Engineering covalently bonded 2D layered materials by self-intercalation.

Two-dimensional (2D) materials1-5 offer a unique platform from which to explore the physics of topology and many-body phenomena. New properties can be generated by filling the van der Waals gap of 2D materials with intercalants6,7; however, post-growth intercalation has usually been limited to alkali metals8-10. Here we show that the self-intercalation of native atoms11,12 into bilayer transition metal dichalcogenides during growth generates a class of ultrathin, covalently bonded materials, which we name ic-2D. The stoichiometry of these materials is defined by periodic occupancy patterns of the octahedral vacancy sites in the van der Waals gap, and their properties can be tuned by varying the coverage and the spatial arrangement of the filled sites7,13. By performing growth under high metal chemical potential14,15 we can access a range of tantalum-intercalated TaS(Se)y, including 25% Ta-intercalated Ta9S16, 33.3% Ta-intercalated Ta7S12, 50% Ta-intercalated Ta10S16, 66.7% Ta-intercalated Ta8Se12 (which forms a Kagome lattice) and 100% Ta-intercalated Ta9Se12. Ferromagnetic order was detected in some of these intercalated phases. We also demonstrate that self-intercalated V11S16, In11Se16 and FexTey can be grown under metal-rich conditions. Our work establishes self-intercalation as an approach through which to grow a new class of 2D materials with stoichiometry- or composition-dependent properties.

Improved Dielectric Response of Solids: Combining the Bethe-Salpeter Equation with the Random Phase Approximation.

The Bethe-Salpeter equation (BSE) can provide an accurate description of low-energy optical spectra of insulating crystals-even when excitonic effects are important. However, due to high computational costs it is only possible to include a few bands in the BSE Hamiltonian. As a consequence, the dielectric screening given by the real part of the dielectric function can be significantly underestimated by the BSE. Here, we show that universally accurate optical response functions can be obtained by combining a four-point BSE-like equation for the irreducible polarizability with a two-point Dyson equation that includes the higher-lying transitions within the random phase approximation. The new method is referred to as BSE+. It has a computational cost comparable to the BSE but a much faster convergence with respect to the size of the electron-hole basis. We use the method to calculate refractive indices and electron energy loss spectra for a test set of semiconductors and insulators. In all cases the BSE+ yields excellent agreement with experimental data across a wide frequency range and outperforms both the BSE and the random phase approximation.

WSe2 as Transparent Top Gate for Infrared Near-Field Microscopy.

Independent control of carrier density and out-of-plane displacement field is essential for accessing novel phenomena in two-dimensional (2D) material heterostructures. While this is achieved with independent top and bottom metallic gate electrodes in transport experiments, it remains a challenge for near-field optical studies as the top electrode interferes with the optical path. Here, we characterize the requirements for a material to be used as the top-gate electrode and demonstrate experimentally that few-layer WSe2 can be used as a transparent, ambipolar top-gate electrode in infrared near-field microscopy. We carry out nanoimaging of plasmons in a bilayer graphene heterostructure tuning the plasmon wavelength using a trilayer WSe2 gate, achieving a density modulation amplitude exceeding 2 × 1012 cm-2. The observed ambipolar gate-voltage response allows us to extract the energy gap of WSe2, yielding a value of 1.05 eV. Our results provide an additional tuning knob to cryogenic near-field experiments on emerging phenomena in 2D materials and moiré heterostructures.

Indirect Band Gap Semiconductors for Thin-Film Photovoltaics: High-Throughput Calculation of Phonon-Assisted Absorption.

Discovery of high-performance materials remains one of the most active areas in photovoltaics (PV) research. Indirect band gap materials form the largest part of the semiconductor chemical space, but predicting their suitability for PV applications from first-principles calculations remains challenging. Here, we propose a computationally efficient method to account for phonon-assisted absorption across the indirect band gap and use it to screen 127 experimentally known binary semiconductors for their potential as thin-film PV absorbers. Using screening descriptors for absorption, carrier transport, and nonradiative recombination, we identify 28 potential candidate materials. The list, which contains 20 indirect band gap semiconductors, comprises well-established (3), emerging (16), and previously unexplored (9) absorber materials. Most of the new compounds are anion-rich chalcogenides (TiS3 and Ga2Te5) and phosphides (PdP2, CdP4, MgP4, and BaP3) containing homoelemental bonds and represent a new frontier in PV materials research. Our work highlights the previously underexplored potential of indirect band gap materials for optoelectronic thin-film technologies.

