2012/04/30 by Sho Yaida · 19 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Density of states #Exponent #Gaussian #Geometry #Instanton #Invariant (physics) #Mathematical physics #Mathematics #Physics #Power law #Quantum and electron transport phenomena #Quantum mechanics #Scale invariance #Scaling #Statistical physics #Theoretical and Computational Physics #Topological Materials and Phenomena #cond-mat.dis-nn #hep-th
paper · pdf · doi:10.1103/physrevb.93.075120
published in Physical review. B./Physical review. B 93(7) (American Physical Society) · 5 pages
arxiv created 2012/04/30 · openalex publication_date 2016/02/09 · arxiv updated 2016/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Some degree of quenched disorder is present in nearly all solids, and can have a marked impact on their macroscopic properties. A manifestation of this effect is the Lifshitz tail of localized states that then gets attached to the energy spectrum, resulting in the nonzero density of states in the band gap. We present here a systematic approach for deriving the asymptotic behavior of the density of states and of the typical shape of the disorder potentials in the Lifshitz tail. The analysis is carried out first for the well-controlled case of noninteracting particles moving in a Gaussian random potential and then for a broad class of disordered scale-invariant models---pertinent to a variety of systems ranging from semiconductors to semimetals to quantum critical systems. For relevant Gaussian disorder, we obtain the general expression for the density of states deep in the tail, with the rate of exponential suppression governed by the dynamical exponent and spatial dimensions. For marginally relevant disorder, however, we would expect a power-law scaling. We discuss the implications of these results for understanding conduction in disordered materials.