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We analyze the microscopic origin and the physical properties of the superconducting phase recently observed in MoS2. We show how the combination of the valley structure of the conduction band, the density dependence of the screening of the long-range Coulomb interactions, the short-range electronic repulsion, and the relative weakness of the electron-phonon interactions makes possible the existence of a phase where the superconducting order parameter has opposite signs in different valleys, resembling the superconductivity found in the pnictides and cuprates. © 2013 American Physical Society. ; F.G. acknowledges financial support fromMINECO, Spain, through Grant No. FIS2011-23713, and the European Union, through Grant No. 290846. R.R. acknowledges financial support from the Juan de la Cierva Program (MINECO, Spain). E.C. acknowledges the Marie CurieGrant No. PIEF-GA-2009-251904. ; Peer Reviewed

A beam of linearly polarized light transmitted through magnetically biased graphene can have its axis of polarization rotated by several degrees after passing the graphene sheet. This large Faraday effect is due to the action of the magnetic field on graphene's charge carriers. As deformations of the graphene membrane result in pseudomagnetic fields acting on the charge carriers, the effect of random mesoscopic corrugations (ripples) can be described as the exposure of graphene to a random pseudomagnetic field. We aim to clarify the interplay of these typically sample inherent fields with the external magnetic bias field and the resulting effect on the Faraday rotation. In principle, random gauge disorder can be identified from a combination of Faraday angle and optical spectroscopy measurements. ; The research leading to these results has received funding from the European Union Seventh Framework Programme under Grant Agreement No. 604391 Graphene Flagship, from the European Research Council through Grant No. 290846, and from the Ministerio de Economía y Competitividad (MINECO), Spain under Projects No. MAT2014-53432-C5-1-R and No. FIS2014-207432. ; Peer Reviewed

We analyze the interaction at the surface of a three-dimensional (3D) topological insulator among 2D electron states belonging to the Dirac cone close to the point of the Brillouin zone and the Rayleigh surface phonon mode. The model deals with an elastic continuum in the long-wavelength limit, in Random Phase Approximation (RPA). Screening of the electronic polarization is quite effective at small wave vectors. On the other hand, the absence of backscattering for the Dirac electrons at the Fermi surface is partly responsible for the reduced influence of the electron-phonon interaction in renormalizing the phonon dispersion at finite wave vectors. We infer that softening of the Rayleigh mode appears as unlikely, at least for the case of a clean and defect-free surface to which our approximate treatment applies. The dielectric response to virtual excitation of the Rayleigh phonon could drive the electron-electron interaction attractive at low frequencies, but the average weak coupling pairing interaction is found to be too small to induce a surface superconducting instability. © 2013 American Physical Society. ; This work was done with financial support from FP7/2007-2013 under Grant No. 264098-MAMA (Multifunctioned Advanced Materials and Nanoscale Phenomena), MIUR-Italy through Prin-Project 2009 "Nanowire high critical temperature superconductor field-effect devices," as well as the Helmholtz Virtual Insitute "New States of Matter." V.P. and F.G. acknowledge financial support from MINECO, Spain, through Grant No. FIS2011-23713, and the European Union, through Grant No. 290846. ; Peer Reviewed

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license. ; The scattering of Dirac electrons by topological defects could be one of the most relevant sources of resistance in graphene and at the boundary surfaces of a three-dimensional topological insulator (3D TI). In the long wavelength, continuous limit of the Dirac equation, the topological defect can be described as a distortion of the metric in curved space, which can be accounted for by a rotation of the Gamma matrices and by a spin connection inherited with the curvature. These features modify the scattering properties of the carriers. We discuss the self-energy of defect formation with this approach and the electron cross-section for intra-valley scattering at an edge dislocation in graphene, including corrections coming from the local stress. The cross-section contribution to the resistivity, ρ, is derived within the Boltzmann theory of transport. On the same lines, we discuss the scattering of a screw dislocation in a two-band 3D TI, like Bi1-xSbx, and we present the analytical simplified form of the wavefunction for gapless helical states bound at the defect. When a 3D TI is sandwiched between two even-parity superconductors, Dirac boundary states acquire superconductive correlations by proximity. In the presence of a magnetic vortex piercing the heterostructure, two Majorana states are localized at the two interfaces and bound to the vortex core. They have a half integer total angular momentum each, to match with the unitary orbital angular momentum of the vortex charge. © 2014 by the authors. ; This work was done with financial support from FP7/2007-2013 under the grant no. 264098—MAMA (Multifunctional Advanced Materials and Nanoscale Phenomena), MIUR (Ministero dell' Istruzione, dell' Università e della Ricerca)-Italy through the Prin-Project 2009 "Nanowire high critical temperature superconductor field-effect devices" and Futuro In Ricerca (FIRB)/2013-2015. Vincenzo Parente and Francisco Guinea acknowledge financial support from MINECO (Ministerio Economía y Competitividad), Spain, through grant FIS2011-23713, and the European Union, through grant 290846. ; Peer Reviewed

