Quasiparticle Gap Research Articles

Optical response and band structure of LiCoO2 including electron-hole interaction effects

The optical response functions and band structures of ${\mathrm{LiCoO}}_{2}$ are studied at different levels of approximation, from density functional theory (DFT) in the generalized gradient approximation (GGA) to quasiparticle self-consistent $\mathrm{QS}GW$ (with $G$ for Green's function and $W$ for screened Coulomb interaction) without and with ladder diagrams $(\mathrm{QS}G\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{W})$ and the Bethe Salpeter Equation (BSE) approach. The $\mathrm{QS}GW$ method is found to strongly overestimate the band gap and electron-hole or excitonic effects are found to be important. They lower the quasiparticle gap by only about 11% but the lowest energy peaks in absorption are found to be excitonic in nature. The contributions from different band to band transitions and the relation of excitons to band-to-band transitions are analyzed. The excitons are found to be strongly localized. A comparison to experimental data is presented.

Time-resolved ARPES Determination of a Quasi-Particle Band Gap and Hot Electron Dynamics in Monolayer MoS2.

The electronic structure and dynamics of 2D transition metal dichalcogenide (TMD) monolayers provide important underpinnings both for understanding the many-body physics of electronic quasi-particles and for applications in advanced optoelectronic devices. However, extensive experimental investigations of semiconducting monolayer TMDs have yielded inconsistent results for a key parameter, the quasi-particle band gap (QBG), even for measurements carried out on the same layer and substrate combination. Here, we employ sensitive time- and angle-resolved photoelectron spectroscopy (trARPES) for a high-quality large-area MoS2 monolayer to capture its momentum-resolved equilibrium and excited-state electronic structure in the weak-excitation limit. For monolayer MoS2 on graphite, we obtain QBG values of ≈2.10 eV at 80 K and of ≈2.03 eV at 300 K, results well-corroborated by the scanning tunneling spectroscopy (STS) measurements on the same material.

Optical absorption spectra of Xene and Xane (X = silic, german, stan)

We study optical absorption spectra of Xene and Xane (X = silic, german, stan). The results show that the optical absorption spectra of Xenes are dominated by a sharp peak near the origin due to direct interband transitions near the K point of the Brillouin zone. Meanwhile, the optical absorption spectra of Xanes are characterized by an excitonic peak. The Xenes are zero-gap materials with a Dirac cone at the K point, whereas Xanes are semiconductors with sizable band gaps. The quasiparticle band gaps of silicane, germanane, and stanane are 3.60, 2.21, and 1.35 eV, respectively; their exciton binding energies are 0.40, 0.33, and 0.20 eV, respectively.

Electronic structure of semiconductor nanoparticles from stochastic evaluation of imaginary-time path integral

In the Kohn-Sham orbital basis imaginary-time path integral for electrons in a semiconductor nanoparticle has a mild Fermion sign problem and is amenable to evaluation by the standard stochastic methods. This is evidenced by the simulations of silicon hydrogen-passivated nanocrystals, such as $Si_{35}H_{36},~Si_{87}H_{76},~Si_{147}H_{100}$ and $Si_{293}H_{172},$ which contain $176$ to $1344$ valence electrons and range in size $1.0 - 2.4~nm$, utilizing the output of density functional theory simulations. We find that approximating Fermion action with just the leading order polarization term results in a positive-definite integrand in the functional integral, and that it is a good approximation of the full action. We compute imaginary-time electron propagators in these nanocrystals and extract the energies of low-lying electron and hole levels. Our quasiparticle gap predictions agree with the results of high-precision calculations using $G_0W_0$ technique. This formalism can be extended to calculations of more complex excited states, such as excitons and trions.

