2014/04/25 by V. Haefner, V. Häfner, Johannes Schindler +12 · 43 citations
Materials Science · Mathematics · Physics and Astronomy · #Bipartite graph #Combinatorics #Condensed matter physics #Coupling (piping) #Density of states #Graphene #Graphene research and applications #Materials science #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum and electron transport phenomena #Quantum mechanics #Singularity #Topological Materials and Phenomena #Type (biology) #Vacancy defect #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevlett.113.186802
published in Physical Review Letters 113(18), 186802 (American Physical Society) · References updated only
arxiv created 2014/04/25 · openalex publication_date 2014/10/29 · arxiv updated 2014/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The density of states \ensuremath\varrho(E) of graphene is investigated numerically and within the self-consistent T-matrix approximation in the presence of vacancies within the tight binding model. The focus is on compensated disorder, where the concentration of vacancies nA and nB in both sublattices is the same. Formally, this model belongs to the chiral symmetry class BDI. The nonlinear sigma model predicts for BDI a Gade-type singularity \ensuremath\varrho(E)\ensuremath∼|E|^\ensuremath-1exp[\ensuremath-|log(E)|^\ensuremath-1/x]. Our numerical data are comparable to this result in a preasymptotic regime that gives way, however, at even lower energies to \ensuremath\varrho(E)\ensuremath∼E^\ensuremath-1|log(E)|^\ensuremath-\stackrel\texttildelowx, 1\ensuremath≤\stackrel\texttildelowx<2. We take this finding as evidence that, similar to the case of dirty d-wave superconductors, generic bipartite random hopping models may also exhibit unconventional (strong-coupling) fixed points for certain kinds of randomly placed scatterers if these are strong enough. Our research suggests that graphene with (effective) vacancy disorder is a physical representative of such systems.