A Protocol for Fast Prediction of Electronic and Optical Properties of Donor-Acceptor Polymers Using Density Functional Theory and the Tight-Binding Method.

The ability of donor-acceptor (D-A) type polymers to control the positions of the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals makes them a popular choice for organic solar cell applications. The alternating D-A pattern in a monomer leads to a weak electronic coupling between the constituent monomers within the polymer chain. Exploiting the weak electronic coupling characteristics, we developed a method to efficiently calculate (1) the electronic properties and (2) the optical gap of such polymer chains. The electronic properties (HOMO and LUMO energies, ionization potential, electron affinity, and quasiparticle gap of an oligomer of any length up to an infinitely long polymer) of the D-A polymers are predicted by combining density functional theory calculation results and a tight-binding model. The weak electronic coupling implies that the optical gap of the polymer is size-independent, and thus, it can be calculated using a monomer. We validated the methods using a set of 104 polymers by checking the consistency where the electronic gap of a polymer is larger than the optical gap. Furthermore, we establish relationships between the results obtained from more accurate, yet slower methods (i.e., B3LYP functional, singlet-ΔSCF) with those obtained from the faster counterparts (i.e., BLYP functional, triplet-ΔSCF). Leveraging the found relationships, we propose a way in which the electronic and optical properties of the polymers can be calculated efficiently while retaining high accuracy. The use of the tight-binding model combined with the approach to estimate more accurate results based on less expensive simulations is crucial in the applications where a large volume of computations needs to be carried out efficiently with sufficiently high accuracy, such as high-throughput computational screening or training a machine-learning model.

Fundamental limitation of electrocatalytic methane conversion to methanol.

The electrochemical oxidation of methane to methanol at remote oil fields where methane is flared is the ultimate solution to harness this valuable energy resource. In this study we identify a fundamental surface catalytic limitation of this process in terms of a compromise between selectivity and activity, as oxygen evolution is a competing reaction. By investigating two classes of materials, rutile oxides and two-dimensional transition metal nitrides and carbides (MXenes), we find a linear relationship between the energy needed to activate methane, i.e. to break the first C-H bond, and oxygen binding energies on the surface. Based on a simple kinetic model we can conclude that in order to obtain sufficient activity oxygen has to bind weakly to the surface but there is an upper limit to retain selectivity. Few potentially interesting candidates are found but this relatively simple description enables future large scale screening studies for more optimal candidates.

Interlayer Excitons and Band Alignment in MoS2/hBN/WSe2 van der Waals Heterostructures.

van der Waals heterostructures (vdWH) are ideal systems for exploring light-matter interactions at the atomic scale. In particular, structures with a type-II band alignment can yield detailed insight into carrier-photon conversion processes, which are central to, for example, solar cells and light-emitting diodes. An important first step in describing such processes is to obtain the energies of the interlayer exciton states existing at the interface. Here we present a general first-principles method to compute the electronic quasi-particle (QP) band structure and excitonic binding energies of incommensurate vdWHs. The method combines our quantum electrostatic heterostructure (QEH) model for obtaining the dielectric function with the many-body GW approximation and a generalized 2D Mott-Wannier exciton model. We calculate the level alignment together with intra- and interlayer exciton binding energies of bilayer MoS2/WSe2 with and without intercalated hBN layers, finding excellent agreement with experimental photoluminescence spectra. A comparison to density functional theory calculations demonstrates the crucial role of self-energy and electron-hole interaction effects.

Defect-Tolerant Monolayer Transition Metal Dichalcogenides.

Localized electronic states formed inside the band gap of a semiconductor due to crystal defects can be detrimental to the material's optoelectronic properties. Semiconductors with a lower tendency to form defect induced deep gap states are termed defect-tolerant. Here we provide a systematic first-principles investigation of defect tolerance in 29 monolayer transition metal dichalcogenides (TMDs) of interest for nanoscale optoelectronics. We find that the TMDs based on group VI and X metals form deep gap states upon creation of a chalcogen (S, Se, Te) vacancy, while the TMDs based on group IV metals form only shallow defect levels and are thus predicted to be defect-tolerant. Interestingly, all the defect sensitive TMDs have valence and conduction bands with a very similar orbital composition. This indicates a bonding/antibonding nature of the gap, which in turn suggests that dangling bonds will fall inside the gap. These ideas are made quantitative by introducing a descriptor that measures the degree of similarity of the conduction and valence band manifolds. Finally, the study is generalized to nonpolar nanoribbons of the TMDs where we find that only the defect sensitive materials form edge states within the band gap.

