New Assembly-Free Bulk Layered Inorganic Vertical Heterostructures

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New Assembly-Free Bulk Layered Inorganic Vertical Heterostructures with Infrared and Optical Bandgaps Evan R Antoniuk, Gowoon Cheon, Aditi Krishnapriyan, Daniel A. Rehn, Yao Zhou, and Evan J. Reed Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b03500 • Publication Date (Web): 10 Dec 2018 Downloaded from http://pubs.acs.org on December 12, 2018

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New Assembly-Free Bulk Layered Inorganic Vertical Heterostructures with Infrared and Optical Bandgaps Evan R. Antoniuk†, Gowoon Cheon‡, Aditi Krishnapriyan§, Daniel A. Rehn∥, Yao Zhou§, and Evan J. Reed §* *E-mail: [email protected]. Phone: (650) 723-2971. Fax: (650) 725-4034. †Department

of Chemistry, ‡Department of Applied Physics, §Department of Materials

Science and Engineering, and ∥Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States

ACS Paragon Plus Environment

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ABSTRACT

In principle, a nearly endless number of unique van der Waals heterostructures can be created through the vertical stacking of two-dimensional (2D) materials, resulting in unprecedented potential for material design. However, this widely employed synthetic method for generating van der Waals heterostructures is slow, imprecise, and prone to introducing interlayer contaminants when compared with synthesis methods that are scalable to industrially relevant scales. Herein, we study the properties of a new class of layered bulk inorganic materials that has recently been reported, which we call assemblyfree bulk layered inorganic heterostructures, wherein the individual layers are of dissimilar chemical composition, distinguishing them from commonly studied layered materials. We find that these bulk materials exhibit properties similar to vertical heterostructures, but without the complex and unscalable stacking process. Using stateof-the-art computational approaches, we study the electronic properties of livingstonite (HgSb4S8), a naturally occurring mineral that is a bulk lattice-commensurate heterostructure. We find that isolated bilayers of livingstonite have an intralayer HSE-06 band gap of 2.08eV. This is the first report of a naturally occurring van der Waals heterostructure with a calculated band gap in the visible spectrum. We also studied the electronic properties of tetragonal Ti3Bi4O12, Sm2Ti3Bi2O12, orthorhombic Ti3Bi4O12, Nb3Bi5O15, LaTiNbBi2O9 and AgPbBrO and found some of them are potentially well suited for photovoltaic applications. We also provide characterization of the electronic structure of the isolated bilayer and monolayer subcomponents of the bulk


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heterostructures. The report of the properties of these materials significantly enhances the library of known van der Waals heterostructures.

KEYWORDS two-dimensional materials; van der Waals heterostructures; density functional theory; layered materials; band gap; heterojunctions TEXT As a result of the ever growing library of two-dimensional (2D) materials, vertical stacks of chemically dissimilar, weakly-bound 2D layered materials known as van der Waals heterostructures have recently garnered significant interest. In particular, these materials allow for control over the chemical composition of the 2D layers and the stacking sequence in the van der Waals heterostructures, which in turn allows for the precise tailoring of the properties of the heterostructure for a specific application1. Furthermore, since the 2D layers are held together through weak van der Waals interactions, these heterostructures can be fabricated without any lattice matching restrictions2. As such, van der Waals heterostructures have been employed in devices including LEDs, photovoltaics, and 2D superconductors.3–5 Owing to their relatively large absorption coefficient, tunable band gap, and ultrathin width, monolayers of 2D transition metal dichalcogenides (TMDs) have widely been explored for use in many photonic applications.6

As a result, recent efforts have

attempted to study photogenerated interlayer excitons in heterostructures composed of