Negative quasiparticle shifts in phosphorene quantum dots

It is commonly believed that electron correlations would open up a quasiparticle gap in semiconductors. Contrary to this intuitive expectation, here we reveal that phosphorene quantum dots (PQDs) may exhibit just the opposite effect. By using a configuration interaction approach beyond the conventional double-excitation scheme, quasiparticle energies are calculated for hexagonal and rectangular PQDs in various dielectric environments. For the hexagonal PQD with a nominal gap of 2.26 eV, it is found that the quasiparticle shift decreases by more than 500 meV and eventually becomes negative when the effective dielectric constant is reduced from 20.0 to 5.0. For other trapezoidal, triangular, and rectangular PQDs, the quasiparticle shift exhibits a similar amount of decrement after the same change in the dielectric environment. Furthermore, the calculation by adopting the Rytova-Keldysh potential, which may be more suitable to describe two-dimensional screening, also shows a very similar result, although with smaller decrement of the quasiparticle shift. The origin of this anomalous quasiparticle shift is believed to be related to the long-range electron-electron interactions in the distinctive lattice structure of PQDs, as a similar phenomenon has never been found in graphene quantum dots.

Cohesion and excitations of diamond-structure silicon by quantum Monte Carlo: Benchmarks and control of systematic biases

We have carried out quantum Monte Carlo (QMC) calculations of silicon crystal focusing on the accuracy and systematic biases that affect the electronic structure characteristics. The results show that 64 and 216 atom supercells provide an excellent consistency for extrapolated energies per atom in the thermodynamic limit for ground, excited, and ionized states. We have calculated the ground state cohesion energy with both $\textit{systematic and statistical errors}$ below $\approx$0.05 eV. The ground state exhibits a fixed-node error of only $1.3(2)\%$ of the correlation energy, suggesting an unusually high accuracy of the corresponding single-reference trial wave function. We obtain a very good agreement between optical and quasiparticle gaps that affirms the marginal impact of excitonic effects. Our most accurate results for band gaps differ from the experiments by about 0.2 eV. This difference is assigned to a combination of residual finite-size and fixed-node errors. We have estimated the crystal Fermi level referenced to vacuum that enabled us to calculate the edges of valence and conduction bands in agreement with experiments.

Efficient Band Structure Calculation of Two-Dimensional Materials from Semilocal Density Functionals.

The experimental and theoretical realization of two-dimensional (2D) materials is of utmost importance in semiconducting applications. Computational modeling of these systems with satisfactory accuracy and computational efficiency is only feasible with semilocal density functional theory methods. In the search for the most useful method in predicting the band gap of 2D materials, we assess the accuracy of recently developed semilocal exchange–correlation (XC) energy functionals and potentials. Though the explicit forms of exchange–correlation (XC) potentials are very effective against XC energy functionals for the band gap of bulk solids, their performance needs to be investigated for 2D materials. In particular, the LMBJ [J. Chem. Theory Comput.2020, 16, 265432097004] and GLLB-SC [Phys. Rev. B82, 2010, 115106] potentials are considered for their dominance in bulk band gap calculation. The performance of recently developed meta generalized gradient approximations, like TASK [Phys. Rev. Res.1, 2019, 033082] and MGGAC [Phys. Rev. B. 100, 2019, 155140], is also assessed. We find that the LMBJ potential constructed for 2D materials is not as successful as its parent functional, i.e., MBJ [Phys. Rev. Lett.102, 2009, 22640119658882] in bulk solids. Due to a contribution from the derivative discontinuity, the band gaps obtained with GLLB-SC are in a certain number of cases, albeit not systematically, larger than those obtained with other methods, which leads to better agreement with the quasi-particle band gap obtained from the GW method. The band gaps obtained with TASK and MGGAC can also be quite accurate.

Substrate effect on excitonic shift and radiative lifetime of two-dimensional materials

