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In recent years, predictive computational modeling has become a cornerstone for the study of fundamental electronic, optical, and thermal properties in complex forms of condensed matter, including Dirac and topological materials. The simulation of quantum transport in realistic materials calls for the development of linear scaling, or order-$N$, numerical methods, which then become enabling tools for guiding experimental research and for supporting the interpretation of measurements. In this review, we describe and compare different order-$N$ computational methods that have been developed during the past twenty years, and which have been used extensively to explore quantum transport phenomena in disordered media. We place particular focus on the zero-frequency electrical conductivities derived within the Kubo-Greenwood and Kubo-Streda formalisms, and illustrate the capabilities of these methods to tackle the quasi-ballistic, diffusive, and localization regimes of quantum transport in the noninteracting limit. The fundamental issue of computational cost versus accuracy of various proposed numerical schemes is addressed in depth. We then illustrate the usefulness of these methods with various examples of transport in disordered materials, such as polycrystalline and defected graphene models, 3D metals and Dirac semimetals, carbon nanotubes, and organic semiconductors. Finally, we extend the review to the study of spin dynamics and topological transport, for which efficient approaches for calculating charge, spin, and valley Hall conductivities are described., 54 pages, 31 figures, Invited Review of Physics Reports

In addition to the known pseudomagnetic field, nonuniform strains independently induce a position-dependent Fermi velocity (PDFV) in graphene. Here we demonstrate that, due to the presence of a PDFV, the Dirac fermions on a nonuniform (strained) honeycomb lattice may experiment a sort of magnetic effect, which is linearly proportional to the momentum of the quasiparticle. As a consequence, the quasiparticles have a sublinear dispersion relation. Moreover, we analyze the general consequence of a PDFV on the Klein tunneling of electrons through pseudomagnetic barriers. In particular, we report an anomalous (Klein) tunneling for an electron passing across velocity barriers with magnetic features. Our findings about the effects induced by a PDFV on Dirac fermions in (2D) strained honeycomb lattice could be extended to (3D) Dirac and Weyl semimetals and/or its analogous artificial systems., Comment: 10 pages, 5 figures; final version as published in PRB

We present a theoretical study of electronic and thermal transport in polycrystalline heterostructures combining graphene (G) and hexagonal boron nitride (hBN) grains of varying size and distribution. By increasing the hBN grain density from a few percent to 100%, the system evolves from a good conductor to an insulator, with the mobility dropping by orders of magnitude and the sheet resistance reaching the MΩ regime. The Seebeck coefficient is suppressed above 40% mixing, while the thermal conductivity of polycrystalline hBN is found to be on the order of 30-120 Wm K. These results, agreeing with available experimental data, provide guidelines for tuning G-hBN properties in the context of two-dimensional materials engineering. In particular, while we proved that both electrical and thermal properties are largely affected by morphological features (e.g., by the grain size and composition), we find in all cases that nanometer-sized polycrystalline G-hBN heterostructures are not good thermoelectric materials., J.E.B.-V. acknowledges support from CONACyT (Mexico, D.F.). This work was supported by European Union Seventh Framework Programme under grant agreement 604391 Graphene Flagship (R.M.G.). S.R. acknowledges the Spanish Ministry of Economy and Competitiveness for funding (MAT2012-33911), the Secretaria de Universidades e Investigacion del Departamento de Economia y Conocimiento de la Generalidad de Cataluna, and the Severo Ochoa Program (MINECO SEV-2013-0295). M.P. and L.C. acknowledge Spanish MINECO (FIS2015-64886-C5-3-P) and Generalitat de Catalunya (2014SGR301). B.M. and T.R. greatly acknowledge the financial support by European Research Council for COMBAT project (grant no. 615132).

Chemical functionalization has proven to be a promising means of tailoring the unique properties of graphene. For example, hydrogenation can yield a variety of interesting effects, including a metal-insulator transition or the formation of localized magnetic moments. Meanwhile, graphene grown by chemical vapor deposition is the most suitable for large-scale production, but the resulting material tends to be polycrystalline. Up to now there has been relatively little focus on how chemical functionalization, and hydrogenation in particular, impacts the properties of polycrystalline graphene. In this work, we use numerical simulations to study the electrical properties of hydrogenated polycrystalline graphene. We find a strong correlation between the spatial distribution of the hydrogen adsorbates and the charge transport properties. Charge transport is weakly sensitive to hydrogenation when adsorbates are confined to the grain boundaries, while a uniform distribution of hydrogen degrades the electronic mobility. This difference stems from the formation of the hydrogen-induced resonant impurity states, which are inhibited when the honeycomb symmetry is locally broken by the grain boundaries. These findings suggest a tunability of electrical transport of polycrystalline graphene through selective hydrogen functionalization, and also have implications for hydrogen-induced magnetization and spin lifetime of this material.

