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 non-homogeneous deformations before rupture. Here, we study the effect of large localized strain in the electronic bandstructure of atomically thin MoS 2 . Using photoluminescence imaging, we observe a strain-induced reduction of the direct bandgap, and funneling of photogenerated excitons towards regions of higher strain.To understand these results, we develop a non-uniform tight-binding model to calculate the electronic properties of MoS 2 nanolayers with complex and realistic local strain geometries, finding good agreement with our experimental results.

Black phosphorus exhibits a high degree of band anisotropy. However, we find that its in-plane static screening remains relatively isotropic for momenta relevant to elastic long-range scattering processes. On the other hand, the collective electronic excitations in the system exhibit a strong anisotropy. Band nonparabolicity, due to interband couplings, leads to a plasmon frequency which scales as n β , where n is the carrier concentration, and β < 1 2 . Screening and charge distribution in the out-of-plane direction are also studied using a nonlinear Thomas-Fermi model.

In this paper we present a paradigmatic tight-binding model for single-layer as well as multilayered semiconducting MoS 2 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.

One of the fascinating properties of the new families of two-dimensional crystals is their high stretchability and the possibility to use external strain to manipulate, in a controlled manner, their optical and electronic properties. Strain engineering, understood as the field that study how the physical properties of materials can be tuned by controlling the elastic strain fields applied to it, has a perfect platform for its implementation in the atomically thin semiconducting materials. The object of this review is to give an overview of the recent progress to control the optical and electronics properties of 2D crystals, by means of strain engineering. We will concentrate on semiconducting layered materials, with especial emphasis in transition metal dichalcogenides (MoS2, WS2, MoSe2 and WSe2). The effect of strain in other atomically thin materials like black phosphorus, silicene, etc., is also considered. The benefits of strain engineering in 2D crystals for applications in nanoelectronics and optoelectronics will be revised, and the open problems in the field will be discussed. Contents

√s NN = 5.02 TeV using the ALICE detector at the LHC. The measurement covers the p T interval 0.5 < p T < 12 GeV/c and the rapidity range −1.065 < y cms < 0.135 in the centre-of-mass reference frame. The contribution of electrons from background sources was subtracted using an invariant mass approach. The nuclear modification factor R pPb was calculated by comparing the p T -differential invariant cross section in p-Pb collisions to a pp reference at the same centre-of-mass energy, which was obtained by interpolating measurements at √ s = 2.76 TeV and √ s = 7 TeV. The R pPb is consistent with unity within uncertainties of about 25%, which become larger for p T below 1 GeV/c. The measurement shows that heavy-flavour production is consistent with binary scaling, so that a suppression in the high-p T yield in Pb-Pb collisions has to be attributed to effects induced by the hot medium produced in the final state. The data in p-Pb collisions are described by recent model calculations that include cold nuclear matter effects. IntroductionThe Quark-Gluon Plasma (QGP) [1,2], a colour-deconfined state of strongly-interacting matter, is predicted to exist at high temperature according to lattice Quantum Chromodynamics (QCD) calculations [3]. These conditions can be reached in ultra-relativistic heavy-ion collisions [4][5][6][7][8][9][10]. Charm and beauty (heavy-flavour) quarks are mostly produced in initial hard scattering processes on a very short time scale, shorter than the formation time of the QGP medium [11], and thus experience the full temporal and spatial evolution of the collision. While interacting with the QGP medium, heavy quarks lose energy via elastic and radiative processes [12][13][14]. Heavy-flavour hadrons are therefore well-suited probes to study the properties of the QGP. The effect of energy loss on heavy-flavour production can be characterised via the nuclear modification factor (R AA ) of heavy-flavour hadrons. The R AA is defined as the ratio of the heavy-flavour hadron yield in nucleusnucleus (A-A) collisions to that in proton-proton (pp) collisions scaled by the average number of binary nucleon-nucleon collisions. The R AA is studied differentially as a function of transverse momentum (p T ), rapidity ( y) and collision centrality. It was measured at the Relativistic Heavy Ion Collider (RHIC) [15][16][17][18] and at the Large Hadron Collider (LHC) [19][20][21][22]. At RHIC, in central The interpretation of the measurements in A-A collisions requires the study of heavy-flavour production in p-A collisions, which provides access to cold nuclear matter (CNM) effects. These effects are not related to the formation of a colour-deconfined medium, but are present in case of colliding nuclei (or protonnucleus). An important CNM effect in the initial state is partondensity shadowing or saturation, which can be described using modified parton distribution functions (PDF) in the nucleus [23] or using the Color Glass Condensate (CGC) effective theory [24]. Further CNM effects include energy loss [25] in...

