Graphene-Like Two-Dimensional Materials

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

The optical properties of graphene and emerging two-dimensional materials including transition metal dichalcogenides are reviewed with an emphasis on nanophotonic applications. Two-dimensional materials exhibit diverse electronic properties, ranging from insulating hexagonal boron nitride and semiconducting transition metal dichalcogenides such as molybdenum disulphide, to semimetallic graphene. In this Review, we first discuss the optical properties and applications of various two-dimensional materials, and then cover two different approaches for enhancing their interactions with light: through their integration with external photonic structures, and through intrinsic polaritonic resonances. Finally, we present a narrow-bandgap layered material — black phosphorus — that serendipitously bridges the energy gap between the zero-bandgap graphene and the relatively large-bandgap transition metal dichalcogenides. The plethora of two-dimensional materials and their heterostructures, together with the array of available approaches for enhancing the light–matter interaction, offers the promise of scientific discoveries and nanophotonics technologies across a wide range of the electromagnetic spectrum.

Two-dimensional material nanophotonics

Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, Delta SCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.

https://iopscience.iop.org/article/10.1088/0953-8984/22/25/253202/pdf

Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

Density functional theory for transition metals and transition metal chemistry

We investigate band-gap tuning in bilayer transition-metal dichalcogenides by external electric fields applied perpendicular to the layers. Using density functional theory, we show that the fundamental band gap of MoS${}_{2}$, MoSe${}_{2}$, MoTe${}_{2}$, and WS${}_{2}$ bilayer structures continuously decreases with increasing applied electric fields, eventually rendering them metallic. We interpret our results in the light of the giant Stark effect and obtain a robust relationship, which is essentially characterized by the interlayer spacing, for the rate of change of band gap with applied external field. Our study expands the known space of layered materials with widely tunable band gaps beyond the classic example of bilayer graphene and suggests potential directions for fabrication of novel electronic and photonic devices.

Tunable band gaps in bilayer transition-metal dichalcogenides

We investigate the electronic and magnetic properties of Mn-doped monolayer MoS${}_{2}$ using a combination of first-principles density functional theory (DFT) calculations and Monte Carlo simulations. Mn dopants that are substitutionally inserted at Mo sites are shown to couple ferromagnetically via a double-exchange mechanism. This interaction is relatively short ranged, making percolation a key factor in controlling long-range magnetic order. The DFT results are parameterized using an empirical model to facilitate Monte Carlo studies of concentration- and temperature-dependent ordering in these systems, through which we obtain Curie temperatures in excess of room temperature for Mn doping in the range of 10--15$%$. Our studies demonstrate the potential for engineering a new class of atomically thin dilute magnetic semiconductors based on Mn-doped MoS${}_{2}$ monolayers.

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Mn-doped monolayer MoS 2 : An atomically thin dilute magnetic semiconductor

Lately rediscovered orthorhombic black phosphorus (BP) exhibits promising properties for near- and mid-infrared optoelectronics. Although recent electrical measurements indicate that a vertical electric field can effectively reduce its transport bandgap, the impact of the electric field on light-matter interaction remains unclear. Here we show that a vertical electric field can dynamically extend the photoresponse in a 5 nm-thick BP photodetector from 3.7 to beyond 7.7 μm, leveraging the Stark effect. We further demonstrate that such a widely tunable BP photodetector exhibits a peak extrinsic photo-responsivity of 518, 30, and 2.2 mA W-1 at 3.4, 5, and 7.7 μm, respectively, at 77 K. Furthermore, the extracted photo-carrier lifetime indicates a potential operational speed of 1.3 GHz. Our work not only demonstrates the potential of BP as an alternative mid-infrared material with broad optical tunability but also may enable the compact, integrated on-chip high-speed mid-infrared photodetectors, modulators, and spectrometers.

/pdf/widely-tunable-black-phosphorus-mid-infrared-photodetector-y63pepnfp9.pdf

Widely tunable black phosphorus mid-infrared photodetector

We investigate band gap tuning of bilayer graphene between hexagonal boron nitride sheets, by external electric fields. Using density functional theory, we show that the gap is continuously tunable from 0 to 0.2 eV and is robust to stacking disorder. Moreover, boron nitride sheets do not alter the fundamental response from that of free-standing bilayer graphene, apart from additional screening. The calculations suggest that graphene−boron nitride heterostructures could provide a viable route to graphene-based electronic devices.

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Tunable band gaps in bilayer graphene-BN heterostructures

https://absimage.aps.org/image/MAR11/MWS_MAR11-2010-006455.pdf

Doron Naveh

Papers

Tunable band gaps in bilayer transition-metal dichalcogenides

Mn-doped monolayer MoS 2 : An atomically thin dilute magnetic semiconductor

Widely tunable black phosphorus mid-infrared photodetector

Tunable band gaps in bilayer graphene-BN heterostructures

Tunable band gaps in bilayer graphene-BN heterostructures