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TMDs including MoS2/WSe2, MoSe2/WSe2, and MoS2/WS2/MoSe2.7–9 The interlayer exciton lifetime in these materials has typically been measured to be on the order of nanoseconds and is substantially lengthened by the spatial separation of the photogenerated electron-hole pairs.9 On the other hand, electrons have been shown to be very quickly and efficiently shuttled between layers in heterostructures. For example, an electron transfer time of 1.5ps has been measured in a trilayer MoS2/WS2/MoSe2 heterostructure.7 Accordingly, these materials have been proposed to be candidates for ultrathin photovoltaic devices.4 However, studies of the charge transfer processes in van der Waals heterostructures have largely been limited to heterostructures composed of monolayers of boron nitride, graphene, or TMDs. Despite the numerous attractive properties of van der Waals heterostructures, their experimental synthesis has faced challenges. One possible synthetic method involves manually stacking individual 2D layers obtained from the mechanical exfoliation of several different bulk layered materials.10

However, this method is susceptible to

contamination as adsorbates attached to the surface of the 2D layers can become trapped in the interface between the two layers. Additionally, the process of manually stacking the layers is arduous and precisely aligning the 2D crystals is challenging. As such, this method faces challenges for large-scale synthesis.11 An alternative method involves the chemical vapor deposition (CVD) growth of layers on top of each other.12 However, due to the restrictive temperature and pressure conditions required for the CVD growth of each 2D crystal, this method has considerable limitations in the variety of heterostructures that it can produce. Although a one-step CVD growth method has been


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reported for the synthesis of vertical stacks of MoS2/WS2 heterostructures, this method has limited control of the size of the heterostructures produced.13 Molecular beam epitaxy approaches have also been employed to generate high quality and well oriented vertically stacked heterostructures. Using this approach, atomically thin van der Waals heterostructures of MoSe2/HfSe2, MoTe2/MoS2, SnSe2/WSe2

and hexagonal boron

nitride/graphene have been produced.14–17 Layered hybrid organic-inorganic materials have also been synthesized with solution fabrication methods.18 For example, solution processing methods have been used to provide an easy and low-cost method for the production of hybrid perovskite solar cells, but have challenges in reliably reproducing large-area films and are generally expected to exhibit lower mobilities than entirely inorganic heterostructures.19 An alternative approach for synthesizing inorganic van der Waals heterostructures involves mechanically exfoliating a bulk crystal that is composed of vertical stacks of chemically dissimilar layers. Since this approach does not require any manual stacking of layers, complications related to interlayer contamination and the misalignment of the layers are avoided. Additionally, this process is considerably less labor-intensive than manually stacking the layers. By exfoliating the bulk heterostructures down to single monolayers, this approach may also serve as a simple means of synthesizing for the previously inaccessible 2D materials. To further simplify the synthetic process, van der Waals heterostructures have been created from the mechanical exfoliation of bulk naturally occurring minerals. In particular, the bulk mineral franckeite, whose structure consists of alternating layers of SnS2 and PbS, has been successfully exfoliated to yield a


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few-layer van der Waals heterostructure.20,21

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Furthermore, mechanically exfoliated

franckeite flakes were then implemented into a near-IR photodetector device, demonstrating the potential applications of these materials.20,21 The use of a naturally occurring mineral eliminates the need for any synthesis of artificial materials while also ensuring the air stability of the bulk crystal. Perhaps even more importantly, in the absence of exfoliation, the bulk materials consist of superlattice heterostructures that may be amenable to photonic and other applications involving charge carrier separation or recombination. The interfacial area in these materials scales with the volume of material, rather than the two-thirds power of volume that one might expect for a single interface. Currently, the main limitation of this approach is the small number of known, bulk, layered crystals with dissimilar layers. In earlier work, we implemented a data mining approach to identify weakly bonded layered materials found within the publicly available databases of tens of thousands of experimentally characterized crystals.22 In this earlier work, we identified over 1000 layered materials, 487 materials consisting of weakly bonded one-dimensional or molecular wire subcomponents, and 98 bulk crystals composed of heterostructures of chemically dissimilar 1D and 2D subcomponents from the Materials Project database of mostly experimentally characterized crystals.22,23 The complete list of materials can be found in the Supporting Information in Reference 22. In the present work, we employ Kohn-Sham density functional theory to investigate the feasibility of generating fewlayer van der Waals heterostructures from these newly uncovered bulk crystals. Furthermore, we explore the electronic structure of the heterostructure bilayers and each


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of its subcomponent monolayers to provide the first characterization of these few-layer materials. While conventional vertical heterostructures require challenging fabrication techniques that are difficult to scale, we find that these materials exhibit the properties of vertical heterostructures in their bulk form, eliminating the need for complex fabrication techniques of nanostructures altogether. Hence, we refer to these bulk materials as assembly-free vertical heterostructures.