The benefits of two-dimensional (2D) materials for applications in nanotechnology can be widened by exploiting the intrinsic anisotropy of some of those crystals, being black phosphorus the most well-known example. In this work we demonstrate that the anisotropy of TiS3, which is even stronger than that of black phosphorus, can be tuned by means of strain engineering. Using density functional theory calculations, we find that the ellipticity of the valence band can be inverted under moderate compressive strain, which is accompanied by an enhancement of the optical absorption. It is shown that the strain tuning of the band anisotropy can be exploited to focus plasmons in the desired direction, a feature that could be used to design TiS3 nanostructures with switchable plasmon channeling. ; This work has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) through the ERC Advanced Grant NOVGRAPHENE (GA No. 290846), European Commission under the Graphene Flagship, Contract CNECTICT-604391, the Spanish MINECO (through Grant Nos. FIS2015-64886-C5-4-P, FIS2014- 58445-JIN, Ramon y Cajal Program RYC-2016-20663, and ́ the Severo Ochoa Centers of Excellence Program under Grant SEV-2015-0496), and the Generalitat de Catalunya (2017SGR1506). ; Peer reviewed

Adensity functional theory study of NbSe2 single-layers in the normal non-modulated and the 3×3 CDWstates is reported.Weshow that, in the single layer, theCDWbarely affects the Fermi surface of the system, thus ruling out a nesting mechanism as the driving force for the modulation. TheCDW stabilizes levels lying around 1.35 eV below the Fermi level within the Se-based valence band but having a substantial Nb–Nb bonding character. The absence of interlayer interactions leads to the suppression of the pancake-like portion of the bulk Fermi surface in the single-layer.Weperform scanning tunneling microscopy simulations and find that the images noticeably change with the sign and magnitude of the voltage bias. The atomic corrugation of the Se sublayer induced by the modulation plays a primary role in leading to these images, but the electronic reorganization also has an important contribution. The analysis of the variation of these images with the bias voltage does not support a Fermi surface nesting mechanism for theCDW. It is also shown that underlying graphene layers (present in some of the recent experimental work) do not modify the conduction band, but do affect the shape of the valence band of NbSe2 single-layers. The relevance of these results in understanding recent physical measurements for NbSe2 single-layers is discussed. Introduction Transition metal dichalcogenides are layered materials, easily exfoliable due to the van der Waals forces linking their layers. They have been the focus of large attention in the past few years because they are ideal systems where to study the influence of the reduced electronic screening brought about by lowering the dimensionality from bulk to layers of different thickness. Among them, 2H-NbSe2 (from now on we will refer to it just as NbSe2) is metallic at room temperature, becomes superconducting (SC) at around 7 K [1, 2] and there are strong indications that it is a twogap superconductor [3–7]. Before reaching the SC state it undergoes a charge density wave (CDW) distortion at around 30 K [8, 9]. The bulk structure of NbSe2 is built from hexagonal layers containing Nb atoms in a trigonal prismatic coordination (see figure 1(a)) [10], but there are also relatively short interlayer Se–Se contacts providing a substantial interlayer coupling. Although ; This work has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) through the ERC Advanced Grant NOVGRAPHENE (GA 290846). Work in Bellaterra was supported by Spanish MINECO (Grant Nos. FIS2015-64886-C5-3-P and FIS2015-64886-C5-4-P, and the Severo Ochoa Centers of Excellence Program under Grants SEV-2013-0295 and SEV-2015-0496), and Generalitat de Catalunya (2014SGR301). We thank M. Ugeda for fruitful discussions. ; Peer reviewed

8 págs.; 7 figs. ; PACS number s : 73.22. f, 73.43. f, 75.75. a ; We develop a long-wavelength approximation in order to describe the low-energy states of carbon nanotubes in a transverse magnetic field. We show that in the limit where the square of the magnetic length l= c eB is much larger than the C-C distance times the nanotube radius R, the low-energy theory is given by the linear coupling of a two-component Dirac spinor to the corresponding vector potential. We investigate in this regime the evolution of the band structure of zigzag nanotubes for values of R l>1, showing that for radius R≈20 nm a clear pattern of Landau levels starts to develop for magnetic field strength B 10 T. The levels tend to be fourfold degenerate, and we clarify the transition to the typical twofold degeneracy of graphene as the nanotube is unrolled to form a curved strip. We show that the dynamics of the Dirac fermions leads to states which are localized at the flanks of the nanotube and that carry chiral currents in the longitudinal direction. We discuss the possibility of observing the quantization of the Hall conductivity in thick carbon nanotubes, which should display steps at even multiples of 2 e2 h, with values doubled with respect to those in the odd-integer quantization of graphene. © 2007 The American Physical Society. ; The financial support of the Ministerio de Educación y Ciencia Spain through Grants Nos. FIS2005-05478-C02- 01/02 and INFN 05-14 is gratefully acknowledged. F.G. acknowledges funding from the European Union under Contract No. 12881 NEST. S.B. and P.O. acknowledge the support of the grant 2006 PRIN "Sistemi Quantistici Macroscopici-Aspetti Fondamentali ed Applicazioni di strutture Josephson Non Convenzionali." E.P. was also supported by INFN under Grant No. 10068. ; Peer Reviewed

