Broken symmetries, zero-energy modes, and quantum transport in disordered graphene: from supermetallic to insulating regimes

Spectral statistics of multiparametric Gaussian ensembles with chiral symmetry

The statistics of chiral matrix ensembles with uncorrelated but multivariate Gaussian distributed elements is intuitively expected to be driven by many parameters. Contrary to intuition, however, our theoretical analysis reveals the existence of a single parameter, a function of all ensemble parameters, which governs the dynamics of spectral statistics. The analysis not only extends the formulation (known as complexity parameter formulation) for Hermitian ensembles without chirality to those with it but also reveals the underlying connection between chiral complex systems with seemingly different system conditions as well as between other complex systems, e.g., multiparametric Wishart ensembles as well as generalized Calogero-Sutherland Hamiltonians.

Mobility gap and quantum transport in a functionalized graphene bilayer

In a Bernal graphene bilayer, carbon atoms belong to two inequivalent sublattices A and B, with atoms that are coupled to the other layer by [Formula: see text] bonds belonging to sublattice A and the other atoms belonging to sublattice B. We analyze the density of states and the conductivity of Bernal graphene bilayers when atoms of sublattice A or B only are randomly functionalized. We find that for a selective functionalization on sublattice B only, a mobility gap of the order of 0.5 eV is formed close to the Dirac energy at concentration of adatoms [Formula: see text]. In addition, at some other energies conductivity presents anomalous behaviors. We show that these properties are related to the bipartite structure of the graphene layer.

Quantum transport localization through graphene

Localization of atomic defect-induced electronic transport through a single graphene layer is calculated using a full-valence electronic structure description as a function of the defect density and taking into account the atomic-scale deformations of the layer. The elementary electronic destructive interferences leading to Anderson localization are analyzed. The low-voltage current intensity decreases with increasing length and defect density, with a calculated localization length ζ = 3.5 nm for a defect density of 5%. The difference from the experimental defect density of 0.5% required for an oxide surface-supported graphene to obtain the same ζ is discussed, pointing out how interactions of the graphene supporting surface and surface chemical modifications also control electronic transport localization.

Lévy Flights due to Anisotropic Disorder in Graphene

We study transport properties of graphene with anisotropically distributed on-site impurities (adatoms) that are randomly placed on every third line drawn along carbon bonds. We show that stripe states characterized by strongly suppressed backscattering are formed in this model in the direction of the lines. The system reveals Lévy-flight transport in the stripe direction such that the corresponding conductivity increases as the square root of the system length. Thus, adding this type of disorder to clean graphene near the Dirac point strongly enhances the conductivity, which is in stark contrast with a fully random distribution of on-site impurities, which leads to Anderson localization. The effect is demonstrated both by numerical simulations using the Kwant code and by an analytical theory based on the self-consistent T-matrix approximation.

The electronic and transport properties of two-dimensional conjugated polymer networks including disorder

Two-dimensional (2D) conjugated polymers exhibit electronic structures analogous to that of graphene with the peculiarity of π-π* bands which are fully symmetric and isolated. In the present letter, the suitability of these materials for electronic applications is analyzed and discussed. In particular, realistic 2D conjugated polymer networks with a structural disorder such as monomer vacancies are investigated. Indeed, during bottom-up synthesis, these irregularities are unavoidable and their impact on the electronic properties is investigated using both ab initio and tight-binding techniques. The tight-binding model is combined with a real space Kubo-Greenwood approach for the prediction of transport characteristics for monomer vacancy concentrations ranging from 0.5% to 2%. As expected, long mean free paths and high mobilities are predicted for low defect densities. At low temperatures and for high defect densities, strong localization phenomena originating from quantum interferences of multiple scattering paths are observed in the close vicinity of the Dirac energy region while the absence of localization effects is predicted away from this region suggesting a sharp mobility transition. These predictions show that 2D conjugated polymer networks are good candidates to pave the way for the ultimate scaling and performances of future molecular nanoelectronic devices.