Figure 1. Structures of the layered, bulk, lattice-commensurate heterostructures studied in this work and their corresponding Materials Project ID: (a) Tetragonal Ti3Bi4O12, Mp2333524 (b) Sm2Ti3Bi2O12, Mp-55743825 (c) Orthorhombic Ti3Bi4O12, Mp-62219826 (d) Nb3Bi5O15, Mp-64559227 (e) LaTiNbBi2O9, Mp-63665428 (f) AgPbBrO, Mp-55947029 and (g) HgSb4S8, Mp-54259630. All of the structures shown are DFT relaxed versions of experimentally characterized, bulk structures as given on the Materials Project database. Structures (a), (b), (c), and (e) are all Aurivillius phase perovskites, which are structures consisting of alternating layers of [Bi2O2]2+ and a perovskite-like layer with the general formula [An-1BnO3n+1]2-. Compound (g) is the bulk structure of the naturally occurring mineral, livingstonite. Calculated interlayer distances and their experimental comparisons can be found in the SI.


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To identify the most promising heterostructures for study with hybrid DFT calculations, we apply a number of filters to shrink the list of 98 bulk heterostructures. First, we limit our study to only those bulk structures with direct experimental report of their synthesis and structural characterization. Next, we include only heterostructures that are composed of layers of 2D subunits. Finally, we limit this study to materials with a calculated bulk PBE band gap between 1-3eV to increase the likelihood that bilayers of these bulk crystals will also have band gaps in the visible or IR spectrum for photonic applications. Although it has a PBE calculated bulk band gap of 0.537eV in the Materials Project database, we also include AgPbBrO as AgBr/PbO systems have been reported to be studied for use in photodiodes.31 Furthermore, a AgBr/ZnO heterojunction has been reported to exhibit considerable photocatalytic activity for the degradation of rhodamine B, an environmentally harmful and non-biodegradable organic dye used in pigmentation industries.32 Applying these requirements reduces the number of bulk heterostructures down to 7 (Figure 1), which is tractable to be investigated with hybrid DFT calculations. Notably, this list includes livingstonite, a naturally occurring bulk mineral whose structure consists of alternating layers of HgSb2S4 and SbS2.33 Additionally, 4 of these compounds belong to a class of materials known as Aurivillius phase oxides.34–36 These compounds are given by the general formula Bi2An-1BnO3n+3 and are comprised of alternating layers of [Bi2O2]2+ and the perovskite-like layer of [An1BnO3n+1]

2-,

where n is the number of layers.37 These materials have previously been

extensively studied for their ferroelectric38 and oxide ion conductivity39 properties. Additionally, Aurivillius phase perovskites have been explored as visible-light


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photocatalysts for the degradation of environmental pollutants.40

Notably, the

Aurivillius phase perovskites studied in this work do not contain Pb, alleviating the environmental concerns typically associated with the processing of lead-based materials including perovskite solar cells.41 To determine the ease at which these bulk heterostructures may be mechanically exfoliated down to few-layer systems, we calculate the interlayer cohesive energy (Equations 1-2) with the PBE exchange-correlation functional (Figure 2).

To better

account for van der Waals interactions, these calculations were performed with the DFTD3 correction method.42 As GGA functionals tend to neglect long-range van der Waals interactions, including this correction resulted in a larger calculated interlayer cohesive energy for all compounds. To validate the use of the D3 correction, the calculated interlayer distances are compared to the experimental values and found to have an average deviation of 0.31Å (see SI).