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and (A.C-G.) andres.castellanos@imdea.org KEYWORDS. Black phosphorus, strain engineering, uniaxial strain, local strain, periodic deformation, quantum confinement, optical absorption. This is the post-peer reviewed version of the following article: J. Quereda et al. "Strong modulation of optical properties in black phosphorus through strain-engineered rippling" Nano Letters (2016) DOI:10.1021/acs.nanolett.5b04670 Which has been published in final form at: http://pubs.acs.org/doi/abs/10.1021/acs.nanolett.5b04670 2 ABSTRACT Controlling the bandgap through local-strain engineering is an exciting avenue for tailoring optoelectronic materials. Two-dimensional crystals are particularly suited for this purpose because they can withstand unprecedented non-homogeneous deformations before rupture: one can literally bend them and fold them up almost like a piece of paper. Here, we study multi-layer black phosphorus sheets subjected to periodic stress to modulate their optoelectronic properties. We find a remarkable shift of the optical absorption band-edge of up to ~0.7 eV between the regions under tensile and compressive stress, greatly exceeding the strain tunability reported for transition metal dichalcogenides. This observation is supported by theoretical models which also predict that this periodic stress modulation can yield to quantum confinement of carriers at low temperatures. The possibility of generating large strain-induced variations in the local density of charge carriers opens the door for a variety of applications including photovoltaics, quantum optics and two-dimensional optoelectronic devices. TEXT.The recent isolation of black phosphorus has unleashed the interest of the community working on 2D materials because of its interesting electronic and optical properties: narrow intrinsic gap, ambipolar field effect and high carrier mobility. [1][2][3][4][5][6][7][8][9][10][11][12] Black phosphorus is composed of phosphorus atoms held together by strong bonds forming layers that interact through weak van der Waals forces holding the layers stacked on top of each other. This structure, without surface dangling This is the post-peer reviewed version of the following article: J. Quereda et al. "Strong modulation of optical properties in black phosphorus through strain-engineered rippling" Nano Letters (2016) DOI:10.1021/acs.nanolett.5b04670 Which has been published in final form at: http://pubs.acs.org/doi/abs/10.1021/acs.nanolett.5b04670 3 bonds, allows black phosphorus susceptible to withstand very large localized deformations without breaking (similarly to graphene and MoS2). [13][14][15] Its outstanding mechanical resilience makes black phosphorus a prospective candidate for strain engineering, i.e. the modification of a material's optical/electrical properties by means of mechanical stress. 16 This is in contrast to conventional 3D semiconductors that tend to break for moderate deformations. Very recent theoretical works explore the effect of strain on the band structure and optical properties of black phosp...

Strain engineering has emerged as a powerful tool to modify the optical and electronic properties of two-dimensional crystals. Here we perform a systematic study of strained semiconducting transition metal dichalcogenides. The effect of strain is considered within a full Slater-Koster tight-binding model, which provides us with the band structure in the whole Brillouin zone. From this, we derive an effective low-energy model valid around the K point of the BZ, which includes terms up to second order in momentum and strain. For a generic profile of strain, we show that the solutions for this model can be expressed in terms of the harmonic oscillator and double quantum well models, for the valence and conduction bands respectively. We further study the shift of the position of the electron and hole band edges due to uniform strain. Finally, we discuss the importance of spin-strain coupling in these 2D semiconducting materials.