Quasiparticle Band Gap Research Articles

Promoting a Weak Coupling of Monolayer MoSe2 Grown on (100)-Faceted Au Foil.

As a two-dimensional semiconductor with many physical properties, including, notably, layer-controlled electronic bandgap and coupled spin-valley degree of freedom, monolayer MoSe2 is a strong candidate material for next-generation opto- and valley-electronic devices. However, due to substrate effects such as lattice mismatch and dielectric screening, preserving the monolayer's intrinsic properties remains challenging. This issue is generally significant for metallic substrates whose active surfaces are commonly utilized to achieve direct chemical or physical vapor growth of the monolayer films. Here, we demonstrate high-temperature-annealed Au foil with well-defined (100) facets as a weakly interacting substrate for atmospheric pressure chemical vapor deposition of highly crystalline monolayer MoSe2. Low-temperature scanning tunneling microscopy/spectroscopy measurements reveal a honeycomb structure of MoSe2 with a quasi-particle bandgap of 1.96 eV, a value comparable with other weakly interacting systems such as MoSe2/graphite. Density functional theory calculations indicate that the Au(100) surface exhibits the preferred energetics to electronically decouple from MoSe2, compared with the (110) and (111) crystal planes. This weak coupling is critical for the easy transfer of monolayers to another host substrate. Our study demonstrates a practical means to produce high-quality monolayers of transition-metal dichalcogenides, viable for both fundamental and application studies.

GW band structure of monolayer MoS2 using the SternheimerGW method and effect of dielectric environment

Monolayers of transition-metal dichalcogenides (TMDs) hold great promise as future nanoelectronic and optoelectronic devices. An essential feature for achieving high device performance is the use of suitable supporting substrates, which can affect the electronic and optical properties of these two-dimensional (2D) materials. Here, we perform many-body GW calculations using the SternheimerGW method to investigate the quasiparticle band structure of monolayer ${\mathrm{MoS}}_{2}$ subject to an effective dielectric screening model, which is meant to approximately describe substrate polarization in real device applications. We show that, within this model, the dielectric screening has a sizable effect on the quasiparticle band gap; for example, the gap renormalization is as large as 250 meV for ${\mathrm{MoS}}_{2}$ with model screening corresponding to ${\mathrm{SiO}}_{2}$. Within the ${\mathrm{G}}_{0}{\mathrm{W}}_{0}$ approximation, we also find that the inclusion of the effective screening induces a direct band gap, in contrast to the unscreened monolayer. We also find that the dielectric screening induces an enhancement of the carrier effective masses by as much as 27% for holes, shifts plasmon satellites, and redistributes quasiparticle weight. Our results highlight the importance of the dielectric environment in the design of 2D TMD-based devices.

Quantum Confinement Effects on Excitonic Properties in the 2D vdW quantum system: The ZnO/WSe2 Case

Quantum confinement effects play important roles in determining the electronic structures and optical properties of 2D quantum systems. Herein, the 2D ZnO/WSe2 van der Waals (vdW) system to study the influence of quantum confinement on excitonic optical properties, considering vdW heterobilayers (HBs), sandwiched trilayers (STs), and superlattice (SL), is taken. First‐principles calculations show that the quasiparticle (QP) bandgap, exciton binding energy, and band alignment depend obviously on quantum confinement. The QP bandgap and exciton binding energy decrease from 2.61 and 0.98 eV (HB) to 2.30 and 0.61 eV (ST), then to 2.02 and 0.28 eV (SL). Moreover, the conduction band offsets can be tuned from 0.87 eV (HB) to 0.79 eV (ST), then to 2.27 eV (SL). In addition, in ZnO/WSe2 vdW HB, increasing interlayer distance from 2.09 to 4.29 Å can induce exciton binding energy increase from 0.77 to 1.02 eV and QP bandgap increase from 2.49 to 2.62 eV. These results may be useful to tune excitonic properties and design optoelectronic devices by forming 2D vdW quantum systems.