Notably, the interlayer cohesive energy value

calculated with Equation 1-2 is the difference between the energy of the heterostructure and the sum of the energies of the two isolated and stress relaxed monolayers. As such, this value includes some component of stress relaxation energy in addition to interlayer van der Waals interactions. Figure 2 also shows an approximate maximum interlayer cohesive energy of potentially exfoliable layered materials of 150 meV/Å2 for comparison.

This upper bound was chosen to correspond with the vdW-optB8843

calculated interlayer cohesive energy of SnSe44, which has previously been reported to form 2D monolayers.45 We find that isolated bilayers of AgPbBrO and HgSb4S8 are weakly bound by interlayer van der Waals interactions with cohesive energies of 5 meV/


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Å2 and 32meV/Å2, respectively, and are likely to be exfoliable. Interestingly, the more strongly bound materials identified here are Aurivillius phase materials which have the general formula of layers of [Bi2O2]2+ and [An-1BnO3n+1]2-. In order to maintain charge neutrality, these materials must contain interlayer charge transfer. This result is further supported by the calculated Bader charges on the atoms at the heterointerface (see SI, Table S4). Since this class of materials is known to have interlayer charge transfer, our choice of screening criteria (PBE calculated bandgap between 1-3 eV) may have disproportionately increased the number of high interlayer binding energy compounds found relative to lower bandgap materials. Neglecting structural relaxation, the calculated bulk cohesive energy of these materials should be twice that of its bilayer cohesive energy per formula unit if the binding is dominated by nearest neighbor van der Waals interactions since the bulk material possesses twice as many bonded interfaces. The two most weakly bonded materials in Figure 2 (HgSb4S8 and AgPbBrO) approximately obey this condition, suggesting van der Waals dominated bonding. However, the oxides exhibit stronger bilayer bonding relative to the bulk, consistent with an ionic charge transfer character. To determine the mechanical stability of the monolayers generated through the exfoliation of these heterostructures in a freely suspended form, we also calculate some of their phonon spectra and elastic constants. The density functional perturbation theory (DFPT) calculated phonon spectrum of the PbO monolayer contains all positive frequencies and its elastic matrix was found to be positive definite, indicating that the PbO monolayer is likely to be mechanically stable as a freely suspended monolayer. Very


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recently, atomic sheets of 𝛼-PbO were reported to be synthesized through a sonochemical exfoliation technique and exhibited a direct, visible band gap and higher thermal stability than monolayer MoS2.46 In addition, these heterostructures offer a feasible route to study the properties of charged monolayers such as BiO2+ which have no bulk counterpart due to charge neutrality constraints.

Figure 2. Calculated interlayer cohesive energy per area of all of the heterostructures considered in this study (Equation 1-2). The values shown here were calculated with the PBE functional with the D3 correction method applied to better account for van der Waals interactions between layers. An approximate upper bound for exfoliable materials is depicted for comparison.44 Due to the presence of glide or mirror planes in the monolayers of all heterostructures, the interlayer cohesive energy values are invariant to the stacking sequence of the layers in the heterostructure bilayer and bulk heterostructures. Calculated energies are with respect to charge neutral and zero stress monolayers. Next, to gain some insight into the electronic structure of these materials, we perform band structure calculations on the bulk heterostructures, the bilayers of the


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heterostructures, and each of the separated monolayers (Figure 3). All of the compounds are composed of two non-metallic monolayers since the bulk materials were chosen to be non-metallic. Furthermore, the majority of the compounds studied have PBE band gaps in the visible region, thus suggesting potential solar photonic applications for these materials.

The PBE functional typically considerably underestimates band gaps,

particularly for oxides. In the case of the AgBr and PbO monolayers, the HSE-06 band gaps are 0.79eV and 0.91eV larger than the PBE calculated band gaps, respectively. As such, a similar increase in the band gaps of the other materials may be expected if the HSE-06 functional was to be used. The difference in the band gaps between the bulk heterostructures and their corresponding bilayers in Nb3Bi5O15, Ti3Bi4O12, and Sm2Ti3Bi2O12 also suggests that these materials may be suitable for band-gap engineering through varying the number of vertically stacked layers.


