Non-vanishing Density of States in Disordered Weyl Semimetals
Abstract
There is disagreement in the literature concerning whether the nodal point of a three-dimensional Weyl semimetal survives weak short-range disorder: instanton calculations including fluctuations claim that the zero-energy density of states ρ(0) vanishes, while exact numerics find a systematically finite number. We settle this disagreement with a full saddle-point calculation, including both instanton and fluctuations. Within the supersymmetric formulation for disorder, the instanton obeys a nonlinear Weyl equation whose solution is an exact j=1/2 hedgehog whose full functional form we numerically compute. We then compute the fluctuations about this saddle point, carefully identifying all zero modes, and computing the reduced superdeterminant as a convergent Fredholm determinant. No fermionic zero mode beyond a Kramers doublet exists, and at finite disorder w, the fluctuations become a finite one-loop prefactor, ρ(0)=𝒜 w−4 exp(−s*/w2)(1+O(w2)), in normalized units with s* = 6.4163(2) and 𝒜 = 27.47(8) for Gaussian-correlated disorder. This expression matches exact numerics on a single Weyl cone over four orders of magnitude with no fitted parameters (the amplitude is × 0.76 the one-loop value), establishing that the density of states is finite for any disorder strength.
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BibTeX
@misc{wilson2026nonvanishing,
title = {{Non-vanishing Density of States in Disordered Weyl Semimetals}},
author = {Justin H. Wilson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30372},
eprint = {2609.30372},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30372},
}
RIS
TY - UNPB
TI - Non-vanishing Density of States in Disordered Weyl Semimetals
AU - Justin H. Wilson
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30372
UR - https://arxiv.org/abs/2609.30372
AB - There is disagreement in the literature concerning whether the nodal point of a three-dimensional Weyl semimetal survives weak short-range disorder: instanton calculations including fluctuations claim that the zero-energy density of states ρ(0) vanishes, while exact numerics find a systematically finite number. We settle this disagreement with a full saddle-point calculation, including both instanton and fluctuations. Within the supersymmetric formulation for disorder, the instanton obeys a nonlinear Weyl equation whose solution is an exact j=1/2 hedgehog whose full functional form we numerically compute. We then compute the fluctuations about this saddle point, carefully identifying all zero modes, and computing the reduced superdeterminant as a convergent Fredholm determinant. No fermionic zero mode beyond a Kramers doublet exists, and at finite disorder w, the fluctuations become a finite one-loop prefactor, ρ(0)=𝒜 w^−4 exp(−s^*/w^2)(1+O(w^2)), in normalized units with s^* = 6.4163(2) and 𝒜 = 27.47(8) for Gaussian-correlated disorder. This expression matches exact numerics on a single Weyl cone over four orders of magnitude with no fitted parameters (the amplitude is × 0.76 the one-loop value), establishing that the density of states is finite for any disorder strength.
ER -