Structural and electronic properties of solid molecular hydrogen from many-electron theories

We study the structural and electronic properties of phase III of solid hydrogen using accurate many-electron theories and compare to state-of-the-art experimental findings. The atomic structures of phase III modelled by C2/c-24 crystals are fully optimized on the level of second-order perturbation theory, demonstrating that previously employed structures optimized on the level of approximate density functionals exhibit errors in the H$_2$ bond lengths that cause significant discrepancies in the computed quasi particle band gaps and vibrational frequencies compared to experiment. Using the newly optimized atomic structures, we study the band gap closure and change in vibrational frequencies as a function of pressure. Our findings are in good agreement with recent experimental observations and may prove useful in resolving long-standing discrepancies between experimental estimates of metallization pressures possibly caused by disagreeing pressure calibrations.

Analytical Calculation of Exciton Binding Energy, Quasi-Particle Band Gap and Optical Gap in Strained Mono-layer MoS2

Strain in two-dimensional (2D) materials induces shifts in the visible spectrum due to strained binding energies, an accurate study of which is critical for materials engineering in the design of optoelectronic applications. Different from previous studies that employed computationally demanding theoretical approaches, we present an analytical approach, based on the difference method to calculate the impact of strained binding energy on the optical gap in mono-layer $${\hbox {MoS}}_{2}$$ by exploiting an existing tight binding (TB) and a fractional Coulomb potential model, for strained band gap and binding energy calculation, respectively. The inclusion of strained binding energy, changing at a rate of $$-8.1 \, \hbox {meV}/\bigtriangleup 1\%$$ of biaxial in-plane tensile strain accompanied with a variation of $$-110 \, \hbox {meV}/\bigtriangleup 1\%$$ of strain in the TB band gap, causes the optical gap to alter at a rate of $$-105.3 \, \hbox {meV}/\bigtriangleup 1\%$$ of strain, supported by first-principles calculations and is benchmarked with reported experimental and theoretical values. The effect of strained binding energies causes a blueshift in the optical gap by a correction factor, increasing from $$\approx 0.5\%$$ to $$\approx 12\%$$ , with an increase in equi-biaxial in-plane tensile strain from 1% to 11%, respectively. Furthermore, binding energy sensitivity to strain decreases linearly with a structural change from a mono-layer to a few layers in the 2D regime and saturates in the bulk regime. The presented framework can be used for the calculation of strained binding energies and optical gaps of other 2D materials and thus allows us to tune optical properties of 2D nanomaterials that are sensitive to lattice deformations.

Transfer learning for materials informatics using crystal graph convolutional neural network

For successful applications of machine learning in materials informatics, it is necessary to overcome the inaccuracy of predictions ascribed to insufficient amount of data. In this study, we propose a transfer learning using a crystal graph convolutional neural network (TL-CGCNN). Herein, TL-CGCNN is pretrained with big data such as formation energies for crystal structures, and then used for predicting target properties with relatively small data. We confirm that TL-CGCNN can improve predictions of various properties such as bulk moduli, dielectric constants, and quasiparticle band gaps, which are computationally demanding, to construct big data for materials. Moreover, we quantitatively observe that the prediction of properties in target models via TL-CGCNN becomes more accurate with an increase in size of training dataset in pretrained models. Finally, we confirm that TL-CGCNN is superior to other regression methods in the predictions of target properties, which suffer from small amount of data. Therefore, we conclude that TL-CGCNN is promising along with compiling big data for materials that are easy to accumulate and relevant to the target properties.

Determining Quasiparticle Bandgap of Two-Dimensional Transition Metal Dichalcogenides by Observation of Hot Carrier Relaxation Dynamics.