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Figure 3. Calculated quasiparticle band gaps of all relaxed bulk heterostructures, the heterostructure bilayers, and their monolayer subcomponents. The band gaps shown here are calculated with the PBE functional except for AgPbBrO and the HgSb4S8 monolayers, which were calculated with HSE-06. Spin-orbit coupling effects were included in the calculation of all PBE band gaps. The chemical composition of each monolayer is shown above each corresponding bar, whereas the bulk chemical composition is shown beneath the bars. Upon ionic relaxation, the BiO2+ monolayer in orthorhombic Ti3Bi4O12 exists in a different structural phase than in the other heterostructures, accounting for its significantly different band gap.


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Figure 4. Partial band structure of the a) HSE-06 AgPbBrO heterostructure and its unrelaxed monolayer subcomponents and b) PBE livingstonite heterostructure. The depictions of the set of high symmetry k-points in reciprocal space can be found in Ref. 65. To allow the band structures to be compared, the vacuum level is set to be 0eV for all band diagrams. a) The PbO and AgBr monolayer band structures shown here were calculated with the structure of the monolayers upon cleavage of the heterostructure bilayer without allowing the monolayer structures to be relaxed to illustrate the effect of interlayer interactions on the band structure. The vacuum level of bulk AgPbBrO is taken to be equal to the vacuum level of the isolated AgPbBrO bilayer. The bulk and bilayer AgPbBrO heterostructure and the PbO monolayer all exhibit a direct band gap at Γ of 1.11eV, 0.85eV and 2.98eV respectively. The AgBr monolayer possesses an indirect band gap of 2.85eV with the valence band maximum located at X and the conduction band minimum located at Γ. Notably, the AgPbBrO bilayer valence band edge closely resembles the PbO monolayer valence band edge, whereas the AgPbBrO bilayer conduction band edge closely resembles the AgBr monolayer conduction band edge. This and the relatively small energy dispersion in the bands along the Γ-Z, interlayer direction in the bulk suggests that the electronic interlayer interactions are relatively weak. The calculated electron effective mass in the interlayer and intralayer directions for bulk AgPbBrO is 0.57me and 0.47me, respectively, while the hole effective mass in the interlayer and intralayer directions is 0.76me and 5.75me. b) The livingstonite band structure is calculated along the monoclinic reciprocal space path: Γ-Y-H-C-E-M1-A-X-Γ-


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Z-D-M Z-A D-Y, where Γ-Y is the interlayer direction. The livingstonite heterostructure bilayer and monolayer SbS2 both have an indirect PBE-calculated band gap of 1.12eV and 1.20eV respectively, with the valence band maximum located between Γ and Z and the conduction band minimum located at Γ. Monolayer HgSb2S4 has a direct band gap at Γ of 1.50eV. The calculated electron effective mass in the interlayer and intralayer directions for bulk livingstonite is 0.51me and 0.40me, respectively, while the hole effective mass in the interlayer and intralayer directions is 1.14me and 0.64me. To further characterize the electronic structure of AgPbBrO and HgSb4S8, we perform band alignment calculations to classify the heterojunction as type I (straddling gap), type II (staggered gap), or type III (broken gap). Figure 4 shows the aligned band structure of the AgPbBrO and livingstonite heterostructure bilayers. We approximate the band alignments of weakly bonded heterostructure bilayers determined from their substituent monolayers using the assumption that the weak interlayer interactions will not significantly alter the magnitude of the band gap or the absolute energy of the Fermi level.47 In Figure 4, we can see this approximation is justified for both AgPbBrO and livingstonite bilayers. For AgPbBrO, the bilayer band structure can be well approximated as the superposition of the AgBr and PbO monolayer band structures. In Figure 4b), the livingstonite bilayer valence band and conduction band edge shape and location more closely resembles that of the SbS2 monolayer bands than the HgSb2S4 monolayer bands. Since the position of the VBM and CBM are insensitive to interlayer interactions, livingstonite is probably closest to a type I heterojunction since both the shape and location of the VBM and CBM most closely resemble that of a single monolayer, the SbS2 monolayer. Notably, this is the first report of a naturally occurring bulk heterostructure that can be mechanically exfoliated to yield a type I heterojunction.

