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Electronic and Optical properties of TwoDimensional #-PbO from First Principles Suvadip Das, Guangsha Shi, Nocona Sanders, and Emmanouil Kioupakis Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b02956 • Publication Date (Web): 13 Sep 2018 Downloaded from http://pubs.acs.org on September 17, 2018

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Chemistry of Materials

Electronic and Optical properties of TwoDimensional α-PbO from First Principles Suvadip Das, Guangsha Shi, Nocona Sanders, and Emmanouil Kioupakis* Materials Science and Engineering, University of Michigan, Ann Arbor MI 48109, United States Corresponding Author *E-mail: [email protected]

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ABSTRACT: We performed first-principles calculations based on density functional theory and many-body perturbation theory to investigate the electronic and optical properties of monolayer, bilayer, and bulk litharge α-PbO, including spin-orbit coupling effects. The fundamental gap is direct for the monolayer (4.48 eV) and indirect for the bilayer (3.44 eV) and the bulk material (2.45 eV). The exciton binding energies are large for the monolayer (1.1 eV) and the bilayer (0.9 eV), indicating that excitons are stable at room temperature. However, the lowest-energy excitons for the monolayer and the bilayer are dark with radiative lifetimes on the order of ms. A pronounced van Hove singularity in the valence band of the few-layer structures suggests it becomes a multiferroic two-dimensional material upon hole doping. Our results indicate strong optical absorbance in the vacuum UV region and transparency in the visible and near UV for monolayer PbO, suggesting applications for atomically thin solar-blind UV photodetectors.


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INTRODUCTION Functional two-dimensional materials such as MoS2 and other transition metal dichalcogenides (TMDs) are promising for advanced atomically thin electronic and optoelectronic devices, such as light emitting diodes (LEDs),1 ultrathin solar cells,2 and valleytronic devices.3 TMD monolayers exhibit a host of desirable functional properties such as sizeable direct band gaps,4 strongly bound excitons,5 broken inversion symmetry, large spin-orbit coupling,6 and strong optical absorbance in the visible.2 The search for novel two-dimensional functional materials beyond TMDs identified the class of layered group-IV monochalcogenide materials (e.g., SnSe, GeSe, etc.). These materials, which are compound analogues of black phosphorous, crystalize in a distorted NaCl-like arrangement.7 Their bulk counterparts (e.g., bulk SnSe) are efficient thermoelectric materials with record high thermoelectric figures of merit.8,9 The monolayers exhibit anisotropic spin transport and strong optical absorbance,10 ferroelectricity,11 and strongly bound excitons.10,12 However, one obstacle to the synthesis of IV-VI materials is their thermodynamic instability with respect to oxidation. They also react with chalcogens (which are commonly used for encapsulation) to form dichalcogenides such as GeSe2 and SnSe2. It is therefore necessary to identify new materials that exhibit similar properties as group-IV monochalcogenides with higher thermodynamic and chemical stability. Litharge α-PbO oxide is such a layered oxidation-resistant member of the IV-VI family displaying a range of desirable properties. In contrast to lighter group-IV elements, which typically occur in the 4+ oxidation state in compounds, Pb preferentially occurs in the 2+ state. Thus, its monochalcogenides and monoxides are more stable than those of the lighter group-IV elements. α-PbO is utilized in increasing the refractive index of glass and to render ceramic materials


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electrically and magnetically inert.13 Recently, atomic layers of α-PbO have been successfully grown for the first time using micromechanical and sonochemical exfoliation.14 Recent density functional theory calculation suggested possible ferromagnetism and superconductivity in multilayers of hole-doped α-PbO arising from the van Hove singularity of valence band edges.15 The interlayer interaction energy for layered α-PbO is 0.016 eV/atom,14 which is lower than graphene and MoS2. Scattering and photoluminescence spectroscopy shows red and green light absorption in five and three layers of α-PbO corresponding to experimental gaps of 1.94 eV (635 nm) and 2.16 eV (570 nm), respectively.14 Considering its rich prospect, a computational investigation of the electronic and optical properties of litharge α-PbO oxide in its bulk and twodimensional forms can provide insights on its fundamental functional properties and guide experimental studies and applications. In this work, we perform first-principles calculations based on density functional theory (DFT) and many-body perturbation theory to investigate the electronic and optical properties of bulk, monolayer and bilayer α-PbO. The fundamental gaps are found to be indirect for the bulk (2.45 eV) and bilayer (3.44 eV), and direct (4.48 eV) for monolayer α-PbO. However, optical transitions across the direct gap of the monolayer are weak. Our calculations reveal a pronounced van Hove singularity of the valence-band density of states with a strong 1/√𝐸 divergence. Inclusion of spin-orbit coupling effects decreases the band gap by 100 meV. Strong absorbance in the UV region for the monolayer indicates its potential for solar-blind UV photodetectors. The exciton binding energy is significantly larger in the monolayer (1.1 eV) and bilayer (0.9 eV) αPbO, compared to its bulk form (0.27 eV) due to the spatial confinement of electrons and holes and the reduced screening of their interaction. Our results indicate promising applications of monolayer α-PbO for atomically thin solar-blind UV photodetectors.