Using excitation-energy-scanning ultrafast infrared microspectroscopy, the excess energy-dependent hot carrier relaxation dynamics in atomically thin two-dimensional transition metal dichalcogenides (2D TMDs) after femtosecond photoexcitation was directly monitored. A good linear relationship between the carrier relaxation time and the excitation wavelength is observed for all measured monolayer (ML) and bilayer (BL) TMD samples, which allows us to determine their quasiparticle bandgaps as well as corresponding exciton binding energies. A carrier-optical-phonon scattering-mediated cascading-relaxation model is proposed, which can perfectly describe all the measured dynamics. As a consequence, the quasiparticle bandgaps of ML MoSe2, ML MoS2, BL MoSe2, and BL WSe2 are determined to be 2.07, 2.11, 1.67, and 1.81 eV, respectively. Our work reveals a general picture for the hot carrier relaxation dynamics in atomically thin TMDs and offers an effective experimental approach in probing the bandgaps of TMDs under ambient conditions.

Self-consistent T-matrix approach to gap renormalization in quantum magnets with bond disorder

The analytical theory of density of states (DOS) in three-dimensional quantum magnets with the bond disorder is proposed based on the self-consistent T-matrix approximation (SCTMA). It successfully describes the DOS both for resonant and non-resonant scattering, whose emergence is governed by the ratio of scattering length and the average distance between impurities, which concentration is denoted as c. Corrections to the quasiparticle band gap in these cases are shown to scale as c2/3 and c, respectively. Moreover, the theory yields a semi-circle form of the DOS for the bound states inside the gap, which results in highly nontrivial DOS in the intermediate parameter region between the two limiting cases when the band DOS and the semi-circle overlap. Long-wavelength excitations are discussed. In the resonant regime their damping scales as c2/3, which, according to Ioffe-Regel criterion, corresponds to their localization. Applicability of the theory is illustrated by its quantitative agreement with the recent experimental data on spin-dimer system Ba3−xSrxCr2O8.

Coulomb-engineered heterojunctions and dynamical screening in transition metal dichalcogenide monolayers

The manipulation of two-dimensional materials via their dielectric environment offers novel opportunities to control electronic as well as optical properties and allows to imprint nanostructures in a non-invasive way. Here we asses the potential of monolayer semiconducting transition metal dichalcogenides (TMDCs) for Coulomb engineering in a material realistic and quantitative manner. We compare the response of different TMDC materials to modifications of their dielectric surrounding, analyze effects of dynamic substrate screening, i.e. frequency dependencies in the dielectric functions, and discuss inherent length scales of Coulomb-engineered heterojunctions. We find symmetric and rigid-shift-like quasi-particle band-gap modulations for both, instantaneous and dynamic substrate screening. From this we derive short-ranged self energies for an effective multi-scale modeling of Coulomb engineered heterojunctions composed of an homogeneous monolayer placed on a spatially structured substrate. For these heterojunctions, we show that band gap modulations on the length scale of a few lattice constants are possible rendering external limitations of the substrate structuring more important than internal effects. We find that all semiconducting TMDCs are similarly well suited for these external and non-invasive modifications.

Tunneling Spectroscopy in Carbon Nanotube-Hexagonal Boron Nitride-Carbon Nanotube Heterojunctions.

Electron tunneling spectroscopy is a powerful technique to probe the unique physical properties of one-dimensional (1D) single-walled carbon nanotubes (SWNTs), such as the van Hove singularities in the density of states or the power-law tunneling probability of a Luttinger liquid. However, little is known about the tunneling behavior between two 1D SWNTs over a large energy spectrum. Here, we investigate the electron tunneling behavior between two crossed SWNTs across a wide spectral window up to 2 eV in the unique carbon nanotube-hexagonal boron nitride-carbon nanotube heterojunctions. We observe many sharp resonances in the differential tunneling conductance at different bias voltages applied between the SWNTs. These resonances can be attributed to elastic tunneling into the van Hove singularities of different 1D subbands in both SWNTs, and they allow us to determine the quasi-particle bandgaps and higher-lying 1D subbands in SWNTs on the insulating substrate.