Simple Screened Hydrogen Model of Excitons in Two-Dimensional Materials.

We present a generalized hydrogen model for the binding energies (E_{B}) and radii of excitons in two-dimensional (2D) materials that sheds light on the fundamental differences between excitons in two and three dimensions. In contrast to the well-known hydrogen model of three-dimensional (3D) excitons, the description of 2D excitons is complicated by the fact that the screening cannot be assumed to be local. We show that one can consistently define an effective 2D dielectric constant by averaging the screening over the extend of the exciton. For an ideal 2D semiconductor this leads to a simple expression for E_{B} that only depends on the excitonic mass and the 2D polarizability α. The model is shown to produce accurate results for 51 transition metal dichalcogenides. Remarkably, over a wide range of polarizabilities the binding energy becomes independent of the mass and we obtain E_{B}^{2D}≈3/(4πα), which explains the recently observed linear scaling of exciton binding energies with band gap. It is also shown that the model accurately reproduces the nonhydrogenic Rydberg series in WS_{2} and can account for screening from the environment.

Dielectric Genome of van der Waals Heterostructures.

Vertical stacking of two-dimensional (2D) crystals, such as graphene and hexagonal boron nitride, has recently lead to a new class of materials known as van der Waals heterostructures (vdWHs) with unique and highly tunable electronic properties. Ab initio calculations should in principle provide a powerful tool for modeling and guiding the design of vdWHs, but in their traditional form such calculations are only feasible for commensurable structures with a few layers. Here we show that the dielectric properties of realistic, incommensurable vdWHs comprising hundreds of layers can be efficiently calculated using a multiscale approach where the dielectric functions of the individual layers (the dielectric building blocks) are computed ab initio and coupled together via the long-range Coulomb interaction. We use the method to illustrate the 2D-3D transition of the dielectric function of multilayer MoS2 crystals, the hybridization of quantum plasmons in thick graphene/hBN heterostructures, and to demonstrate the intricate effect of substrate screening on the non-Rydberg exciton series in supported WS2. The dielectric building blocks for a variety of 2D crystals are available in an open database together with the software for solving the coupled electrodynamic equations.

Single-molecule electrochemical transistor utilizing a nickel-pyridyl spinterface.

Using a scanning tunnelling microscope break-junction technique, we produce 4,4'-bipyridine (44BP) single-molecule junctions with Ni and Au contacts. Electrochemical control is used to prevent Ni oxidation and to modulate the conductance of the devices via nonredox gating--the first time this has been shown using non-Au contacts. Remarkably the conductance and gain of the resulting Ni-44BP-Ni electrochemical transistors is significantly higher than analogous Au-based devices. Ab-initio calculations reveal that this behavior arises because charge transport is mediated by spin-polarized Ni d-electrons, which hybridize strongly with molecular orbitals to form a "spinterface". Our results highlight the important role of the contact material for single-molecule devices and show that it can be varied to provide control of charge and spin transport.

Adiabatic-connection fluctuation-dissipation DFT for the structural properties of solids-The renormalized ALDA and electron gas kernels.

We present calculations of the correlation energies of crystalline solids and isolated systems within the adiabatic-connection fluctuation-dissipation formulation of density-functional theory. We perform a quantitative comparison of a set of model exchange-correlation kernels originally derived for the homogeneous electron gas (HEG), including the recently introduced renormalized adiabatic local-density approximation (rALDA) and also kernels which (a) satisfy known exact limits of the HEG, (b) carry a frequency dependence, or (c) display a 1/k(2) divergence for small wavevectors. After generalizing the kernels to inhomogeneous systems through a reciprocal-space averaging procedure, we calculate the lattice constants and bulk moduli of a test set of 10 solids consisting of tetrahedrally bonded semiconductors (C, Si, SiC), ionic compounds (MgO, LiCl, LiF), and metals (Al, Na, Cu, Pd). We also consider the atomization energy of the H2 molecule. We compare the results calculated with different kernels to those obtained from the random-phase approximation (RPA) and to experimental measurements. We demonstrate that the model kernels correct the RPA's tendency to overestimate the magnitude of the correlation energy whilst maintaining a high-accuracy description of structural properties.