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METHODOLOGY Our first-principles calculations are based on DFT and many-body perturbation theory, which can predictively determine the electronic and optical properties of two-dimensional materials.16 We employed the generalized gradient approximation (GGA) for the exchange correlation functional17 and the plane-wave norm-conserving pseudopotential method as implemented in the Quantum ESPRESSO code.18 Our Pb pseudopotential includes the 5d, 6s and 6p electrons in the valence. The single-particle wave functions were evaluated with DFT using a plane-wave cutoff of 60 Ry. The unrelaxed lattice parameters a = b = 3.972 Å, c = 5.023 Å used in the calculations were obtained from the International Crystal Structure and Materials Project Database. The quasiparticle band structures (Figs. S1-S3) were evaluated using the single-shot GW approximation, as implemented in the BerkeleyGW code.19 We calculated the static dielectric matrix using a plane-wave cutoff of 20 Ry, and extended it to finite frequencies using the Hybertsen-Louie plasmon-pole model (HL-GPP).20 The Coulomb-hole self-energy term was calculated using the static-remainder approach21 and a sum over unoccupied bands up to 16 Ry above the valence-band maximum. Spin-orbit coupling interactions were incorporated into the GW energy eigenvalues in a non-self-consistent fashion by computing the off-diagonal elements of the spin-orbit matrix elements22 and subsequently diagonalizing the Hamiltonian in the spinor basis. We evaluated the polarizability matrices and quasiparticle energies using Brillouin-zone (BZ) sampling grids of 666 for bulk and 16161 for few-layered α-PbO. For the few-layered calculations, we truncated the Coulomb interaction23 to eliminate interactions between periodic slab images. The vacuum space was chosen to accommodate 99% of the total electronic charge density within half the computational cell volume. We interpolated the spin-orbit coupling matrix elements and the quasiparticle energies to fine grids in the Brillouin zone using the maximally


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localized Wannier function method24 and the wannier90 code.25 The absolute valence and conduction band extrema positions of the few-layer structures were aligned to the vacuum level by subtracting the value of the plane-averaged electrostatic potential in the vacuum region. For the bulk material we determined the absolute band positions by referencing them to the average electrostatic potential in the bulk cell, and subtracting the difference between the average electrostatic potential within the bilayer slab and the vacuum level. Optical spectra and exciton binding were calculated with the Bethe-Salpeter equation (BSE) method26 as implemented in BerkeleyGW. We interpolated the electron-hole interaction kernel between the top 6 valence bands and the lowest 6 conduction bands on a on 181818 BZ sampling grid for bulk and a 16161 grid for few-layer α-PbO. Convergence tests for the band gap (Fig. S4) and exciton binding energies (Fig. S5) are analyzed in the Supplementary Information. RESULTS AND DISCUSSION Property Bulk Monolayer Bilayer Quasiparticle band gap (eV) 2.45 4.48 3.44 Ionization potential (eV) 5.69 6.75 6.05 Electron affinity (eV) 3.24 2.27 2.61 Spin-orbit gap correction (eV) -0.06 -0.1 -0.11 Exciton binding energy (eV) 0.27 1.1 0.9 Lowest exciton energy (eV) 2.18 3.38 2.54 Table 1. Quasiparticle band gap, ionization potential, electron affinity, spin-orbit coupling correction to the band gap, exciton binding energy, and lowest exciton energy of bulk, monolayer, and bilayer litharge α−PbO.


