Polarity‐Driven Atomic Displacements at the 2D Mg2TiO4‐MgO (001) Oxide Interface for Hosting Potential Interlayer Excitons

Interlayer excitons in solid‐state systems have emerged as candidates for realizing novel platforms ranging from excitonic transistors and optical qubits to exciton condensates. Interlayer excitons have been discovered in 2D transition metal dichalcogenides, with large exciton binding energies and the ability to form various van der Waals heterostructures. Here, an oxide system consisting of a single unit cell of Mg2TiO4 on MgO (001) is proposed as a platform for hosting interlayer excitons. Using a combination of density functional theory (DFT) calculations, molecular beam epitaxy growth, and in situ crystal truncation rod measurements, it is shown that the Mg2TiO4‐MgO interface can be precisely controlled to yield an internal electric field suitable for hosting interlayer excitons. The atoms in the polar Mg2TiO4 layers are observed to be displaced to reduce polarity at the interface with the non‐polar MgO (001) surface. Such polarity‐driven atomic displacements strongly affect electrostatics of the film and the interface, resulting in localization of filled and empty band‐edge states in different layers of the Mg2TiO4 film. The DFT calculations suggest that the electronic structure is favorable for localization of photoexcited electrons in the bottom layer and holes in the top layer, which may bind to form interlayer exciton states.