Remarkable Band-Gap Renormalization via Dimensionality of the Layered Material C3B

Layer-dependent electronic and structural properties of emerging graphitic carbon boron compound C3B are investigated using both density functional theory and the GW approximation. We discover that, in contrast to a moderate quasiparticle band gap of 2.55 eV for monolayer C3B, the calculated quasiparticle band gap of perfectly stacked bulk phase C3B is as small as 0.17 eV. Therefore, our results suggest that layered material C3B exhibits a remarkably large band gap renormalization of over 2.3 eV due to the interlayer coupling and screening effects, providing a single material with an extraordinary band gap tunability. The quasiparticle band gap of monolayer C3B is also over 1.0 eV larger than that of C3N, a closely related two-dimensional semiconductor. Detailed inspections of the near-edge electronic states reveal that the conduction and valence band edges of C3B are formed by out-of-plane and in-plane electronic states, respectively, suggesting an interesting possibility of tuning the band edges of such layered material separately by modulating the in-plane and out-of-plane interactions.

Influence of high-energy local orbitals and electron-phonon interactions on the band gaps and optical absorption spectra of hexagonal boron nitride

We report ab initio band diagram and optical absorption spectra of hexagonal boron nitride ($h$-BN), focusing on unravelling how the completeness of the basis set for $GW$ calculations and electron-phonon interactions (EPIs) impact on them. The completeness of the basis set, an issue which was seldom discussed in previous optical spectra calculations of $h$-BN, is found crucial in providing converged quasiparticle band gaps. In the comparison among three different codes, we demonstrate that by including high-energy local orbitals in the all-electron linearized augmented plane waves based $GW$ calculations, the quasiparticle direct and fundamental indirect band gaps are widened by $\ensuremath{\sim}0.2$ eV, giving values of 6.81 eV and 6.25 eV, respectively at the $G{W}_{0}$ level. EPIs, on the other hand, reduce them to 6.62 eV and 6.03 eV respectively at 0 K, and 6.60 eV and 5.98 eV respectively at 300 K. With clamped crystal structure, the first peak of the absorption spectrum is at 6.07 eV, originating from the direct exciton contributed by electron transitions around $K$ in the Brillouin zone. After including the EPIs-renormalized quasiparticles in the Bethe-Salpeter equation, the exciton-phonon coupling shifts the first peak to 5.83 eV at 300 K, lower than the experimental value of $\ensuremath{\sim}6.00$ eV. This accuracy is acceptable to an ab initio description of excited states with no fitting parameter.

Anisotropic Optical Properties of 2D Silicon Telluride

ABSTRACTSilicon telluride (Si2Te3) is a silicon-based 2D chalcogenide with potential applications in optoelectronics. It has a unique crystal structure where Si atoms form Si-Si dimers to occupy the “metal” sites. In this paper, we report an ab initio computational study of its optical dielectric properties using the GW approximation and the Bethe-Salpeter equation (BSE). Strong in-plane optical anisotropy is discovered. The imaginary part of the dielectric constant in the direction parallel to the Si-Si dimers is found to be much lower than that perpendicular to the dimers. The optical measurement of the absorption spectra of 2D Si2Te3 nanoplates shows modulation of the absorption coefficient under 90-degree rotation, confirming the computational results. We show the optical anisotropy originates from the particular compositions of the wavefunctions in the valence and conduction bands. Because it is associated with the Si dimer orientation, the in-plane optical anisotropy can potentially be dynamically controlled by electrical field and strain, which may be useful for new device design. In addition, BSE calculations reduce GW quasiparticle band gap by 0.3 eV in bulk and 0.6 eV in monolayer, indicating a large excitonic effect in Si2Te3. Furthermore, including electron-hole interaction in bulk calculations significantly reduces the imaginary part of the dielectric constant in the out-of-plane direction, suggesting strong interlayer exciton effect in Si2Te3 multilayers.

Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. The routinely used single-shot GW-approximation (G0W0) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth to check how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of non-interacting G such that only diagonal elements are retained, whereas, the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle bandgap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7% that validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms like the vertex correction.