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Figure 1. Calculated GW electronic structure and density of states (DOS) per unit cell of (a) bulk, (b) monolayer, and (c) bilayer α-PbO, with and without spin-orbit (LS) coupling effects. Monolayer α-PbO exhibits a direct band-gap of 4.48 eV, whereas the band gap is indirect for bulk (2.45 eV) and bilayer (3.44 eV) α-PbO. There is a pronounced van Hove singularity at the valence band maximum as is apparent from the density of states for the monolayer and bilayer. Inclusion of spin-orbit coupling decreases the band gap of monolayer α-PbO by 100 meV. The structure of bulk litharge α-PbO in the tetragonal ordered phase belongs to the P4/nmm space group. It consists of planes of O atoms arranged in a square lattice, with Pb atoms on top of the centers of the O squares on alternating sides of the plane [Fig. 1(a) inset]. The Pb atom in PbO produces stereochemically active lone-pair electrons that yield the lower-symmetry layered structure (as opposed, e.g., to the rocksalt structure of lead monochalcogenides). The relaxed inplane and out of plane lattice constants of a=b=4.069 Å and c=5.134 Å for bulk α-PbO shows a mismatch with the experimental lattice parameters of 3.972 Å and 5.023 Å by 3.1% and 4.2%, respectively.14 However, our relaxed in-plane lattice constant of 4.071 Å for the monolayer and the bilayer matches well with that of the relaxed in-plane lattice constant of bulk α-PbO, suggesting that the lattice constants of the two-dimensional forms are very similar to the bulk. We therefore used the experimental lattice constants in our calculations of two-dimensional structures to reduce


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computational artifacts arising from the mismatch in lattice constants and ensure higher predictive accuracy of our electronic and optical calculations.

Figure 2. Absolute positions of the VBM (ionization potential) and CBM (electron affinity) of bulk, bilayer, and monolayer PbO. The band gap straddles the redox potentials of H+/H2 and O2/H2O for all three materials. The calculated band structure and density of states of bulk α-PbO, including quasiparticle and spin-orbit coupling corrections, are shown in Fig. 1 (a). The band gap is indirect: the valence band maximum (VBM) is located slightly away from the Γ point along the Γ−X direction, while the conduction band minimum (CBM) is at the M point. Since the Pb cation is in the 2+ charge state, the lowest conduction band consists predominantly of Pb 6p atomic orbitals, while the O 2p orbitals form the topmost valence band. The dispersive parabolic conduction band edge at the Γ point gives rise to small electron effective masses, whereas the flat non-dispersive valence band edges result in large hole effective masses. Moreover, the valence band is flat and forms a Mexican-hat-like feature around the Γ point. The valence band dispersion is expressed by 𝐸(𝑘) = 𝐴𝑘 4 + 𝐵𝑘 2 + 𝐸0 and comprises of global extrema in the annular region of radius √(-𝐵/2𝐴). Moreover, the density of states for bulk α-PbO exhibits a 1/√𝐸 divergence at the VBM,


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characteristic of van-Hove singularities in the system. The DFT gap is 1.36 eV. G0W0 corrections increase it to 2.51 eV, while spin-orbit coupling decreases the conduction band minimum by 0.065 eV. The spin-orbit interaction does not alter the doubly degenerate VBM as a result of the strong oxygen orbital character, which is a light element that does not exhibit strong relativistic effects. The resulting quasiparticle band gap in bulk α-PbO is therefore 2.45 eV, while the experimentally measured optical gaps are 1.95 eV and 2.0 eV at a temperature of 300 K and 4 K, respectively.27 We attribute the difference to excitonic effects discussed below. The band structure and density of states for monolayer and bilayer α-PbO, including quasiparticle and spin-orbit corrections, are shown in Figs. 1 (b) and (c). Although the gap of the bilayer is indirect and the valence band structure is similar to bulk α-PbO, the α-PbO monolayer has a direct gap at the Γ point. Therefore, α-PbO is similar to MoS2 in that only the monolayer structure exhibits a direct band gap. The band gaps for monolayer and bilayer α-PbO are 4.48 eV and 3.44 eV, respectively (Table I). The increasing band gap with reducing number of atomic layers is consistent with quantum confinement. The spin-orbit coupling interaction decreases the CBM at Γ by 100 meV for the monolayer and 110 meV for the bilayer (Table I). Note that this is comparable in magnitude to the spin-orbit coupling interaction of 146 meV observed for the VBM of MoS2 28 monolayers. The non-dispersive nature of the valence band maximum leads to a sharp rise in the density of states at the valence edges in monolayer and bilayer α-PbO, which may cause a valence-edge electronic instability that could lead to ferromagnetism and ferroelasticity under ptype doping.28 The absolute positions of the VBM (ionization potential) and CBM (electron affinity) with respect to vacuum for all three examined structures are listed in Table 1 and shown in Fig. 2. We found that their gap straddles the redox potentials of H+/H2 (-4.44 eV) and O2/H2O (-5.67 eV),29


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and can thus act as photocatalysts for solar hydrogen production. However, the toxicity of lead and the solubility of PbO in water are compelling barriers to applications.

