Optical Hall effect in strained graphene

When passing an optical medium in the presence of a magnetic field, the polarization of light can be rotated either when reflected at the surface (Kerr effect) or when transmitted through the material (Faraday rotation). This phenomenon is a direct consequence of the optical Hall effect arising from the light-charge carrier interaction in solid state systems subjected to an external magnetic field, in analogy with the conventional Hall effect. The optical Hall effect has been explored in many thin films and also more recently in 2D layered materials. Here, an alternative approach based on strain engineering is proposed to achieve an optical Hall conductivity in graphene without magnetic field. Indeed, strain induces lattice symmetry breaking and hence can result in a finite optical Hall conductivity. First-principles calculations also predict this strain-induced optical Hall effect in other 2D materials. Combining with the possibility of tuning the light energy and polarization, the strain amplitude and direction, and the nature of the optical medium, large ranges of positive and negative optical Hall conductivities are predicted, thus opening the way to use these atomistic thin materials in novel specific opto-electro-mechanical devices.Comment: 20 pages, 9 figures, submitted for publicatio

Transport Length Scales in Disordered Graphene-based Materials: Strong Localization Regimes and Dimensionality Effects

We report on a numerical study of quantum transport in disordered two dimensional graphene and graphene nanoribbons. By using the Kubo and the Landauer approaches, transport length scales in the diffusive (mean free path, charge mobilities) and localized regimes (localization lengths) are computed, assuming a short range disorder (Anderson-type). In agreement with localization scaling theory, the electronic systems are found to undergo a conventional Anderson localization in the zero temperature limit. Localization lengths in weakly disordered ribbons are found to differ by two orders of magnitude depending on their edge symmetry, but always remain several orders of magnitude smaller than those computed for 2D graphene for the same disorder strength. This pinpoints the role of transport dimensionality and edge effects.Comment: 4 pages, Phys. rev. Lett. (in press

Velocity renormalization and Dirac cone multiplication in graphene superlattices with various barrier edge geometries

The electronic properties of one-dimensional graphene superlattices strongly depend on the atomic size and orientation of the 1D external periodic potential. Using a tight-binding approach, we show that the armchair and zigzag directions in these superlattices have a different impact on the renormalization of the anisotropic velocity of the charge carriers. For symmetric potential barriers, the velocity perpendicular to the barrier is modified for the armchair direction while remaining unchanged in the zigzag case. For asymmetric barriers, the initial symmetry between the forward and backward momentum with respect to the Dirac cone symmetry is broken for the velocity perpendicular (armchair case) or parallel (zigzag case) to the barriers. At last, Dirac cone multiplication at the charge neutrality point occurs only for the zigzag geometry. In contrast, band gaps appear in the electronic structure of the graphene superlattice with barrier in the armchair direction.Comment: 13 pages, 14 figure

Thermal and electronic transport characteristics of highly stretchable graphene kirigami

For centuries, cutting and folding the papers with special patterns have been used to build beautiful, flexible and complex three-dimensional structures. Inspired by the old idea of kirigami (paper cutting), and the outstanding properties of graphene, recently graphene kirigami structures were fabricated to enhance the stretchability of graphene. However, the possibility of further tuning the electronic and thermal transport along the 2D kirigami structures have remained original to investigate. We therefore performed extensive atomistic simulations to explore the electronic, heat and load transfer along various graphene kirigami structures. The mechanical response and thermal transport were explored using classical molecular dynamics simulations. We then used a real-space Kubo-Greenwood formalism to investigate the charge transport characteristics in graphene kirigami. Our results reveal that graphene kirigami structures present highly anisotropic thermal and electrical transport. Interestingly, we show the possibility of tuning the thermal conductivity of graphene by four orders of magnitude. Moreover, we discuss the engineering of kirigami patterns to further enhance their stretchability by more than 10 times as compared with pristine graphene. Our study not only provides a general understanding concerning the engineering of electronic, thermal and mechanical response of graphene but more importantly can be useful to guide future studies with respect to the synthesis of other 2D material kirigami structures, to reach highly flexible and stretchable nanostructures with finely tunable electronic and thermal properties.Comment: 29 pages, 9 figures, 1 supplementary figur

Large phosphorene in-plane contraction induced by interlayer interactions in graphene-phosphorene heterostructures

