The effects of disorder and interactions on the Anderson transition in doped graphene

Abstract

We undertake an exact numerical study of the effects of disorder on the Anderson localization of electronic states in graphene. Analyzing the scaling behaviors of inverse participation ratio and geometrically averaged density of states, we find that the Anderson metal-insulator transition can be introduced by the presence of quenched random disorder. In contrast with the conventional picture of localization, four mobility edges can be observed for the honeycomb lattice with specific disorder strength and impurity concentration. Considering the screening effects of interactions on disorder potentials, the experimental findings of the scale enlargements of puddles can be explained by reviewing the effects of both interactions and disorder.

Electronic Transport in Graphene with Aggregated Hydrogen Adatoms

“…For hydrogenated graphene, a model based on massless Dirac fermions with δ-function point potentials confirms this prediction of the unitary class, though in 2D systems localization lengths can be strongly energy-dependent and, eventually, very large [13]. However, no unanimous consensus has been reached since experiments on hydrogenated graphene point towards metal-insulator transition, theoretically justified by the presence of electron-hole puddles (2D percolation class) [14][15][16][17].…”

“…For hydrogenated graphene, a model based on massless Dirac fermions with δ-function point potentials confirms this prediction of the unitary class, though in 2D systems localization lengths can be strongly energy-dependent and, eventually, very large [13]. However, no unanimous consensus has been reached since experiments on hydrogenated graphene point towards metal-insulator transition, theoretically justified by the presence of electron-hole puddles (2D percolation class) [14][15][16][17].Early works treating finite concentrations of resonant impurities in graphene assumed that the total scattering cross section deviates little from the incoherent addition of the individual cross sections, for example in the Boltzmann equation framework [18]. This picture is valid for low defect concentrations, low charge-carrier densities, and random adatom distributions.…”

Observation of spin-polarized Anderson state around charge neutral point in graphene with Fe-clusters

“…Here, the presence of the exchange coupling between the itinerant and local spins can further enhance Anderson localization above Kondo temperature 18 . Anderson metal insulator transition (MIT) upon changing carrier density was also predicted when adatoms is on the center of the honeycomb hexagon forming impurity plaquette 11,16 .…”

“…Electron band structure of pristine graphene has been extensively studied over the last decade because of its unusual transport properties 8,9 , and it has been shown that physical properties of graphene can be strongly modified when it is functionalized with various adatoms [10][11][12][13][14][15][16][17][18][19][20][21][22][23] , or proximity effect from heterostructures [24][25][26][27][28][29][30] . Disordered graphene by heavy adatoms could exhibit diverse condensed matter phenomena such as spin Hall effect and QSH state (topological insulator state) due to the instilled spin-orbit coupling and honeycomb lattice distortion.…”

Kernel polynomial method to Anderson transition in disordered β-graphyne

“…For graphene, due to the linear dispersion at the Dirac point, there was debated the issue whether the one-parameter scaling theory can hold [25][26][27][28]. Amini et al study the effect of on-site uncorrelated disorder on the electronic properties of graphene [25], and find that weak disorder can decrease the velocities of Dirac fermions, with extended states remaining.…”