In this paper we present a paradigmatic tight-binding model for single-layer as well as multilayered semiconducting MoS2 and similar transition metal dichalcogenides. We show that the electronic properties of multilayer systems can be reproduced in terms of a tight-binding modeling of the single-layer hopping terms by simply adding the proper interlayer hoppings ruled by the chalcogenide atoms. We show that such a tight-binding model makes it possible to understand and control in a natural way the transition between a direct-gap band structure, in single-layer systems, and an indirect gap in multilayer compounds in terms of a momentum/orbital selective interlayer splitting of the relevant valence and conduction bands. The model represents also a suitable playground to investigate in an analytical way strain and finite-size effects. © 2013 American Physical Society. ; F.G. acknowledges financial support from MINECO, Spain, through Grant No. FIS2011-23713, and the European Union, through Grant No. 290846. R.R. acknowledges financial support from the Juan de la Cierva Program (MINECO, Spain). E.C. acknowledge support from the European FP7 Marie Curie Project No. PIEF-GA-2009-251904. J.A.S.-G. and P.O. acknowledge support from Spanish MINECO (Grants No. FIS2009-12721-C04-01, No. FIS2012-37549-C05-02, and No. CSD2007-00050). J.A.S.-G. was supported by an FPI Fellowship from MINECO. ; Peer Reviewed

We analyze the properties of strongly coupled excitons and photons in systems made of semiconducting two-dimensional transition-metal dichalcogenides embedded in optical cavities. Through a detailed microscopic analysis of the coupling, we unveil novel, highly tunable features of the spectrum that result in polariton splitting and a breaking of light-matter selection rules. The dynamics of the composite polaritons is influenced by the Berry phase arising both from their constituents and from the confinement-enhanced coupling. We find that light-matter coupling emerges as a mechanism that enhances the Berry phase of polaritons well beyond that of its elementary constituents, paving the way to achieve a polariton anomalous Hall effect. ; A. G.-R., L. M.-M., and F. G. acknowledge the European Commission under the Graphene Flagship, Contract No. CNECTICT-604391. L. C. and F. G. acknowledge funding from the European Union's Seventh Framework Program (FP7/2007-2013) through the ERC Advanced Grant NOVGRAPHENE (Grant Award No. 290846), and L. C. acknowledges the Comunidad deMadrid through Grant No. MAD2D-CM, S2013/MIT-3007. L. M.-M. and F. J. G.-V. acknowledge financial support by the Spanish MINECO under Contract No. MAT2014-53432-C5. ; Peer reviewed

The electrostatic screening in single and few-layer MoS2 sheets is studied. Electrostatic force microscopy is used to probe the electric field generated by charge impurities in the substrate and incompletely screened by MoS2 sheets. A non-linear Thomas-Fermi theory is employed to interpret the experimental results, demonstrating the important role of the interlayer coupling in the screening of MoS2. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. ; This work was supported by MICINN/MINECO (Spain) through the programs MAT2011-25046 and CONSOLIDER-INGENIO-2010 "Nanociencia Molecular" CSD-2007-00010, Comunidad de Madrid through program Nanobiomagnet S2009/MAT-1726 and the European Union (FP7) through the programs RODIN and ELFOS. E.C. acknowledges a Marie Curie Grant, PIEF-GA-2009-251904. ; Peer Reviewed

Controlling the bandstructure through local-strain engineering is an exciting avenue for tailoring optoelectronic properties of materials at the nanoscale. Atomically thin materials are particularly well-suited for this purpose because they can withstand extreme nonhomogeneous deformations before rupture. Here, we study the effect of large localized strain in the electronic bandstructure of atomically thin MoS2. Using photoluminescence imaging, we observe a strain-induced reduction of the direct bandgap and funneling of photogenerated excitons toward regions of higher strain. To understand these results, we develop a nonuniform tight-binding model to calculate the electronic properties of MoS2 nanolayers with complex and realistic local strain geometries, finding good agreement with our experimental results. © 2013 American Chemical Society. ; This work was supported by the European Union (FP7) through the program RODIN and the Dutch organization for Fundamental Research on Matter (FOM). A.C.-G. acknowledges financial support through the FP7-Marie Curie Project PIEF-GA-2011- 300802 ("STRENGTHNANO"). R.R. acknowledges financial support from the Juan de la Cierva Program (MINECO, Spain). E.C. acknowledges financial support through the FP7-Marie Curie Project PIEF-GA-2009-251904. F.G. and R.R. acknowledge support from MINECO (Spain), through grant FIS2011-23713 and ERC Advanced grant no. 290846. ; Peer Reviewed

