Broken symmetries and localization lengths in Anderson insulators: Theory and experiment

Pichard, Jean‐Louis; Sanquer, M.; Slevin, Keith; Debray, Philippe

doi:10.1103/physrevlett.65.1812

Cited by 131 publications

(100 citation statements)

References 21 publications

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“…This behavior has not been reported in any strongly localized systems before and appears to be difficult to reconcile with existing theories, which lack such features. Interestingly, l B = 8.5 nm at 9 T becomes comparable to the mean free path (l e = 5 nm at 200 K) and brings in the tantalizing possibility of the Hofstadter regime [24].If the large negative MR in our samples indeed originates from quantum interference effects, it is quite extraordinary that nearly 100% of the resistance of our samples comes from interference. The unusual parameter regime (l e  l B <<   ) our data probe certainly presents several challenges and opportunities to further theoretical studies on this subject.…”

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confidence: 69%

Colossal negative magnetoresistance in dilute fluorinated graphene

et al. 2011

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Adatoms offer an effective route to modify and engineer the properties of graphene.In this work, we create dilute fluorinated graphene using a clean, controlled and reversible approach. At low carrier densities, the system is strongly localized and exhibits an unexpected, colossal negative magnetoresistance. The zero-field resistance is reduced by a factor of 40 at the highest field of 9 T and shows no sign of saturation. Unusual "staircase" field dependence is observed below 5 K. The magnetoresistance is highly anisotropic. We discuss possible origins, considering quantum interference effects and adatom-induced magnetism in graphene.Defects and adsorbates have proven powerful in altering the electronic properties of graphene through doping, scattering and band gap induction [1][2][3][4][5][6][7][8]. In particular, point defects such as vacancies and adatoms can perturb the electronic states of graphene strongly, leading to midgap states [1] and drastic change of transport properties [4][5][6][7][8].With the ability to control the form and density of defects and the assistance of microscopic imaging tools, defect-engineered graphene can be used as model systems to 2 study the complex role of disorder in two dimensions. Moreover, it has been predicted that point defects may also introduce local magnetic moments and magnetic interactions unavailable in pristine graphene. Calculations show that the peculiar nature of Dirac fermions gives rise to ferromagnetic (antiferromagnetic) interactions among moments occupying the same (opposite) graphene sublattice and possible competing magnetic orders [9,10]. Evidence of magnetism in single-layer graphene remains elusive to date. A controllable defect coverage together with in situ wide tunability of the electronic states makes defective graphene an ideal venue to explore the above novel physical phenomena.In this Letter, we create clean, dilute fluorinated graphene (DFG) and report the observation of unexpected, colossal, negative magnetoresistance (MR). As the electron density is reduced to below the density of fluorine adatoms, the system undergoes a transition from weak to strong localization. In the strongly localization regime, a perpendicular magnetic field drastically reduces the DFG resistance by up to 40-fold at 9 T, while an-plane magnetic field causes only a very small positive MR. We compare our data to existing orbital mechanisms and discuss the possibility of magnetism in our samples.Fluorination controls the properties of carbon materials effectively [11]. Fluorine adatoms are chemically simple and stable in ambient conditions. In this study, we work in the extreme dilute limit such that the properties of graphene dominate. Fluorine adatoms are covalently attached to graphene using CF 4 plasma [12]. This fluorination process is nearly completely reversible. We monitor the concentrations of fluorine adatoms and the unintentionally generated vacancies using Raman spectroscopy (Fig. 1a). With a carefully optimized recipe, the number of vacancies is min...

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confidence: 69%

Colossal negative magnetoresistance in dilute fluorinated graphene

et al. 2011

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“…The localization length in the unitary class is known to be twice the localization length in the orthogonal class, at fixed diffusion constant (i.e. at fixed K and e here) [62,63,59]:…”

Section: Orthogonal and Unitary Classmentioning

confidence: 99%

Coherent backscattering and forward-scattering peaks in the quantum kicked rotor

et al. 2017

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Abstract. We propose and analyze an experimental scheme using the quantum kicked rotor to observe the newly-predicted coherent forward scattering peak together with its long-known twin brother, the coherent backscattering peak. Contrary to coherent backscattering, which arises already under weak-localization conditions, coherent forward scattering is only triggered by Anderson or strong localization. So far, coherent forward scattering has not been observed in conservative systems with elastic scattering by spatial disorder. We propose to turn to the quantum kicked rotor, which has a long and succesful history as an accurate experimental platform to observe dynamical localization, i.e., Anderson localization in momentum space. We analyze the coherent forward scattering effect for the quantum kicked rotor by extensive numerical simulations, both in the orthogonal and unitary class of disordered quantum systems, and show that an experimental realization involving phase-space rotation techniques is within reach of state-of-the-art cold-atom experiments.arXiv:1612.02091v1 [cond-mat.quant-gas] 7 Dec 2016Coherent back and forward scattering peaks in the quantum kicked rotor 2

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“…As mentioned above, this increment is expected on general grounds due to the breaking of time reversal symmetry, and the consequent suppression of the interference effects that lead to localization-the magnitude of the increment on 2D systems is not universal unlike the 1D case. 8 In the graphene case in particular, there is also a rather peculiar orbital effect that, as we numerically verified, contributes to the delocalization effect but that it is difficult to disentangle from the previous 'phase factor' effect. Namely, the impurity states are always very close in energy to the 0-LL, which is pinned to the DP.…”

Section: Ri Rjmentioning

confidence: 59%

“…Let us now discuss the effect of a perpendicular magnetic field B. In this case, the resistance is expected first to decrease, as a result of an increase of the localization length, 8 and show a crossover to a different regime when B is large enough so that the magnetic length ℓ B = c/eB gets of the order of ℓ i and the shrinking of the wave function precludes the coupling between impurities, |g r ij (R ij > ℓ B )| ∼ 0. We analyze the regime ℓ B ℓ i using the same methods as above to calculate both ρ and ξ in the presence of B = 0.…”

Section: Ri Rjmentioning

confidence: 99%

“…[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][13][14][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.…”

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confidence: 99%

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

2014

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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...

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Broken symmetries and localization lengths in Anderson insulators: Theory and experiment

Cited by 131 publications

References 21 publications

Colossal negative magnetoresistance in dilute fluorinated graphene

Colossal negative magnetoresistance in dilute fluorinated graphene

Coherent backscattering and forward-scattering peaks in the quantum kicked rotor

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

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