(a)

(b)

Figure 3. (a) In-plane and (b) out-of-plane plots of the modulus squared of the electron part of the lowest-energy exciton wave function for a fixed hole position of bulk α-PbO. The exciton is 1slike in nature and is localized in real space approximately within 11 Angstroms/3 unit cells) perpendicular to the atomic layer. The square-like (four-fold symmetric) envelop of the exciton wave function as seen along the c axis (a) is indicative of the square symmetry of the twodimensional Brillouin zone. The ellipse in (b) is a guide to the eye and is indicative of the asymmetric nature of the exciton along the in-plane and out-of-plane directions. We further investigated excitonic effects in bulk, monolayer, and bilayer α-PbO. The exciton binding energy of bulk α-PbO is large (270 meV) compared to inorganic semiconductors such as ZnO (60 meV)30 and GaN (20.4 meV)31 due to the larger effective mass and resulting small excitonic Bohr radius. Figure 3 shows the in-plane and out-of-plane plots of the modulus squared


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of the electron part of the lowest-energy exciton wave function for a fixed hole position in bulk αPbO. The envelope function reflects the symmetry of the two-dimensional Brillouin zone of square lattice. We estimate the size of the exciton by the full-width half-maximum (FWHM) of the envelope function. The wave function is strongly localized in real space within an in-plane distance of 11 Å. The large binding energies and localization of the excitons are indicative of Frenkel-like character of the lowest energy excitons. In the few-layer structures, in addition to the band-gap blue shift, the strong confinement increases the strength of excitonic interactions. The exciton binding energy is 1.1 eV and 0.9 eV for monolayer and bilayer α-PbO, respectively. The strongly bound excitons, which are thermally stable at room temperature, and the direct band gap of the α-PbO monolayer suggest it may exhibit desirable properties for light emission. However, our calculated values for the thermally averaged radiative lifetime32 of the lowest-energy exciton in monolayer PbO at 300 K is 0.9 ms, which implies that the lowest-energy exciton is dark, and non-radiative processes dominate exciton recombination. The corresponding exciton lifetime for the bilayer is 11.9 ms. Our calculations for the exciton lifetimes were performed ignoring spin-orbit coupling effects, which are not very strong in PbO. The inclusion of spin-orbit coupling increases the matrix element across the direct gap of the monolayer only by a factor of 50%, and thus the transition is dark even with inclusion of spin-orbit coupling. Our predicted lowest-exciton energy for the bulk material (2.18 eV) is larger than the experimental gap of 1.95 eV at room temperature due to temperature corrections to the quasiparticle energies, as well as errors arising from the intrinsic accuracy of the GW method, both of which are of the order of 0.1 eV. Moreover, the experimental optical gaps of 1.94 eV and 2.16 eV for five-layer and three-layer structures of α-PbO from photoluminescence and optical spectroscopy measurements14 are lower than our predicted data for the monolayer and bilayer, and


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closer to the bulk material. The disagreement with our calculations for the monolayer and bilayer originates both from temperature and inherent-accuracy effects, as well as the smaller blue shift of the band gap due to the reduced quantum confinement in these thicker layers. The orbital character of the modulus squared (real and reciprocal space plots) of the first four lowest-energy exciton wave functions in monolayer α-PbO are shown in Fig. 4. The lowest two excitons at 3.43 eV and 3.73 eV are both approximately spherically symmetric, slightly distorted by the two-dimensional square lattice. These two excitons originate from optical transitions between the top of the valence band and the lowest two conduction bands separated by 0.24 eV. The degenerate third and fourth excitons are the 2px and 2py exciton energy levels of the two-dimensional hydrogenic atom with an energy of 3.88 eV. The 2p exciton levels in monolayer α-PbO are lower in energy than the 2s levels (i.e., the fifth excitonic state, Fig. S6) because states with larger angular momenta have larger radii and are less screened, as in the case of MoS2.33 The corresponding excitonic amplitudes for the four excitons in momentum space are displayed in Fig. 4 (e)-(h). We observe spherically symmetric distribution of the reciprocal-space amplitudes for the first two s excitons, whereas a central node is observed for the subsequent px and py exciton states.