Intralayer deformation in van der Waals (vdW) heterostructures is generally assumed to be negligible due to the weak nature of the interactions between the layers, especially when the interfaces are found incoherent. In the present work, graphene-phosphorene vdW-heterostructures are investigated with the Density Functional Theory (DFT). The challenge of treating nearly incommensurate (very large) supercell in DFT is bypassed by considering different energetic quantities in the grand canonical ensemble, alternative to the formation energy, in order to take into account the mismatch elastic contribution of the different layers. In the investigated heterostructures, it is found that phosphorene contracts by ~4% in the armchair direction when compared to its free-standing form. This large contraction leads to important changes in term of electronic properties, with the direct electronic optical transition of phosphorene becoming indirect in specific vdW-heterostructures. More generally, such a contraction indicates strong substrate effects in supported or encapsulated phosphorene -neglected hitherto- and paves the way to substrate-controlled stress- tronic in such 2D crystal. In addition, the stability of these vdW-heterostructures are investigated as a function of the rotation angle between the layers and as a function of the stacking composition. The alignment of the specific crystalline directions of graphene and phosphorene is found energetically favored. In parallel, several several models based on DFT-estimated quantities are presented; they allow notably a better understanding of the global mutual accommodation of 2D materials in their corresponding interfaces, that is predicted to be non-negligible even in the case of incommensurate interfaces.Comment: 33 pages, 6 figure

Band widths and gaps from the Tran-Blaha functional : Comparison with many-body perturbation theory

For a set of ten crystalline materials (oxides and semiconductors), we compute the electronic band structures using the Tran-Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TB09) functional. The band widths and gaps are compared with those from the local-density approximation (LDA) functional, many-body perturbation theory (MBPT), and experiments. At the density-functional theory (DFT) level, TB09 leads to band gaps in much better agreement with experiments than LDA. However, we observe that it globally underestimates, often strongly, the valence (and conduction) band widths (more than LDA). MBPT corrections are calculated starting from both LDA and TB09 eigenenergies and wavefunctions. They lead to a much better agreement with experimental data for band widths. The band gaps obtained starting from TB09 are close to those from quasi-particle self-consistent GW calculations, at a much reduced cost. Finally, we explore the possibility to tune one of the semi-empirical parameters of the TB09 functional in order to obtain simultaneously better band gaps and widths. We find that these requirements are conflicting.Comment: 18 pages, 16 figure

First-principles prediction of lattice coherency in van der Waals heterostructures

The emergence of superconductivity in slightly-misaligned graphene bilayer [1] and moir\'e excitons in MoSe$_2$-WSe$_2$ van der Waals (vdW) heterostructures [2] is intimately related to the formation of a 2D superlattice in those systems. At variance, perfect primitive lattice matching of the constituent layers has also been reported in some vdW-heterostructures [3-5], highlighting the richness of interfaces in the 2D world. In this work, the determination of the nature of such interface, from first principles, is demonstrated. To do so, an extension of the Frenkel-Kontorova (FK) model [6] is presented, linked to first-principles calculations, and used to predict lattice coherency for a set of 56 vdW-heterostructures. Computational predictions agree with experiments, when available. New superlattices as well as perfectly-matching interfaces are predicted.Comment: 16 pages, 3 figure

Two-Dimensional Graphene with Structural Defects: Elastic Mean Free Path, Minimum Conductivity, and Anderson Transition

4 páginas, 4 figuras.-- PACS numbers: 73.23. b, 72.15.Rn, 73.43.Qt.-- et al.Quantum transport properties of disordered graphene with structural defects (Stone-Wales and divacancies) are investigated using a realistic π-π* tight-binding model elaborated from ab initio calculations. Mean free paths and semiclassical conductivities are then computed as a function of the nature and density of defects (using an order-N real-space Kubo-Greenwood method). By increasing the defect density, the decay of the semiclassical conductivities is predicted to saturate to a minimum value of 4e2/πh over a large range (plateau) of carrier density (>0.5×1014  cm-2). Additionally, strong contributions of quantum interferences suggest that the Anderson localization regime could be experimentally measurable for a defect density as low as 1%.J.-C. C. and A. L. acknowledge financial support from the FNRS of Belgium. Parts of this work are connected to the Belgian Program on Interuniversity Attraction Poles (PAI6), to the NanoHymo ARC, to the ETSF e-I3 project (Grant No. 211956), and to the NANOSIM-GRAPHENE Project No. ANR-09-NANO-016-01.Peer reviewe