Type I


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heterostructures spatially isolate holes and electrons to a single layer which allows for efficient recombination and photon emission. As such, heterostructures of this type have seen use in LED and laser applications.48,49 Figure 5 shows the band alignments of HSE–06 calculations on the monolayers of AgPbBrO and livingstonite. Both HSE-06 and PBE calculations on the relaxed monolayers of livingstonite incorrectly suggest that HgSb4S8 exists as a type II heterojunction with the conduction band edge residing in the SbS2 layer and the valence band edge residing in the HgSb2S4 layer. However, performing the same calculations while constraining the atomic positions and lattice constants of the isolated monolayers to that of the bulk livingstonite heterostructure results in a type I heterojunction shown in Figure 5a). In this case, the relaxation of the monolayers significantly impacts the classification of the heterostructure and results in the misclassification of the livingstonite bilayer.

A

previous report suggests strong optical absorptions in mercury chalcogenide compounds as a result of electronic transitions from the chalcogen s orbitals in the valence band to mercury and chalcogen s orbitals in the conduction band, suggesting strong intralayer absorption.40 Figure 5a) shows AgPbBrO to be a type II heterojunction with the conduction band edge residing in the AgBr layer and the valence band edge residing in the PbO layer. This result agrees with previously proposed band alignments in AgBr/PbO emulsions.31 In the type II band alignment, injected electrons and holes become spatially separated into the conduction band and valence band layers, respectively. Assuming these particles have a sufficiently long lifetime, the electron and hole can then be removed through an


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external circuit. As such, heterojunctions of this type allow for charge separation across the two different layers and have been proposed for use in photovoltaics.4

Figure 5. a) HSE-06 calculated band alignment of isolated constituent monolayers of HgSb4S8 (livingstonite) and AgPbBrO constrained to the atomic positions and lattice


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constants of their respective bulk heterostructures. The value located next to each bar represents the energy of the corresponding band edge relative to the vacuum level and the value located next to the arrow is the magnitude of the quasi-particle gap. To align the bands, the band structures of the two monolayers in each heterostructure are shifted such that the calculated vacuum level is 0eV. In agreement with PBE results in Figure 4, these results also suggest that livingstonite and AgPbBrO form type-I and type II heterojunctions, respectively. b) PBE calculated plot of the imaginary part of the KuboGreenwood dielectric function for bulk AgPbBrO, its heterostructure bilayer, and its monolayer substituents. The in-plane component of the dielectric tensor corresponds to either the x or y directions since the dielectric tensor is isotropic in-plane, whereas the out-of-plane component corresponds to the z direction. The bulk and bilayer heterostructure show considerable interlayer absorption at ~0.5eV, consistent with the PBE calculated quasiparticle band gap of 0.39eV. TMDs have shown promise for use in ultrathin photonic devices in part due to their relatively strong light absorption.51 To further investigate the promise of AgPbBrO and livingstonite for use in optoelectronic applications, we determine the effective masses of electrons and holes in the bulk. For AgPbBrO, the HSE-06 calculated electron effective mass in the interlayer and intralayer directions for bulk AgPbBrO is 0.57me and 0.47me, respectively, while the hole effective mass in the interlayer and intralayer directions is 0.76me and 5.75me. Remarkably, the holes in AgPbBrO have a smaller effective mass in the interlayer direction than the intralayer direction. The calculated hole effective masses in AgPbBrO are consistent with previously calculated hole effective masses in bulk PbO of 1.12me in the interlayer direction and 5.91me in the intralayer direction.52 In particular, the large in-plane hole effective mass in PbO has been attributed to the strong localization of valence band electron density on the oxygen atoms.52 Our calculations of the valence band electron density in bulk AgPbBrO (see Supporting Information) also show strong localization of electron density on the oxygen atoms.