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(a) 3.43 eV

(e)

(b) 3.73 eV

(c) 3.88 eV

(g)

(f)

(d) 3.88 eV

(h)

Figure 4. In-plane plots of the modulus squared of the electron part of the exciton wave function for a fixed hole position in real space for the (a) first, (b) second, (c) third, and (d) fourth lowestenergy excitons, respectively, for monolayer α-PbO. The first two [(a) and (b)] are s-like exciton states arising from the VBM and the two lowest conduction bands. The third and fourth [(c) and (d)] excitons are px and py in nature. The corresponding excitonic amplitudes Avck for the four excitons in momentum space are shown in (e-h) for verification of the orbital character of the excitonic states. The excitons in monolayers are highly localized in real space and thus require a comparatively coarser k-point grid for convergence.


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Figure 5. (a) The imaginary part of the dielectric function of bulk α-PbO and the absorbance spectrum of (b) monolayer and (c) bilayer α-PbO with and without the inclusion of excitonic effects. The exciton binding energy is 0.27 eV for bulk α-PbO, 1.1 eV for the monolayer, and 0.9 eV for the bilayer. Monolayer and bilayer α-PbO exhibit a large maximum absorbance of 15% and 24% respectively. The absorbance spectrum of the monolayer is ideally suited for solar-blind UV photodetectors. The absorbance of the bilayer begins in the red-orange region of the spectrum, although it is overall weak in the visible.


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The optical absorption spectrum of bulk, monolayer, and bilayer α-PbO, including excitonic effects, is shown in Fig. 5 (and in logarithmic scale in Figs. S8-S9). The absorbance of the few-layer structures 𝐴(𝐸) as a function of the photon energy 𝐸 is 𝐴(𝐸) = 1 − 𝑒 −𝛼(𝐸)𝑑 = 1 − 𝑒 −2𝜋𝐸𝜀2(𝐸)𝑑/ℎ𝑐 , where 𝛼(𝐸) is the absorption coefficient, 𝜀2 (𝐸) is the imaginary part of the dielectric matrix, and 𝑑 is the thickness of the simulation cell perpendicular to the slab. The absorption spectrum shifts to lower photon energies with the inclusion of attractive excitonic interactions. The absorbance is large for few-layer α-PbO approaching maximum values of 15% for the monolayer and 24% for the bilayer, which originates from the large valence-band density of states. We note that α-PbO bilayers show an overall weak absorbance in the red-orange region of the visible spectrum. Moreover, the monolayer is almost entirely transparent (absorbance less than 0.1%) in the visible and near UV (i.e., photon wavelengths longer than 280 nm) but exhibits strong absorbance (on the order of 5-10%) in the deep UV, and could be used for atomically thin solar-blind photodetectors for, e.g., efficient detection of flames. CONCLUSIONS In summary, we investigated the electronic and optical properties of bulk, monolayer and bilayer litharge α-PbO. The monolayer has a direct band gap of 4.48 eV, while the gaps of the bulk material (2.45 eV) and the bilayer (3.44 eV) are indirect. The bilayer valence band has a Mexicanhat-like dispersion and can become ferromagnetic with doping. The exciton binding energy is 1.1 eV in monolayer α-PbO, which leads to thermally stable excitons at room temperature. However, the lowest-energy excitons are dark and their radiative lifetimes are long. The α-PbO monolayer is nearly transparent in the visible and near UV, and absorbs strongly in the vacuum-UV range, which is promising for solar-blind UV photodetectors. Our results demonstrate that 2D α-PbO


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exhibits a synergy of desirable electronic and optical properties with oxidation resistance and possible multifunctionality.

ACKNOWLEDGMENT We thank Dylan Bayerl for valuable discussions. This work was supported by the NSF ECCSCDS&E program (1607796). Computational resources were provided by the DOE NERSC facility under Contract No. DE-AC02-05CH11231. Graphics were generated with VESTA.37 SUPPORTING INFORMATION Convergence of quasiparticle band gaps and excitonic binding energy, plots of excitonic wave function. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest. REFERENCES (1)

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Dimensional Crystals: Monolayer MoS2. Phys. Rev. B 2016, 93 (23), 235435.

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