reduced superdeterminant is evaluated as a convergent Fredholm determinant. No fermionic zero mode beyond a Kramers doublet survives to annihilate the result. What emerges is the Nandkishore–Huse–Sondhi form with both its exponent and its absolute prefactor, ρ(0) = A w-4 exp(−s/w2) with s = 6.4163(2) and A = 27.47(8) for Gaussian-correlated disorder, matching exact single-cone numerics over four orders of magnitude with no fitted parameters. The density of states is therefore nonvanishing at any finite disorder strength, and the semimetal–metal transition is avoided rather than critical.