Narrow depression in the density of states at the Dirac point in disordered graphene

Abstract

The electronic properties of non-interacting particles moving on a two-dimensional bricklayer lattice are investigated numerically. In particular, the influence of disorder in form of a spatially varying random magnetic flux is studied. In addition, a strong perpendicular constant magnetic field B is considered. The density of states ρ(E) goes to zero for E → 0 as in the ordered system, but with a much steeper slope. This happens for both cases: at the Dirac point for B = 0 and at the center of the central Landau band for finite B. Close to the Dirac point, the dependence of ρ(E) on the system size, on the disorder strength, and on the constant magnetic flux density is analyzed and fitted to an analytical expression proposed previously in connection with the thermal quantum Hall effect. Additional short-range on-site disorder completely replenishes the indentation in the density of states at the Dirac point.

Shape of the zeroth Landau level in graphene with nondiagonal disorder

“…The broadening of LLs in graphene due to nondiagonal disorder has been studied numerically in Refs. [20][21][22][23][24][25][26][27]. The results of simulations in all the above papers are consistent with each other.…”

“…Under the assumption adopted above, that the disorder h 2 (x, y) is weak, the shape of the density of states de-velops a sharp feature at small energies, as illustrated in Fig. 2, which is somewhat reminiscent of the numerical data [20][21][22][23][24][25][26][27] , but does not capture the robust low-energy behavior revealed in these papers. We argue that the reason of the discrepancy lies in the fact that we disregarded the energy dependence of the matrix element (h 2 ) ν,ν .…”

Correlated random hopping disorder in graphene at high magnetic fields: Landau level broadening and localization properties

“…In contrast, the PR peaks are almost independent of system size, provided the lattice dimensions exceed both the magnetic and correlation lengths, indicating that the states in these energy regions are extended (critical). previously observed and discussed for uncorrelated random hopping disorder 21,24 (and for the similar case of uncorrelated random magnetic flux disorder 31,32 ). The novel and interesting aspect we observe here is that the splitting is rather robust and survives even the sharp width reduction of the n=0 LL due to the increasing correlation length.…”

“…Regarding the localization properties of the lowest LL, numerical simulations using uncorrelated hopping disorder 21,24 and white-noise random magnetic flux disorder 31,32 observe an interesting distinct qualitative feature in the quantum Hall spectrum of graphene, namely, a splitting. It was found that, in such chiral disorder models, the lowest LL splits into two Gaussian shaped peaks, even in the absence of both a Zeeman term and electron-electron interactions.…”

Electron transfer kinetics on natural crystals of MoS2 and graphite

“…5 The difference in kinetics between the cleaved and aged samples therefore suggests modification of the surface via airborne contaminants or oxidation and subsequent depression of the DOS in the uppermost layers of the electrode. 87,[89][90][91] Worded differently, despite the low DOS, the electrode kinetics on bulk graphite should still be independent of the redox potential (and therefore also applied potential). Despite the significant electroactivity, rate constants on in situ cleaved graphite are still 2 -3 orders of magnitude lower than values predicted from Marcus theory for an outersphere process on a metallic electrode.…”