Electrochemical control of single-molecule conductance by Fermi-level tuning and conjugation switching.

Controlling charge transport through a single molecule connected to metallic electrodes remains one of the most fundamental challenges of nanoelectronics. Here we use electrochemical gating to reversibly tune the conductance of two different organic molecules, both containing anthraquinone (AQ) centers, over >1 order of magnitude. For electrode potentials outside the redox-active region, the effect of the gate is simply to shift the molecular energy levels relative to the metal Fermi level. At the redox potential, the conductance changes abruptly as the AQ unit is oxidized/reduced with an accompanying change in the conjugation pattern between linear and cross conjugation. The most significant change in conductance is observed when the electron pathway connecting the two electrodes is via the AQ unit. This is consistent with the expected occurrence of destructive quantum interference in that case. The experimental results are supported by an excellent agreement with ab initio transport calculations.

Optimizing porphyrins for dye sensitized solar cells using large-scale ab initio calculations.

In the search for sustainable energy sources, dye sensitized solar cells (DSSCs) represent an attractive solution due to their low cost, relatively high efficiencies, and flexible design. Porphyrin-based dyes are characterized by strong absorption in the visible part of the spectrum and easy customization allowing their electronic properties to be controlled by structural variations. Here we present a computational screening study of more than 5000 porphyrin-based dyes obtained by modifying the porphyrin backbone (metal center and axial ligands), substituting hydrogen by fluorine, and adding different side and anchoring groups. Based on the calculated frontier orbital energies and optical gaps we quantify the energy level alignment with the TiO2 conduction band and different redox mediators. An analysis of the energy level-structure relationship reveals a significant structural diversity among the dyes with the highest level alignment quality, demonstrating the large degree of flexibility in porphyrin dye design. As a specific example of dye optimization, we show that the level alignment of the high efficiency record dye YD2-o-C8 [Yella et al., Science, 2011, 334, 629-634] can be significantly improved by modest structural variations. All the presented data have been stored in a publicly available database.

Cross-conjugation and quantum interference: a general correlation?

We discuss the relationship between the π-conjugation pattern, molecular length, and charge transport properties of molecular wires, both from an experimental and a theoretical viewpoint. Specifically, we focus on the role of quantum interference in the conductance properties of cross-conjugated molecules. For this, we compare experiments on two series of dithiolated wires. The first set we synthesized consists of three dithiolated oligo(phenylene ethynylene) (OPE) benchmark compounds with increasing length. The second series synthesized comprises three molecules with different π-conjugation patterns, but identical lengths, i.e. an anthracene (linear conjugation), an anthraquinone (cross-conjugation), and a dihydroanthracene (broken conjugation) derivative. To benchmark reliable trends, conductance experiments on these series have been performed by various techniques. Here, we compare data obtained by conductive-probe atomic force microscopy (CP-AFM) for self-assembled monolayers (SAMs) with single-molecule break junction and multi-molecule EGaIn data from other groups. For the benchmark OPE-series, we consistently find an exponential decay of the conductance with molecular length characterized by ß = 0.37 ± 0.03 Å(-1) (CP-AFM). Remarkably, for the second series, we do not only find that the linearly conjugated anthracene-containing wire is the most conductive, but also that the cross-conjugated anthraquinone-containing wire is less conductive than the broken-conjugated derivative. We attribute the low conductance values for the cross-conjugated species to quantum interference effects. Moreover, by theoretical modeling, we show that destructive quantum interference is a robust feature for cross-conjugated structures and that the energy at which complete destructive interference occurs can be tuned by the choice of side group. The latter provides an outlook for future devices in this fascinating field connecting chemistry and physics.

Static correlation beyond the random phase approximation: dissociating H2 with the Bethe-Salpeter equation and time-dependent GW.