Layer-Dependent Quasiparticle Electronic Structure of the P3HT:PCBM Interface from a First-Principles Substrate Screening GW Approach

A prototypical organic photovoltaic material is a heterojunction composed of the blend of regioregular poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl-C$_{61}$-butyric acid methyl ester (PCBM). Microscopic understanding of the energy conversion mechanism in this system involves the relationship between the electronic structure and the atomistic geometry of P3HT:PCBM interfaces. In this work, the effect of the number of P3HT layers on the electronic structure of the P3HT:PCBM interface is studied by means of first-principles $GW$. We apply the substrate screening approach to accelerate such calculations and to better understand the many-body dielectric screening at the interface. The quasiparticle band gap of the entire interface is found to decrease as the number of P3HT layers increases. The gaps of the individual components of the interface are found to be smaller than their isolated counterparts, with strong dependence on the number of P3HT layers. Importantly, when comparing the system of P3HT:PCBM - where a single interface is present - and the system of P3HT:PCBM:P3HT, where an interface is formed on either side of PCBM, we find that the two systems exhibit very different quasiparticle energy level alignments. We discuss possible implications of our findings in related experiments. The observed trends in layer-dependent quasiparticle electronic structure of P3HT:PCBM interfaces provide computational insight into energy conversion pathways in these materials.

Estimation of the single-particle band gap and exciton binding energy in two dimensional insulators: a modified G0W0-BSE method approach

In this paper we present an alternative G0W0-BSE procedure, suitable for calculation of the quasi-particle and optical properties in 2D semiconductors. The method completely excludes the spurious Coulomb interaction with 2D crystal replicas. The calculated band gap energies of hexagonal boron nitride (hBN), MoS2 and MoTe2 monolayers are in good agreement with other theoretical results. The 2D Bethe–Salpeter equation is derived and reduced to a 2D-hydrogen Schrödinger equation in which enter the G0W0 band gap, DFT effective masses, and RPA screened Coulomb interaction. This formulation is applied to the problems of determining exciton binding energies and estimating the quasiparticle band gap in hBN, as well as in some transition-metal dichalcogenides. A semiclassical procedure is used in the limit of high polarizability λ in order to obtain the analytical expression for exciton binding energies.

Quasiparticle energies and excitonic effects of chromium trichloride: From two dimensions to bulk

Layered van der Waals (vdW) magnetic materials have attracted significant research interest to date. In this work, we employ the first-principles many-body perturbation theory to calculate excited-state properties of a prototype vdW magnet, chromium trichloride (CrCl3), covering monolayer, bilayer, and bulk structures. Unlike usual non-magnetic vdW semiconductors, in which many-electron interactions and excited states are sensitive to dimensionality, many-electron interactions are always enhanced and dominate quasiparticle energies and optical responses of both two-dimensional and bulk CrCl3. The electron-hole (e-h) binding energy can reach 3 eV in monolayer and remains as high as 2 eV in bulk. Because of the cancellation effect between self-energy corrections and e-h binding energies, the lowest-energy exciton (optical gap) is almost not affected by the change of dimensionality. Besides, for the excitons with similar e-h binding energies, their dipole oscillator strength can differ by a few orders of magnitude.Our analysis shows that such a big difference is from a unique interference effect between complex exciton wavefunctions and interband transitions. Finally, we find that the interlayer stacking sequence and magnetic coupling barely change quasiparticle band gaps and optical absorption spectra of CrCl3. Our calculated low-energy exciton peak positions agree with available measurements. These findings give insight into the understanding of many-electron interactions and the interplay between magnetic orders and optical excitations in vdW magnetic materials.