We perform systematic investigations of transport through graphene on hexagonal boron nitride (hBN) substrates, together with confocal Raman measurements and a targeted theoretical analysis, to identify the dominant source of disorder in this system. Low-temperature transport measurements on many devices reveal a clear correlation between the carrier mobility μ and the width n* of the resistance peak around charge neutrality, demonstrating that charge scattering and density inhomogeneities originate from the same microscopic mechanism. The study of weak localization unambiguously shows that this mechanism is associated with a long-ranged disorder potential and provides clear indications that random pseudomagnetic fields due to strain are the dominant scattering source. Spatially resolved Raman spectroscopy measurements confirm the role of local strain fluctuations, since the linewidth of the Raman 2D peak-containing information of local strain fluctuations present in graphene-correlates with the value of maximum observed mobility. The importance of strain is corroborated by a theoretical analysis of the relation between μ and n* that shows how local strain fluctuations reproduce the experimental data at a quantitative level, with n* being determined by the scalar deformation potential and μ by the random pseudomagnetic field (consistently with the conclusion drawn from the analysis of weak localization). Throughout our study, we compare the behavior of devices on hBN substrates to that of devices on SiO2 and SrTiO3, and find that all conclusions drawn for the case of hBN are compatible with the observations made on these other materials. These observations suggest that random strain fluctuations are the dominant source of disorder for high-quality graphene on many different substrates, and not only on hexagonal boron nitride. ; A. F. M. gratefully acknowledges support by the Swiss National Science Foundation (SNF) and by the National Center of Competence in Research on Quantum Science and Technology (NCCR QSIT). F. G. acknowledges support from the Spanish Ministry of Economy (MINECO) through Grant No. FIS2011-23713 and the European Research Council (ERC) Advanced Grant (Contract No. 290846). C. S. and S. E. acknowledge experimental help from F. Buckstegge, J. Dauber, B. Terrés, F. Volmer, and M. Drögeler and financial support from Deutsche Forschungsgemeinschaft (DFG) and European Research Council (ERC) (Contract No. 280140). A. F. M., F. G., and C. S. acknowledge funding from the European Union (EU) under the Graphene Flagship.

In recent years, enhanced light-matter interactions through a plethora of dipole-type polaritonic excitations have been observed in two-dimensional (2D) layered materials. In graphene, electrically tunable and highly confined plasmon-polaritons were predicted and observed, opening up opportunities for optoelectronics, bio-sensing and other mid-infrared applications. In hexagonal boron nitride, low-loss infrared-active phonon-polaritons exhibit hyperbolic behaviour for some frequencies, allowing for ray-like propagation exhibiting high quality factors and hyperlensing effects. In transition metal dichalcogenides, reduced screening in the 2D limit leads to optically prominent excitons with large binding energy, with these polaritonic modes having been recently observed with scanning near-field optical microscopy. Here, we review recent progress in state-of-the-art experiments, and survey the vast library of polaritonic modes in 2D materials, their optical spectral properties, figures of merit and application space. Taken together, the emerging field of 2D material polaritonics and their hybrids provide enticing avenues for manipulating light-matter interactions across the visible, infrared to terahertz spectral ranges, with new optical control beyond what can be achieved using traditional bulk materials. ; T.L. acknowledges financial support by DARPA grant award FA8650-16-2-7640. A.C. acknowledges support by CNPq, through the PRONEX/FUNCAP and Science Without Borders programs. J.D.C. acknowledges financial support from the Office of Naval Research that was administered by the NRL Nanoscience Institute. A.K. and N.X.F. acknowledge the financial support by AFOSR MURI (Award No. FA9550-12-1-0488). L.M.M. acknowledges the Spanish Ministry of Economy and Competitiveness under project MAT2014-53432-C5-1-R. F.K. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the 'Severo Ochoa' Programme for Centres of Excellence in R&D (SEV-2015-0522), support by Fundacio Cellex Barcelona, the European Union H2020 Programme under grant agreement no 604391 Graphene Flagship', the ERC starting grant (307806, CarbonLight), and project GRASP (FP7-ICT-2013-613024-GRASP). ; Peer Reviewed