We investigate various approximations to the correlation energy of a H2 molecule in the dissociation limit, where the ground state is poorly described by a single Slater determinant. The correlation energies are derived from the density response function and it is shown that response functions derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly for intermediate binding distances. A Hubbard model for the dimer allows us to obtain exact analytical results for the various approximations, which is readily compared with the exact diagonalization of the model. Moreover, the model is shown to reproduce all the qualitative results from the ab initio calculations and confirms that BSE greatly improves the RPA and TDHF results despite the fact that the BSE excitation spectrum breaks down in the dissociation limit. In contrast, second order screened exchange gives a poor description of the dissociation limit, which can be attributed to the fact that it cannot be derived from an irreducible response function.

High-throughput computational stacking reveals emergent properties in natural van der Waals bilayers.

Stacking of two-dimensional (2D) materials has emerged as a facile strategy for realising exotic quantum states of matter and engineering electronic properties. Yet, developments beyond the proof-of-principle level are impeded by the vast size of the configuration space defined by layer combinations and stacking orders. Here we employ a density functional theory (DFT) workflow to calculate interlayer binding energies of 8451 homobilayers created by stacking 1052 different monolayers in various configurations. Analysis of the stacking orders in 247 experimentally known van der Waals crystals is used to validate the workflow and determine the criteria for realisable bilayers. For the 2586 most stable bilayer systems, we calculate a range of electronic, magnetic, and vibrational properties, and explore general trends and anomalies. We identify an abundance of bistable bilayers with stacking order-dependent magnetic or electrical polarisation states making them candidates for slidetronics applications.

Computational screening of functionalized zinc porphyrins for dye sensitized solar cells.

An efficient dye sensitized solar cell (DSSC) is one possible solution to meet the world's rapidly increasing energy demands and associated climate challenges. This requires inexpensive and stable dyes with well-positioned frontier energy levels for maximal solar absorption, efficient charge separation, and high output voltage. Here we demonstrate an extensive computational screening of zinc porphyrins functionalized with electron donating side groups and electron accepting anchoring groups. The trends in frontier energy levels versus side groups are analyzed and a no-loss DSSC level alignment quality is estimated. Out of the initial 1029 molecules, we find around 50 candidates with level alignment qualities within 5% of the optimal limit. We show that the level alignment of five zinc porphyrin dyes which were recently used in DSSCs with high efficiencies can be further improved by simple side group substitutions. All frontier energy levels, gaps and level alignment quality values are stored in a database publicly available.

Energy level alignment and quantum conductance of functionalized metal-molecule junctions: density functional theory versus GW calculations.

We study the effect of functional groups (CH3*4, OCH3, CH3, Cl, CN, F*4) on the electronic transport properties of 1,4-benzenediamine molecular junctions using the non-equilibrium Green function method. Exchange and correlation effects are included at various levels of theory, namely density functional theory (DFT), energy level-corrected DFT (DFT+Σ), Hartree-Fock and the many-body GW approximation. All methods reproduce the expected trends for the energy of the frontier orbitals according to the electron donating or withdrawing character of the substituent group. However, only the GW method predicts the correct ordering of the conductance amongst the molecules. The absolute GW (DFT) conductance is within a factor of two (three) of the experimental values. Correcting the DFT orbital energies by a simple physically motivated scissors operator, Σ, can bring the DFT conductances close to experiments, but does not improve on the relative ordering. We ascribe this to a too strong pinning of the molecular energy levels to the metal Fermi level by DFT which suppresses the variation in orbital energy with functional group.

Combining experiments on luminescent centres in hexagonal boron nitride with the polaron model and ab initio methods towards the identification of their microscopic origin.

The two-dimensional material hexagonal boron nitride (hBN) hosts luminescent centres with emission energies of ∼2 eV which exhibit pronounced phonon sidebands. We investigate the microscopic origin of these luminescent centres by combining ab initio calculations with non-perturbative open quantum system theory to study the emission and absorption properties of 26 defect transitions. Comparing the calculated line shapes with experiments we narrow down the microscopic origin to three carbon-based defects: C2CB, C2CN, and VNCB. The theoretical method developed enables us to calculate so-called photoluminescence excitation (PLE) maps, which show excellent agreement with our experiments. The latter resolves higher-order phonon transitions, thereby confirming both the vibronic structure of the optical transition and the phonon-assisted excitation mechanism with a phonon energy ∼170 meV. We believe that the presented experiments and polaron-based method accurately describe luminescent centres in hBN and will help to identify their microscopic origin.