On the density of states for two-level systems in amorphous solids

Recently proposed distribution functions for the asymmetry (Δ) and tunnel (λ) parameters are used to explore the density of states, ρ(E), for two-level systems (TLS). For intrinsic TLS it is shown that ρ(E) is a slowly increasing function of the tunnel splitting E (∝ E^μ) with 0.2 ≲ μ ≲ 0.5 over a broad energy range as recently predicted. For the distribution parameters believed to be appropriate for the more slowly relaxing extrinsic TLS, TLS_ext, μ ≈ 0 over a comparable energy range. In addition, the results demonstrate that a gap (at low E) in ρ(E) emerges in a natural way from the model. At much higher tunnel splittings, the DOS is shown to turn over yielding a negative slope with the turn over point related to a distribution function parameter for Δ. Comparison of the calculated results with experiment is provided.