Quantum Transport Length Scales in Silicon-based Semiconducting Nanowires: Surface Roughness Effects

We report on a theoretical study of quantum charge transport in atomistic models of silicon nanowires with surface roughness-based disorder. Depending on the nanowires features (length, roughness profile) various conduction regimes are explored numerically by using efficient real space order N computational approaches of both Kubo-Greenwood and Landauer-Buttiker transport frameworks. Quantitative estimations of the elastic mean free paths, charge mobilities and localization lengths are performed as a function of the correlation length of the surface roughness disorder. The obtained values for charge mobilities well compare with the experimental estimates of the most performant undoped nanowires. Further the limitations of the Thouless relationship between the mean free path and the localization length are outlined.Comment: 13 pages, to appear in PR

Simulation of electronic transport in defective graphene. From point defects to amorphous structures.

Graphene, a one atom-thick membrane, has sparked out intense research activities from both experimental and theoretical sides since almost a decade now. The striking properties of graphene in various fields, such as mechanical, thermal, or electronic transport properties, are intrinsically related to its two-dimensional aspect and to its honeycomb lattice structure yielding both to the peculiar electronics of Dirac Fermions. From the electronic transport point of view, clean graphene samples exhibit particularly long coherence length and high electronic mobility both interesting for devices applications in nanoelecronics. Graphene provide simultaneously a genuine playground for fundamental researches such as exploration of Anderson (anti-)localization phenomena in real two-dimensional systems. In this presentation, simulations of electronic transport in defective graphene membranes are exposed. Employing tight-binding models validated by ab initio calculations, and using a real-space order-N Kubo-Greenwood transport method [1-2], the effect of structural defects disrupting the ideal honeycomb lattice is theoretically investigated. The case of various concentrations of “point defects” or single structural defects such as vacancies and Stone-Wales defects is first studied (Fig.1). Then, electronic and transport properties in the presence of a mixture of different structural defects is examined. Finally, using molecular dynamics simulations, highly defective graphene membranes presenting domains of amorphous graphene structure [3-5] are created (Fig.2), and their transport properties are carefully inspected. Structural defects are found to induce strong resonant scattering states at different energies depending on the nature and the concentration of defects [6-8]. These induced resonant scattering states can yield to extremely short mean free paths and low mobilities. At low temperatures, they also lead to an enhanced contribution of quantum interferences driving to localization phenomena in the quantum transport regime. In case of highly defective graphene membrane, the amorphization of the structure changes the system into a strong two-dimensional Anderson insulator material [9], which could be experimentally confirmed by the observation of a variable range hopping transport behavior at low temperatures. References [1] S. Roche, D. Mayou, Phys. Rev. Lett. 79 (1997) 2518 [2] A. Lherbier, X. Blase, Y.M. Niquet, F. Triozon, S. Roche, Phys. Rev. Lett 101 (2008) 036808 [3] J. Kotakoski, A.V. Krasheninnikov, U. Kaiser, J.C. Meyer, Phys. Rev. Lett 106 (2011) 105505 [4] V. Kapko, D.A. Drabold, M.F. Thorpe, Phys. Status Solidi B 247 (2010) 1197 [5] E. Holmström, J. Fransson, O. Eriksson, R. Lizárraga, B. Sanyal, S. Bhandary, M.I. Katsnelson, Phys. Rev. B 84 (2011) 205414 [6] T.O. Wehling, S. Yuan, A.I. Lichtenstein, A.K. Geim, M.I. Katsnelson, Phys. Rev. Lett. 105 (2010) 056802 [7] Y.V. Skrypnyk, V.M. Loktev, Phys. Rev. B 82 (2010) 085436 [8] A. Lherbier, S.M.-M. Dubois, X. Declerck, S. Roche, Y.M. Niquet, J.-C. Charlier, Phys. Rev. Lett. 106 (2011) 046803 [9] A. Lherbier, S. Roche, O.A. Restrepo, Y.M. Niquet, A. Delcorte, J.-C. Charlier, submitted for publication (2012)