Partial preservation of chiral symmetry and colossal magnetoresistance in adatom-doped graphene

Abstract

We analyze the electronic properties of adatom doped graphene in the low impurity concentration regime. We focus on the Anderson localized regime and calculate the localization length (ξ) as a function of the electron doping and an external magnetic field. The impurity states hybridize with carbon's pz states and form a partially filled band close to the Dirac point. Near the impurity band center, the chiral symmetry of the system's effective Hamiltonian is partially preserved which leads to a large enhancement of ξ. The sensitivity of transport properties, namely Mott's variable range hopping scale T0, to an external magnetic field perpendicular to the graphene sheet leads to a colossal magnetoresistance effect, as observed in recent experiments. PACS numbers: 73.22.Pr, 72.80.Vp, 71.23.An, 72.20.Ee The peculiar electronic structure of graphene, with chiral quasiparticles behaving as massless Dirac fermions, gives rise to a number of remarkable and counterintuitive phenomena 1 that manifest both in pristine and disordered graphene. In disordered systems, electron localization depends on dimensionality and on the nature of disorder.2,3 Due to the particular symmetries of graphene and the way different types of disorder break these symmetries, the problem of electron localization requires revisiting some of the basic and conceptual issues. 4,5 Much has been done during the last years in this direction and it is now clear that in the absence of short range disorder Dirac fermions elude Anderson localization as in that case the system belongs to the symplectic universality class. Short range disorder due to defects at the atomic scale generates inter-valley mixing and breaks the symplectic symmetry. Within this scenario, the symmetry of functionalized graphene belongs to the orthogonal universality class and, like in other more conventional two-dimensional (2D) systems, Anderson localization might occur. However, properties at zero energy, the Dirac point (DP), are peculiar with adatoms and vacancies leading to different behaviour. [5][6][7] It is well known that the localization properties of 2D materials can be studied by applying a perpendicular (out of plane) magnetic field that suppress the quantum interference effects responsible for the electron localization. 8 The magnetic field can also introduce orbital effects for large fields. [9][10][11] In the case of graphene, one might then expect an anomalous behaviour of the localization 12-15 or the transport properties 16 since the Landau levels (LLs) present an unusual spectrum with the zeroth LL (0-LL) pinned to the DP and a large energy splitting between LLs. In practice short range disorder can be controlled by chemical functionalization, hydrogenation 17,18 and fluorination 16 being among the most studied cases although adsorption of transition metal atoms, oxygen and molecules have also been considered. 19,20 Most of these defects, either adatoms or vacancies, generate resonant states close to the DP 21 and, with the appropriate concentration, may lead t...

Critical Delocalization of Chiral Zero Energy Modes in Graphene

“…Recently, disordered graphene in the chiral symmetry class has been the focus of much attention [10][11][12][13]. In chiral models defined on bipartite lattices, disordered wave functions come in electron-hole pairs with energies AEE linked by a unitary matrix diagonal in the sublattice space, i.e., jϕ AE i¼σ z jϕ ∓ i.…”

Impurities and electronic localization in graphene bilayers

“…As discussed in Ref. [24], the Chebyshev polynomials method becomes numerically inefficient to this end. However, for long distances and low energy, the propagators of the pristine BLG can be evaluates analytically using the continuous approximation.…”

“…We present a model that aims to describe fluorinated BLG, an extension of the model of Ref. [24] used to discuss the experiments of Ref. [13].…”

Impurity states and Localization in Bilayer Graphene: the Low Impurity Concentration Regime

“…To estimate R(ω) we then resort to the method described in Ref. [6]. The impurity propagator matrix G with matrix elements G ij (ω) satisfies the Dyson equation…”

“…The problem of adatoms in graphene has been the subject of an intense activity for they could be used to modify and control the electronic properties of the material. Diluted adatoms or molecules necessarily generates disorder [1] and in some regimes may lead to strong localization of the electronic states [2,3,4,5,6,7]. Electron localization in graphene is quite peculiar, Dirac fermions tend to elude localization in systems with Anderson-type disorder.…”