The appearance of a pseudo-gap and the build up of states around the Dirac point for doped graphene can be elucidated by an analysis of the density of states spectral moments. Such moments are calculated by using the Cyrot-Lackmann theorem, which highlights the importance of the network local topology. Using this approach, we sum over all disorder realizations up to a certain radius to show how the spectral moments change. As a result, the spectrum becomes unimodal, however, strictly localized states appears at the Dirac point. Such states are important for the magnetic properties of graphene, and are calculated as a function of the doping concentration. By removing these states in the count of the spectral moments, it is finally seen that the density of states increases its bimodal character and the tendency for a pseudo-gap opening. This result is important to understand the trends in the magnetic and electronic properties of doped graphene. In graphene with vacancies, the same ideas can also be useful to isolate in a rough way which effects are due solely to topology.

arXiv:1608.00311v1.-- et al., Recent advances in large-scale synthesis of graphene and other 2D materials have underscored the importance of local defects such as dislocations and grain boundaries (GBs), and especially their tendency to alter the electronic properties of the material. Understanding how the polycrystalline morphology affects the electronic properties is crucial for the development of applications such as flexible electronics, energy harvesting devices or sensors.Wehere report on atomic scale characterization of several GBs and on the structural-dependence of the localized electronic states in their vicinity. Using low temperature scanning tunneling microscopy and spectroscopy, together with tight binding and ab initio numerical simulations we explore GBs on the surface of graphite and elucidate the interconnection between the local density of states and their atomic structure.Weshow that the electronic fingerprints of these GBs consist of pronounced resonances which, depending on the relative orientation of the adjacent crystallites, appear either on the electron side of the spectrum or as an electron-hole symmetric doublet close to the charge neutrality point. These two types of spectral features will impact very differently the transport properties allowing, in the asymmetric case to introduce transport anisotropy which could be utilized to design novel growth and fabrication strategies to control device performance., E.Y.A, G.L and A L-M acknowledge support from DOE-FG02-99ER45742. This work has received funding from the European Union Seventh Framework Programme under grant agreement 604391 Graphene Flagship. S.R. acknowledges the Spanish Ministry of Economy and Competitiveness for funding (MAT2012-33911), the Secretaria de Universidades e Investigacion del Departamento de Economia y Conocimiento de la Generalidad de Cataluna and the Severo Ochoa Program (MINECO SEV-2013-0295). G.A. and O.V.Y. acknowledge support by the Swiss National Science Foundation (grant No. PP00P2_133552) and NCCR Marvel. First-principles calculations have been performed at the Swiss National Supercomputing Centre (CSCS) under project s675. JTF and MB are supported by the Lundbeck Foundation (R95-A10510) and the Center for Nanostructured Graphene (CNG) sponsored by the Danish National Research Foundation (Project DNRF103).

The next-nearest neighbor interaction (NNN) is included in a tight-binding Kubo formula calculation of the electronic spectrum and conductivity of doped graphene. As a result, we observe a wide variation of the behavior of the conductivity, as happens in carbon nanotubes, since the Fermi energy and the resonance peak are not shifted by the same amount when the NNN interaction is included. This finding may have a profound effect on the idea of explaining the minimal conductivity of graphene as a consequence of impurities or defects. Finally, we also estimate the mean free path and relaxation time due to resonant impurity scattering.

Nonuniform strain in graphene induces a position dependence of the Fermi velocity, as recently demonstrated by scanning tunnelling spectroscopy experiments. In this work, we study the effects of a position-dependent Fermi velocity on the local density of states (LDOS) of strained graphene, without and with the presence of a uniform magnetic field. The variation of LDOS obtained from tight-binding calculations is successfully explained by analytical expressions derived within the Dirac approach. These expressions also rectify a rough Fermi velocity substitution used in the literature that neglects the strain-induced anisotropy. The reported analytical results could be useful for understanding the nonuniform strain effects on scanning tunnelling spectra of graphene, as well as when it is exposed to an external magnetic field., Revised version as published in JPCM

An analysis of the electron localization properties in doped graphene is performed by carrying out a numerical multifractal analysis for finite systems of a size smaller than the possible localization length. By obtaining the singularity spectrum of a tight-binding model, it is found that the electron wave functions present a multifractal behavior for systems up to 20 nm. Such multifractality is preserved even for next-to-nearest neighbor hopping interaction, which needs to be taken into account if a comparison with experimental results is desired. States close to the Dirac point have a wider multifractal character than those far from this point as the impurity concentration is increased. The analysis of the results allows one to conclude that in the split-band limit, where impurities act as vacancies, the system can be described well by a chiral orthogonal symmetry class.