Substrates have strong effects on optoelectronic properties of two-dimensional (2D) materials, which have emerged as promising platforms for exotic physical phenomena and outstanding applications. To reliably interpret experimental results and predict such effects at 2D interfaces, theoretical methods accurately describing electron correlation and electron-hole interaction such as first-principles many-body perturbation theory are necessary. In our previous work (2020 Phys. Rev. B 102 205113), we developed the reciprocal-space linear interpolation method that can take into account the effects of substrate screening for arbitrarily lattice-mismatched interfaces at the GW level of approximation. In this work, we apply this method to examine the substrate effect on excitonic excitation and recombination of 2D materials by solving the Bethe–Salpeter equation. We predict the nonrigid shift of 1s and 2s excitonic peaks due to substrate screening, in excellent agreements with experiments. We then reveal its underlying physical mechanism through 2D hydrogen model and the linear relation between quasiparticle gaps and exciton binding energies when varying the substrate screening. At the end, we calculate the exciton radiative lifetime of monolayer hexagonal boron nitride with various substrates at zero and room temperature, as well as the one of WS2 where we obtain good agreement with experimental lifetime. Our work answers important questions of substrate effects on excitonic properties of 2D interfaces.

Superfluid quantum criticality in liquid He3 in anisotropic aerogel

In the novel superfluid polar phase realized in liquid 3He in highly anisotropic aerogels, a quantum transition to the polar-distorted A (PdA) phase may occur at a low but finite pressure Pc(0). It is shown that a nontrivial quantum dynamics of the critical fluctuation of the PdA order is induced by the presence of both the columnar-like impurity scattering leading to the Anderson's Theorem for the polar phase and the line node of the quasiparticle gap in the state, and that, in contrast to the situation of the normal to the B phase transition in isotropic aerogels, a weakly divergent behavior of the compressibility appears in the quantum critical region close to Pc(0).

Solving the Bethe-Salpeter equation on a subspace: Approximations and consequences for low-dimensional materials

It is well known that the ambient environment can dramatically renormalize the quasiparticle gap and exciton binding energies in low-dimensional materials, but the effect of the environment on the energy splitting of the spin-singlet and spin-triplet exciton states is less understood. A prominent effect is the renormalization of the exciton binding energy and optical strength (and hence the optical spectrum) through additional screening of the direct Coulomb term describing the attractive electron-hole interaction in the kernel of the Bethe-Salpeter equation (BSE). The repulsive exchange interaction responsible for the singlet-triplet slitting, on the other hand, is unscreened within formal many-body perturbation theory. However, Loren Benedict argued that in practical calculations restricted to a subspace of the full Hilbert space, the exchange interaction should be appropriately screened by states outside of the subspace, the so-called $S$ approximation \cite{Benedict2002}. Here, we systematically explore the accuracy of the $S$ approximation for different confined systems, including a molecule and heterostructures of semiconducting and metallic layered materials. We show that the $S$ approximation is actually exact in the limit of small exciton binding energies (i.e., small direct term) and can be used to significantly accelerate convergence of the exciton energies with respect to the number of empty states, provided that a particular effective screening consistent with the conventional Tamm-Dancoff approximation is employed. We further find that the singlet-triplet splitting in the energy of the excitons is largely unaffected by the external dielectric environment for most quasi-two-dimensional materials.

Band alignment of monolayer CaP3, CaAs3, BaAs3 and the role of p-d orbital interactions in the formation of conduction band minima.

Recently, a number of new two-dimensional (2D) materials based on puckered phosphorene and arsenene have been predicted with moderate band gaps, good absorption properties and carrier mobilities superior to those of transition metal dichalcogenides. For heterojunction applications, it is important to know the relative band alignment of these new 2D materials. We report the band alignment of puckered CaP3, CaAs3 and BaAs3 monolayers at the quasiparticle level of theory (G0W0), calculating band offsets for isolated monolayers according to the electron affinity rule. Our calculations suggest that monolayer CaP3, CaAs3 and BaAs3 all form type-II (staggered) heterojunctions which makes them suitable for solar-energy conversion applications. Their quasiparticle gaps are 2.1 (direct), 1.8 (direct) and 1.5 eV (indirect), respectively. We also examine trends in the electronic structure in the light of chemical bonding analysis. We show that the indirect band gap in monolayer BaAs3 is caused by relatively strong As 3p-Ba 5d bonding interactions. Our results provide guidance for the design of phosphorene-like materials and their heterojunction applications.