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We also determine the strength of light interactions with AgPbBrO by calculating the imaginary part of the dielectric function for bulk AgPbBrO, its heterostructure bilayer, and its monolayer substituents (Figure 5b).

The magnitudes of the out of plane

component of the interlayer absorption peaks of the heterostructure are comparable in magnitude to the out of plane intralayer absorption peaks of the AgBr and PbO monolayers. This result as well as the relatively low effective masses provides promising evidence for the efficient generation of spatially separated electrons and holes in bulk AgPbBrO. The calculated electron effective mass in the interlayer and intralayer directions for bulk livingstonite is 0.51me and 0.40me, respectively, while the hole effective mass in the interlayer and intralayer directions is 1.14me and 0.64me. The band offsets in Figure 5a) suggest that the valence band holes must tunnel through the gap of the HgSb2S4 layer to move in the interlayer direction, consistent with the larger effective electron mass for propagation in the interlayer direction. No such restriction is placed on the conduction band electrons.

For comparison, the HSE-06 effective masses of bulk 2H-MoS2 in the

interlayer direction are reported to be 0.49me for electrons and 0.80me for holes.53 The effective masses for livingstonite suggest promise for the use of livingstonite in photonic applications. One of the current state-of-the-art materials used in solar cells is the hybrid inorganic-organic perovskite: methylammonium lead iodide.54 These materials boast low hole and electron effective masses (0.29 me and 0.23me ),55 but have issues associated with stability as well as lead toxicity.


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While bulk MoS2 has been reported to exhibit a relatively weak exciton binding of ~84 meV,56 single layer TMDs have been reported to exhibit photogenerated holes and electrons that are tightly bound by Coulombic interactions as excitons. In these single layer systems, the exciton binding energy is typically approximately 0.5eV depending on the local environment and reflects the difference between the quasiparticle band gap and the optical absorption band gap of the material.57 It is possible to speculate that exciton binding energies could also follow a similar trend for livingstonite and AgPbBrO, with bulk binding energies suppressed by dielectric screening and single layer or bilayer structures exhibiting higher potential for strong binding. In summary, we have employed DFT to investigate the electronic and mechanical properties of newly uncovered bulk superlattice van der Waals heterostructures. These materials have been previously reported to be mined or synthesized directly into heterostructure forms, eliminating the need for challenging layer by layer fabrication procedures typically employed to create heterostructures of other layered materials. We find that the interlayer cohesive energies of AgPbBrO and HgSb4S8 are small enough to be suitable for mechanical exfoliation. The band structures of all heterostructure bilayers and their monolayer constituents were calculated. We find that the relatively weak interlayer interactions present in AgPbBrO and livingstonite allows for the electronic band structure of the heterostructure bilayers to be approximated as the superposition of the electronic band structures of their constituent monolayers. Our results suggest that AgPbBrO and livingstonite form type-II and type I heterojunctions, respectively. This is the first report of a naturally-occurring bulk van der Waals heterostructure with a


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calculated band gap in the visible spectrum.

We find that both AgPbBrO and

livingstonite exhibit photocarrier effective masses comparable to those reported in bulk MoS2.53 These results suggest promising potential uses for these materials in photocatalytic or photovoltaic applications. All Kohn-Sham density functional theory (KS DFT)58,59 computations were performed with the Vienna ab initio simulation package (VASP 5.4.1)60 with the projector augmented-wave (PAW) method.61 All bilayer heterostructures and 2D monolayers were initially relaxed to an ionic step energy convergence of 10-4 eV using self-consistent, periodic DFT. A vacuum space of ~20Å is included between slabs to ensure there is no interaction between periodic images. A 9x9x1 Monkhorst-Pack k-point mesh is initially used to sample the Brillouin zone with denser meshes used to check for total energy convergence.62 A plane wave basis set is implemented with a kinetic energy cut-off of 520eV for all oxygen containing structures, whereas a cut-off of 340eV is used for HgSb4S8. The exchange-correlation energy is treated with the generalized gradient approximation (GGA) PBE functional for the relaxation of structures.63 Once the relaxed structures have been obtained, the interlayer cohesive energy, Ecoh is then calculated as 𝐸𝑐𝑜ℎ = 𝐸𝑐𝑜ℎ =

