Quantum transport in chemically functionalized graphene at high magnetic field: defect-induced critical states and breakdown of electron-hole symmetry

Leconte, Nicolás; Ortmann, Frank; Cresti, Alessandro; Charlier, Jean‐Christophe; Roche, Stephan

doi:10.1088/2053-1583/1/2/021001

Cited by 15 publications

(12 citation statements)

References 78 publications

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“…Such an approach should become a useful computational tool to simulate QHE in very large size complex disordered materials such as polycrystalline graphene [44], graphene subjected to weak van der Waals interaction such as by a boron-nitride substrate [45], or other types of disordered two-dimensional materials. It should also allow one to corroborate the formation of zero-energy plateaus of σ xy driven by disorder-induced critical states, and disconnected from degeneracy lifting of Landau levels [26], an issue of genuine fundamental interest in the context of topological interpretation of the quantized conductance.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, we have studied the case of oxidized graphene, and have shown the formation of disorder-induced resonant critical states appearing in the zero-energy Landau level with finite σ xx and suggesting a zero-energy σ xy quantized plateau [26]. The confirmation of such a plateau will demand revising the description of the topological invariant in disordered graphene, an exciting direction of work.…”

Section: Introductionmentioning

confidence: 99%

“…18 The role of disorder in graphene is also debated and the QHE features, with very robust behavior to large disorder 19 , also present additional peculiarities depending on the symmetry breaking aspects conveyed by defects. [20][21][22][23][24] Recently, we have studied the case of oxidized graphene, and have shown the formation of disorder-induced resonant critical states appearing in the zero-energy Landau level with finite σ xx and suggesting a zero-energy σ xy quantized plateau 25 . The confirmation of such a plateau will demand to revise the description of topological invariant in disordered graphene, an exciting direction of work.…”

Section: Introductionmentioning

confidence: 99%

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Efficient linear scaling approach for computing the Kubo Hall conductivity

2015

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We report an order-N approach to compute the Kubo Hall conductivity for disorderd two-dimensional systems reaching tens of millions of orbitals, and realistic values of the applied external magnetic fields (as low as a few Tesla). A time-evolution scheme is employed to evaluate the Hall conductivity σ xy using a wave-packet propagation method and a continued fraction expansion for the computation of diagonal and off-diagonal matrix elements of the Green functions. The validity of the method is demonstrated by comparison of results with brute-force diagonalization of the Kubo formula, using (disordered) graphene as the system of study. This approach to mesoscopic system sizes is opening an unprecedented perspective for so-called reverse engineering in which the available experimental transport data are used to get a deeper understanding of the microscopic structure of the samples. Besides, this will not only allow addressing subtle issues in terms of resistance standardization of large-scale materials (such as wafer scale polycrystalline graphene), but will also enable the discovery of new quantum transport phenomena in complex two-dimensional materials, out of reach with classical methods.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient linear scaling approach for computing the Kubo Hall conductivity

2015

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“…Indeed, SVs locally break the sublattice symmetry and induce stronger localization effects, whereas DVs locally preserve the sublattice symmetry. Both of these defect models retain electron-hole symmetry, which simplifies calculations and analysis of the physics at play, unhindered by the full complexity of density-functional-theory-fitted models, such as for oxygenated graphene [45].…”

Section: Model and Methodsmentioning

confidence: 99%

Unconventional features in the quantum Hall regime of disordered graphene: Percolating impurity states and Hall conductance quantization

et al. 2016

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We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy band gap and Landau-level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large-size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size, and magnetic length, we elucidate the origin of anomalous quantum Hall features as magnetic-fielddependent impurity states, which percolate at some critical energies. These findings shed light on unidentified states and quantum-transport anomalies reported experimentally.

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“…The larger value of σ SC (E ∼ 0) may be related to a low energy behavior, similar to the effect caused by zero-energy modes around lattice monovacancies [50][51][52] . The value of σ 0 actually separates two different transport regimes, which are also identified by scrutinizing the long time behavior of D(E, t) [51][52][53][54][55][56] . As long as σ(E) > σ 0 , the system remains diffusive in a metallic (i.e.…”

Section: Localization Effectsmentioning

confidence: 99%

Quantum transport in graphene in presence of strain-induced pseudo-Landau levels

Settnes¹,

Leconte²,

Vargas³

et al. 2016

2D Mater.

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We report on mesoscopic transport fingerprints in disordered graphene caused by strain-field induced pseudomagnetic Landau levels (pLLs). Efficient numerical real space calculations of the Kubo formula are performed for an ordered network of nanobubbles in graphene, creating pseudomagnetic fields up to several hundreds of Tesla, values inaccessible by real magnetic fields. Strain-induced pLLs yield enhanced scattering effects across the energy spectrum resulting in lower mean free path and enhanced localization effects. In the vicinity of the zeroth order pLL, we demonstrate an anomalous transport regime, where the mean free paths increases with disorder. We attribute this puzzling behavior to the low-energy sub-lattice polarization induced by the zeroth order pLL, which is unique to pseudomagnetic fields preserving time-reversal symmetry. These results, combined with the experimental feasibility of reversible deformation fields, open the way to tailor a metal-insulator transition driven by pseudomagnetic fields.Inhomogeneous lattice deformations in graphene generate an effective gauge field modulating the electronic spectrum 1-3 . However, compared to a real magnetic field, the formation of a pseudomagnetic field preserves time reversal symmetry, having an opposite sign in the two inequivalent K and K' valleys 4-6 . This leads to different behavior than for real magnetic field especially when introducing disorder. Experimentally, scanning-tunneling measurements on graphene nanobubbles have revealed an electronic spectrum consisting of pseudo-Landau levels (pLL), including a zero-energy peak, showing that moderate spatial deformations can introduce pseudomagnetic field values reaching hundreds of Tesla 7-9 . Pseudomagnetic fields (PMF) have also been analyzed in deformed crystals by an atomically controlled arrangement of CO molecules on a gold surface 10 , graphene on Ir with intercalated Pb monolayer islands 11 , or have been harnessed for designing innovative electronic and photonic graphene devices 12-17 .However, the intrinsic quantum transport fingerprints of graphene in presence of pseudomagnetic fields still needs investigation, especially in disordered systems. In particular, random strain fluctuations are believed to be the dominating disorder source in high-quality onsubstrate graphene devices 18,19 . A signature of the pseudomagnetic n = 0 pLL state has been predicted for stretched graphene ribbons in the form of a quadruplet low-energy conductance resonance split by edge-induced valley mixing16 , but its experimental confirmation remains challenging, and the variable range of transport features in deformed graphene still require further indepth exploration.Here we study the effect of pLLs, generated by an ordered network of graphene nanobubbles (or pseudomagnetic dots), using an efficient real space Kubo quantum transport methodology. We consider samples containing electron-hole puddles caused by substrate interactions where the presence of pLLs leads to several anomalous transport features resultin...

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Quantum transport in chemically functionalized graphene at high magnetic field: defect-induced critical states and breakdown of electron-hole symmetry

Cited by 15 publications

References 78 publications

Efficient linear scaling approach for computing the Kubo Hall conductivity

Efficient linear scaling approach for computing the Kubo Hall conductivity

Unconventional features in the quantum Hall regime of disordered graphene: Percolating impurity states and Hall conductance quantization

Quantum transport in graphene in presence of strain-induced pseudo-Landau levels

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