Probing quantum confinement effects on the excitonic property and electronic band structures of MoS2

We systemically investigate the effects of quantum confinement on the excitonic property and electronic band structures of centimeter-scale MoS2 films (number of layers: N = 1, 2, 4, and 18) through spectroscopic ellipsometry. The optical properties including optical conductivity, exciton binding energy and critical points (CPs) are traced as a function of layer number. We find that A and B excitons have the largest binding energies in monolayer MoS2 compared with the values in multilayer MoS2 because of the absence of interlayer coupling in former. Nevertheless, the peak positions of A and B excitons are almost the same, even when the layer number changes. This is because of the canceling out of differences between quasi-particle band gap and excitonic binding energy. Furthermore, the threshold energies of the eight CPs are calculated; using these values, the valence and conduction band alignments of the CPs are determined. It is noteworthy that the electronic band structures of MoS2 become stable when the layer number is more than four, which can be attributed to the largely weakened quantum confinement effect in these cases. The results of our study help us better understand the effect of quantum confinement on photoelectronic and photovoltaic applications using MoS2 films.

Giant enhancement of solid solubility in monolayer alloys by selective orbital coupling

Solid solubility (SS) is one of the most important features of alloys, which is usually difficult to be largely tuned in the entire alloy concentrations by external approaches. Some alloys that were supposed to have promising physical properties could turn out to be much less useful because of their poor SS, e.g., the case for monolayer BNC [(BN)1-x(C2)x] alloys. Until now, an effective approach on significantly enhancing SS of (BN)1-x(C2)x in the entire x is still lacking. In this article, a novel mechanism of selective orbital coupling between high energy wrong-bond states and surface states mediated by the specific substrate has been proposed to stabilize the wrong-bonds and in turn significantly enhance the SS of (BN)1-x(C2)x alloys. Surprisingly, we demonstrate that five ordered alloys, exhibiting variable direct quasi-particle bandgaps from 1.35 to 3.99 eV, can spontaneously be formed at different x when (BN)1-x(C2)x is grown on hcp-phase Cr. Interestingly, the optical transitions around the band edges in these ordered alloys, accompanied by largely tunable exciton binding energies of ~1 eV at different x, are significantly strong due to their unique band structures. Importantly, the disordered (BN)1-x(C2)x alloys, exhibiting fully tunable bandgaps from 0 to ~6 eV in the entire x, can be formed on Cr substrate at the miscibility temperature of ~1200 K, which is greatly reduced compared to that of 4500~5600 K in free-standing form or on other substrates. Our discovery not only may resolve the long-standing SS problem of BNC alloys, but also could significantly extend the applications of BNC alloys for various optoelectronic applications.

Many-body effects in an MXene Ti2CO2 monolayer modified by tensile strain: GW-BSE calculations.

MXenes, two-dimensional (2D) layered transition metal carbide/nitride materials with a lot of advantages including high carrier mobility, tunable band gap, favorable mechanical properties and excellent structural stability, have attracted research interest worldwide. It is imperative to accurately understand their electronic and optical properties. Here, the electronic and optical response properties of a Ti2CO2 monolayer, a typical member of MXenes, are investigated on the basis of first-principles calculations including many-body effects. Our results show that the pristine Ti2CO2 monolayer displays an indirect quasi-particle (QP) band gap of 1.32 eV with the conduction band minimum (CBM) located at the M point and valence band maximum (VBM) located at the Γ point. The optical band gap and binding energy of the first bright exciton are calculated to be 1.26 eV and 0.56 eV, respectively. Under biaxial tensile strains, the lowest unoccupied band at the Γ point shifts downward, while the lowest unoccupied band at the M point shifts upward. Then, a direct band gap appears at the Γ point in 6%-strained Ti2CO2. Moreover, the optical band gap and binding energy of the first bright exciton decrease continuously with the increase of the strain due to the increase of the lattice parameter and the expansion of the exciton wave function. More importantly, the absorbed photon flux of Ti2CO2 is calculated to be 1.76–1.67 mA cm−2 with the variation of the strain, suggesting good sunlight optical absorbance. Our work demonstrates that Ti2CO2, as well as other MXenes, hold untapped potential for photo-detection and photovoltaic applications.