On the density of states of graphene in the nearest-neighbor approximation

Abstract

We propose an alternative analytical expression for the density of states of a clean graphene in the nearestneighbor approximation. In contrast to the previously known expression, it can be written as a single formula valid for the whole energy range. The correspondence with the previously known expression is shown and the limiting cases are analyzed.

Unpinned Dirac-Fermions in Carbon–Phosphorus–Arsenic-Based Ternary Monolayers

“…Contributions of these two characteristic dispersions to the total DOS are quite different. For Dirac-Fermions in the graphene-like honeycomb lattice, the DOS is directly proportional to the modulus of energy (DOS ∝ | E – E D |). , On the other hand, the DOS for the free particles depends strongly on dimensionality of a given system. In two dimensions, the DOS is independent of energy, and thus, it shows a characteristic step function [DOS ∝ Θ­( E – E P )].…”

Role of the Lifshitz topological transitions in the thermodynamic properties of graphene

“…The two-dimensional nature of graphene should exhibit special types of van Hove singularities and LTTs. This statement is illustrated by the general argument that in two dimensions, the saddle-points produce logarithmic singularities (Table 1), and the spectrum extrema produce finite discontinuities of the electron density of states [also see ref. 49, 53, and 54].…”

“…The analytic expression without derivation for the total DOS in graphene for model (3.7) was provided by Hobson and Nierenberg in 1953. 53 In a recent paper, 54 the expression for this model was derived for the total DOS (per unit hexagonal cell of area ( Fig. 2a ) and one spin component), valid for region 0 < | ε | < 3 γ 0 : where K ( ξ ) is the complete elliptic integral of the first kind, i.e.…”