((𝐸𝑚𝑜𝑛𝑜𝑙𝑎𝑦𝑒𝑟,1 + 𝐸𝑚𝑜𝑛𝑜𝑙𝑎𝑦𝑒𝑟,2) ― 𝐸𝑏𝑖𝑙𝑎𝑦𝑒𝑟) 𝐴𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 ((𝐸𝑚𝑜𝑛𝑜𝑙𝑎𝑦𝑒𝑟,1 + 𝐸𝑚𝑜𝑛𝑜𝑙𝑎𝑦𝑒𝑟,2) ―𝐸𝑏𝑢𝑙𝑘) 𝐴𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒

(Equation 1) (Equation 2)

for the bilayer and bulk cohesive energies, respectively. Here, Ebilayer is the free energy of the relaxed heterostructure bilayer, Ebulk is the free energy of the relaxed bulk heterostructure, Emonolayer,1,2 are the free energies of the relaxed individual monolayer constituents of the heterostructure, and Ainterface is the area of the interface between the


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two monolayers. Due to the in plane mirror symmetry present in all of the studied monolayers, the relative ordering of the layers in the heterostructure bilayer does not affect the calculated cohesive energy values. The DFT-D3 correction method is employed to provide a more accurate description of interlayer van der Waals interactions.42 Dipole corrections are applied to all slab calculations to correct for the artificial electric field created in the supercell as a result of using periodic boundary conditions.64 The band structures for all heterostructure bilayers and 2D monolayers are calculated along lines of k-points according to the symmetry of the solid.65 The PBE functional is employed for all band structure computations, while the HSE-06 functional is also used to provide a more accurate band structure of AgPbBrO and the monolayers of HgSb4S8.66 Spin-orbit coupling was included in the calculation of all PBE band structures. Band alignment calculations were also performed for HgSb4S8 and AgPbBrO.

The band

structures of the two isolated monolayers in each compound were aligned by first calculating the maximum of the Kohn-Sham potential in the middle of the vacuum region for each monolayer. Then, all of the energy bands in each monolayer are shifted such that the vacuum level of the two monolayers are equal. The effective masses of HgSb4S8 and AgPbBrO were determined from the PBE and HSE-06 calculated band structures of each bulk heterostructure. The electron and hole effective masses are calculated by fitting the band structures to Equation 3 and Equation 4, respectively. The calculated effective masses as a function of the number of k-points included can be found in the Supporting Information.


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∂2𝐸𝑘 ―1

(Equation 3)

𝑚 ∗ 𝑒 = ℏ2( ∂𝑘2 )

∂2𝐸𝑘 ―1

(Equation 4)

𝑚 ∗ ℎ = ―ℏ2( ∂𝑘2 )

ASSOCIATED CONTENT Supporting Information Charge density plots of the valence band and conduction band of bulk AgPbBrO. Calculated effective masses as a function of number of k-points included. Calculated interlayer distances and their comparison to experimental values for all bulk heterostructures. Calculated density of states of isolated bilayers of AgPbBrO and livingstonite and their monolayer components. Calculated Bader charges on atoms at the heterointerfaces.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Phone: (650) 723-2971. Fax: (650) 725-4034. ACKNOWLEDGMENT


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This work was partially supported by Army Research Office Grant W911NF-15-1-0570, by Office of Naval Research Grant N00014-15-1-2697, by NSF Grant DMR-1455050 and EECS-1436626. REFERENCES (1) (2) (3)

(4) (5) (6) (7) (8)

(9) (10) (11) (12) (13)

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New Assembly-Free Bulk Layered Inorganic Vertical Heterostructures

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