Predicting a new graphene derivative C3H as potential photocatalyst for water splitting and CO2 reduction

Abstract A new graphene derivative C3H monolayer is identified theoretically by swarm-intelligence structural search and first-principles calculations. The single-layer C3H with a planar conformation is built by annular C18H6 units and shows high thermodynamic stability, due to the sp2 hybridization between C atoms. It is a direct bandgap semiconductor with a quasi-particle (QP) gap of 3.44 eV. The valence band maximum (VBM) and conduction band minimum (CBM) are mainly contributed by pz orbital of C atom. The C3H monolayer has both high electron and hole mobilities in the order of magnitude of 103 cm2 ⋅V−1 ⋅s−1. Furthermore, the optical bandgap of C3H is 2.47 eV with a high exciton binding energy of 0.97 eV. On the other hand, the energy level positions of VBM and CBM straddle the redox potential of water splitting and CO2 reduction, indicating potential photocatalytic activity. All these desirable functional properties of C3H open a wealth of opportunity for applications in electronics, photo-electronics and photocatalyst.

A first-principles Quantum Monte Carlo study of two-dimensional (2D) GaSe

Two-dimensional (2D) post-transition metal chalcogenides (PTMCs) have attracted attention due to their suitable bandgaps and lower exciton binding energies, making them more appropriate for electronic, optical, and water-splitting devices than graphene and monolayer transition metal dichalcogenides. Of the predicted 2D PTMCs, GaSe has been reliably synthesized and experimentally characterized. Despite this fact, quantities such as lattice parameters and band character vary significantly depending on which density functional theory (DFT) functional is used. Although many-body perturbation theory (GW approximation) has been used to correct the electronic structure and obtain the excited state properties of 2D GaSe, and solving the Bethe-Salpeter equation (BSE) has been used to find the optical gap, we find that the results depend strongly on the starting wavefunction. In an attempt to correct these discrepancies, we employed the many-body Diffusion Monte Carlo (DMC) method to calculate the ground and excited state properties of GaSe because DMC has a weaker dependence on the trial wavefunction. We benchmark these results with available experimental data, DFT [local-density approximation, Perdew-Burke-Ernzerhof (PBE), strongly constrained and appropriately normed (SCAN) meta-GGA, and hybrid (HSE06) functionals] and GW-BSE (using PBE and SCAN wavefunctions) results. Our findings confirm that monolayer GaSe is an indirect gap semiconductor (Γ-M) with a quasiparticle electronic gap in close agreement with experiment and low exciton binding energy. We also benchmark the optimal lattice parameter, cohesive energy, and ground state charge density with DMC and various DFT methods. We aim to present a terminal theoretical benchmark for pristine monolayer GaSe, which will aid in the further study of 2D PTMCs using DMC methods.

Superconducting pairing symmetry and spin-orbit coupling in proximitized graphene

Graphene may exhibit different topological phases as a result of proximity to different substrates. We study the effect of superconductivity in such systems using the effective Bogolyubov-de Gennes Hamiltonian with different superconducting pairing order parameters. We analyze the topological phase transition and symmetry class of the system in different parameter regimes. A particularly interesting situation occurs when nearest-neighbor spin-singlet superconducting pairing is present in phases of proximitized graphene that exhibit either inverted band or quantum spin Hall behavior. Both superconducting phases show similar characteristics in the low-energy range, including the appearance of robust edge states, and are neighboring phases across a transition that closes the quasiparticle gap as the chemical potential changes. Detailed construction and analysis of the existence and nature of edge states are presented in different system regimes.

Spin resonances in iron selenide high- Tc superconductors by proximity to a hidden spin density wave