Transient unidirectional energy flow and diode-like phenomenon induced by non-Markovian environments

Relying on an exact time evolution scheme, we identify a novel transient energy transfer phenomenon in an exactly-solvable quantum microscopic model consisting of a three-level system coupled to two non-Markovian zero-temperature bosonic baths through two separable quantum channels. The dynamics of this model can be solved exactly using the quantum-state-diffusion equation formalism, demonstrating finite intervals of unidirectional energy flow across the system, typically, from the non-Markovian environment towards the more Markovian bath. Furthermore, when introducing a spatial asymmetry into the system, an analogue of the rectification effect is realized. In the long time limit, the dynamics arrives at a stationary state and the effects recede. Understanding temporal characteristics of directional energy flow will aid in designing microscopic energy transfer devices.

Critical Delocalization of Chiral Zero Energy Modes in Graphene

Graphene subjected to chiral-symmetric disorder is believed to host zero energy modes (ZEMs) resilient to localization, as suggested by the renormalization group analysis of the underlying nonlinear sigma model. We report accurate quantum transport calculations in honeycomb lattices with in excess of 10^{9} sites and fine meV resolutions. The Kubo dc conductivity of ZEMs induced by vacancy defects (chiral BDI class) is found to match 4e(2)/πh within 1% accuracy, over a parametrically wide window of energy level broadenings and vacancy concentrations. Our results disclose an unprecedentedly robust metallic regime in graphene, providing strong evidence that the early field-theoretical picture for the BDI class is valid well beyond its controlled weak-coupling regime.

Electronic transport in graphene with aggregated hydrogen adatoms

Hydrogen adatoms and other species covalently bound to graphene act as resonant scattering centers affecting the electronic transport properties and inducing Anderson localization. We show that attractive interactions between adatoms on graphene and their diffusion mobility strongly modify the spatial distribution, thus fully eliminating isolated adatoms and increasing the population of larger size adatom aggregates. Such spatial correlation is found to strongly influence the electronic transport properties of disordered graphene. Our scaling analysis shows that such aggregation of adatoms increases conductance by up to several orders of magnitude and results in significant extension of the Anderson localization length in the strong localization regime. We introduce a simple definition of the effective adatom concentration x*, which describes the transport properties of both random and correlated distributions of hydrogen adatoms on graphene across a broad range of concentrations.

Sublattice asymmetry of impurity doping in graphene: A review

In this review we highlight recent theoretical and experimental work on sublattice asymmetric doping of impurities in graphene, with a focus on substitutional nitrogen dopants. It is well known that one current limitation of graphene in regards to its use in electronics is that in its ordinary state it exhibits no band gap. By doping one of its two sublattices preferentially it is possible to not only open such a gap, which can furthermore be tuned through control of the dopant concentration, but in theory produce quasi-ballistic transport of electrons in the undoped sublattice, both important qualities for any graphene device to be used competetively in future technology. We outline current experimental techniques for synthesis of such graphene monolayers and detail theoretical efforts to explain the mechanisms responsible for the effect, before suggesting future research directions in this nascent field.

Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point

We explore the longitudinal conductivity of graphene at the Dirac point in a strong magnetic field with two types of short-range scatterers: adatoms that mix the valleys and "scalar" impurities that do not mix them. A scattering theory for the Dirac equation is employed to express the conductance of a graphene sample as a function of impurity coordinates; an averaging over impurity positions is then performed numerically. The conductivity σ is equal to the ballistic value 4e2/πh for each disorder realization, provided the number of flux quanta considerably exceeds the number of impurities. For weaker fields, the conductivity in the presence of scalar impurities scales to the quantum-Hall critical point with σ≃4×0.4e2/h at half filling or to zero away from half filling due to the onset of Anderson localization. For adatoms, the localization behavior is also obtained at half filling due to splitting of the critical energy by intervalley scattering. Our results reveal a complex scaling flow governed by fixed points of different symmetry classes: remarkably, all key manifestations of Anderson localization and criticality in two dimensions are observed numerically in a single setup.

Conductivity of graphene with resonant and nonresonant adsorbates

We propose a unified description of transport in graphene with adsorbates that fully takes into account localization effects and loss of electronic coherence due to inelastic processes. We focus in particular on the role of the scattering properties of the adsorbates and analyze in detail cases with resonant or nonresonant scattering. For both models, we identify several regimes of conduction, depending on the value of the Fermi energy. Sufficiently far from the Dirac energy and at sufficiently small concentrations, the semiclassical theory can be a good approximation. Near the Dirac energy, we identify different quantum regimes, where the conductivity presents universal behaviors.