E. Cappelluti

Local strain engineering in atomically thin MoS2.

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.

Tight-binding model and direct-gap/indirect-gap transition in single-layer and multilayer MoS2

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.

Strain engineering in semiconducting two-dimensional crystals.

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.

Electric‐Field Screening in Atomically Thin Layers of MoS2: the Role of Interlayer Coupling

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.

Dielectric screening in atomically thin boron nitride nanosheets

Two-dimensional (2D) hexagonal boron nitride (BN) nanosheets are excellent dielectric substrate for graphene, molybdenum disulfide, and many other 2D nanomaterial-based electronic and photonic devices. To optimize the performance of these 2D devices, it is essential to understand the dielectric screening properties of BN nanosheets as a function of the thickness. Here, electric force microscopy along with theoretical calculations based on both state-of-the-art first-principles calculations with van der Waals interactions under consideration, and nonlinear Thomas-Fermi theory models are used to investigate the dielectric screening in high-quality BN nanosheets of different thicknesses. It is found that atomically thin BN nanosheets are less effective in electric field screening, but the screening capability of BN shows a relatively weak dependence on the layer thickness.

Electronic properties of single-layer and multilayer transition metal dichalcogenides MX2 (M = Mo, W and X = S, Se)

Single- and few-layer transition metal dichalcogenides have recently emerged as a new family of layered crystals with great interest , not only from the fundamental point of view, but also because of their potential application in ultrathin devices. Here the electronic properties of semiconducting MX2, where M =Mo or W and X = S or Se, are reviewed. Based on of density functional theory calculations, which include the effect of spin-orbit interaction, the band structure of single-layer, bilayer and bulk compounds is discussed. The band structure of these compounds is highly sensitive to elastic deformations, and it is reviewed how strain engineering can be used to manipulate and tune the electronic and optical properties of those materials. Further, the effect of disorder and imperfections in the lattice structure and their effect on the optical and transport properties of MX2 is discussed. The superconducting transition in these compounds, which has been observed experimentally, is analyzed, as well as the different mechanisms proposed so far to explain the pairing. Finally, a discussion on the excitonic effects which are present in these systems is included.

Small Fermi energy and phonon anharmonicity in MgB2 and related compounds

The remarkable anharmonicity of the E_{2g} phonon in MgB_2 has been suggested in literature to play a primary role in its superconducting pairing. We investigate, by means of LDA calculations, the microscopic origin of such an anharmonicity in MgB_2, AlB_2, and in hole-doped graphite. We find that the anharmonic character of the E_{2g} phonon is essentially driven by the small Fermi energy of the sigma holes. We present a simple analytic model which allows us to understand in microscopic terms the role of the small Fermi energy and of the electronic structure. The relation between anharmonicity and nonadiabaticity is pointed out and discussed in relation to various materials.

Interactions and superconductivity in heavily doped MoS2

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.

Theory of strain in single-layer transition metal dichalcogenides

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.

Small Fermi energy, zero-point fluctuations, and nonadiabaticity in MgB 2

Small Fermi energy effects are induced in MgB2 by the low hole doping in the s bands which are characterized by a Fermi energy E F , 0.5 eV. We show that due to the particularly strong deformation potential relative to the E2g phonon mode, lattice fluctuations are reflected in strong fluctuations in the electronic band structure. Quantum fluctuations associated to the zero-point lattice motion are responsible for an uncertainty of the Fermi energy of the order of the Fermi energy itself, leading to the breakdown of the adiabatic principle underlying the Born-Oppenheimer approximation in MgB2 even if vph/ EF, 0.1˛ 0.2, where vph are the characteristic phonon frequencies. This amounts to a new nonadiabatic regime, which could be relevant to other unconventional superconductors.