Recent inelastic neutron scattering studies by Pan et al., Nature Communications 8, 123 (2017), find evidence for spin excitations at energies above the quasi-particle gap in an iron-selenide high-Tc superconductor. The momenta of the spin excitations form a diamond around the checkerboard wavevector, Q_AF, that is associated with the square lattice of iron atoms that makes up the system. It has been suggested that such a "hollowed-out" spin-excitation spectrum is due to hidden Neel order. We study such a hidden spin-density wave (hSDW) state that results from nested Fermi surfaces at the center and at the corner of the unfolded Brillouin zone. It emerges within mean field theory from an extended Hubbard model over a square lattice of iron atoms that contain the minimal d_xz and d_yz orbitals. Opposing Neel order exists over the isotropic d+ = d_xz + i d_yz and d- = d_xz - i d_yz orbitals. The dynamical spin susceptibility of the hSDW is computed within the random phase approximation, at perfect nesting. Unobservable Goldstone modes that disperse acoustically are found at Q_AF. A threshold is found in the spectrum of observable spin excitations that forms a "floating ring" at Q_AF also. The ring threshold moves down in energy toward zero with increasing Hund's Rule coupling, while it moves up in energy with increasing magnetic frustration. Comparison with the normal-state features of the spin-excitation spectrum shown by electron-doped iron selenide is made. Also, recent predictions of a Lifshitz transition from the nested Fermi surfaces to Fermi surface pockets at the corner of the folded Brillouin zone will be discussed.

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.

Theoretical investigation of the structural, elastic, electronic, and dielectric properties of alkali-metal-based bismuth ternary chalcogenides

The past decade has witnessed the rapid introduction of organic-inorganic hybrid compounds in photovoltaic applications. Motivated by the strong demand for stable and nontoxic materials in this class, we report a theoretical study on the structural, elastic, electronic, thermodynamic and dielectric properties of alkali-metal-based bismuth ternary chalcogenides. In particular, we employ state-of-the-art density functional theory to explore the potential of $A\mathrm{Bi}{X}_{2}$ and $A\mathrm{Bi}{X}_{3}$ ($A=\mathrm{Na}$, K and $X=$ O, S) as light-absorbing media. All the compounds under investigation are found to be thermodynamically and mechanically stable, with a semiconductor band structure. The Kohn-Sham band gaps range between 0.80 eV and 1.80 eV, when calculated with semilocal functionals, values that increase to 1.24--2.47 eV with hybrid ones. Although all but ${\mathrm{NaBiO}}_{2}$ and ${\mathrm{KBiO}}_{2}$ are indirect band-gap semiconductors, the onset of the imaginary part of their dielectric functions, the optical gap, is only marginally larger than the quasiparticle gap. This is due to the generally flat nature of both the conduction and the valence bands. We then expect these compounds to absorb light in the upper part of the visible spectrum. In all cases the valence band is dominated by $\mathrm{O}\text{\ensuremath{-}}p$ and S-$p$ orbitals and the conduction one by Bi-$p$, suggesting the possibility of excitons with low binding energy. The only exceptions are ${\mathrm{NaBiO}}_{2}$ and ${\mathrm{KBiO}}_{2}$ for which the $\mathrm{O}\text{\ensuremath{-}}p$ states dominate the density of states at both sides of the band gap.

Tuned and screened range-separated hybrid density functional theory for describing electronic and optical properties of defective gallium nitride

We apply a hybrid density functional theory approach, based on a tuned and screened range-separated hybrid (SRSH) exchange-correlation functional, to describe the optoelectronic properties of defective gallium nitride (GaN). SRSH and time-dependent SRSH (TDSRSH) are tuned to produce accurate energetics for the pristine material and applied to the study of a series of point defects in bulk GaN, a blue light-emitting material that degrades in the presence of defects. We first establish the accuracy of the method by comparing the predicted quasiparticle gap and low-energy excitation spectra of (TD)SRSH and many-body perturbation theory for both pristine GaN and GaN containing a single nitrogen vacancy. Aided by the reduced computational cost of (TD)SRSH, we then report on three additional technologically relevant point defects and defect complexes in GaN: the gallium vacancy, the carbon interstitial, and the carbon-silicon complex. We compute the low-energy optical absorption spectra for these defects and show the presence of defect-centered transitions. Furthermore, by estimating the Stokes shift, we predict, in agreement with previous studies, that the carbon substitutional defect is a candidate for the detrimental yellow luminescence in GaN. This study indicates that TDSRSH is a promising and computationally feasible approach for quantitatively accurate, first-principles modeling of defective semiconductors.

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.

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.