Introduction
An exciton is a bosonic quasiparticle that is attractive for novel applications when it can be manipulated electronically and optically. For example, optical qubits with ultrafast control and fast excitonic switches have been demonstrated using excitons in InAs quantum dots (QDs), AlAs-GaAs coupled quantum wells (CQWs), and MoS 2 -WSe 2 van der Waals (vdW) heterostructures. [1][2][3][4] Also, signatures of Bose-Einstein condensates of excitons have been reported in materials such as MoSe 2 -WSe 2 heterostructures and GaAs-AlGaAs CQWs, along with the prediction of superconductivity in exciton condensates. [5][6][7][8][9] For practical applications, large exciton binding energies and long lifetimes ensure the stability of the excitonic states. [1,10] To this end, interlayer excitons in transition metal dichalcogenide (TMD) heterostructures have emerged as prominent candidates. 2D TMDs that are Interlayer excitons in solid-state systems have emerged as candidates for realizing novel platforms ranging from excitonic transistors and optical qubits to exciton condensates. Interlayer excitons have been discovered in 2D transition metal dichalcogenides, with large exciton binding energies and the ability to form various van der Waals heterostructures. Here, an oxide system consisting of a single unit cell of Mg 2 TiO 4 on MgO (001) is proposed as a platform for hosting interlayer excitons. Using a combination of density functional theory (DFT) calculations, molecular beam epitaxy growth, and in situ crystal truncation rod measurements, it is shown that the Mg 2 TiO 4 -MgO interface can be precisely controlled to yield an internal electric field suitable for hosting interlayer excitons. The atoms in the polar Mg 2 TiO 4 layers are observed to be displaced to reduce polarity at the interface with the non-polar MgO (001) surface. Such polarity-driven atomic displacements strongly affect electrostatics of the film and the interface, resulting in localization of filled and empty band-edge states in different layers of the Mg 2 TiO 4 film. The DFT calculations suggest that the electronic structure is favorable for localization of photoexcited electrons in the bottom layer and holes in the top layer, which may bind to form interlayer exciton states. monolayer or bilayer thick can host strongly bound excitons with large binding energies (>100 meV). [11,12] When 2D TMDs of different materials are layered to form heterostructures, photo excited electrons and holes can be localized in distinct layers that are spatially separated. These electrons and holes can bind to form interlayer excitons, which have order of magnitude longer lifetimes. [13][14][15] Recently, interlayer exciton research has expanded to investigate of interlayer excitons in heterostructures with various form factors such as moiré superlattices, [16][17][18][19][20][21][22][23] cavity-coupled TMD heterostructures, [16,[24][25][26][27][28][29][30][31][32] in-plane lateral heterostructures and TMD-metal hybrid structures. [33][34][35][36] These structures have proven to be powerful platforms for tuning the exciton behavior. For example, moiré potentials lead to exciton localization and modified optical selection rules for the excitons. [16][17][18][19][20][21][22][23]37,38] Cavity-coupled TMD heterostructures can enhance spontaneous emission or enable lasing of the interlayer excitons through the Purcell effect, which has important implications for creating tunable and valley-polarized semiconductor lasers. [16,[24][25][26][27][28][29][30][31][32] Moreover, in-plane lateral heterostructures and TMD-metal hybrid structures such as MoS 2 -Ag have shown plasmon-exciton coupling that leads to a plexciton polaron state, which improves surface catalytic reaction efficiency. [33,34] These examples illustrate the importance of the structure in which the excitons reside for modifying or improving the excitons' performance.
Motivated by the efforts to enhance exciton properties via heterostructuring, we extend our focus to transition metal oxide (TMO) systems. Recently, 2D transition metal oxides (TMOs) have been predicted to exhibit even larger exciton binding energies, on the order of 1 eV. [39][40][41] Moreover, it has been reported that TMOs such as anatase TiO 2 can host strongly bound excitons even in bulk form. [42][43][44] TMOs can also be robust under ambient conditions, are conducive to size scaling using wellestablished thin film growth techniques, and allow integration with both existing metal-oxide technologies and novel complex oxide devices. [45][46][47][48][49] For example, enhanced and tunable photocurrent has been reported for a ferroelectric BaTiO 3 (BTO) sandwiched between SrTiO 3 (STO) and CaTiO 3 (CTO) layers. [50] It has been suggested that the binding energy of the excitons in the BTO is reduced due to the higher permittivity of the STO-BTO-CTO superlattices, which results in enhanced dissociation of the excitons. [50] However, using oxides for hosting interlayer excitons poses unique challenges. Unlike 2D TMDs, for which vdW epitaxy or exfoliation is readily achieved, oxide epitaxy is often complicated by issues such as lattice mismatch and interfacial intermixing; moreover, interaction of the film with the substrate leads to atomic-scale structural distortions at the interface, which can alter the electronic properties of the film. For instance, Mg 2+ ions at the Fe 3 O 4 -MgO interface have multiple diffusion pathways and kinetics that lead to the formation of either spinel Mg 1-x Fe 2+x O 4 or rocksalt Mg 1-y Fe y O layers, depending on the annealing conditions. [51] Here, based on density functional theory (DFT) calculations, we propose that a single unit cell (uc) of 2D Mg 2 TiO 4 on an MgO (001) substrate can host interlayer excitons, grown on large area substrates, and is robust to dry air exposure. While measuring interlayer excitons is beyond the scope of this work, we present experimental growth, structural characterization, and theoretical band structure calculation results for Mg 2 TiO 4 on MgO (001) that suggest this system can host interlayer excitons. We grow and characterize the Mg 2 TiO 4 -MgO structure using molecular beam epitaxy (MBE) and perform in situ crystal truncation rod (CTR) measurements to determine the interface and film structure. DFT calculations predict that the photoexcited electrons and holes are spatially separated and localized at the bottom and the top Mg 2 TiO 4 layers respectively, which can then bind to form interlayer excitons. This spatial separation is favored by a polarization within the film that is predicted theoretically and inferred experimentally from the displacement of Mg tetrahedral sites at the interface. Through in situ CTR measurements, we confirm such displacements at the interface and resolve the Mg 2 TiO 4 -MgO structure at the atomic level.

Design Considerations for Oxides with Interlayer Exciton States
The main challenge in creating oxide heterostructures that can host long-lived interlayer excitons is finding a material structure that has both suitable band alignment and accessible synthesis window. Regarding growth, one needs to use a latticematched substrate and film to achieve epitaxial growth, which is needed for a high-quality interface, and to fabricate a 2D film that has low enough defect densities to avoid degrading exciton lifetimes.
To confine the low-energy excitons to the 2D film, the substrate bandgap must be larger than the film bandgap. [52] If the substrate bandgap is smaller than the film bandgap, either the 2D substrate's conduction band minimum (CBM) or valence band maximum (VBM), or both, will be inside the bandgap of the 2D film and the photoexcited carriers can easily delocalize into the thick substrates. For example, if the substrate CBM is within the film bandgap, photoexcited electrons can move about the substrate instead of staying in the film.
The standard approach to achieving excitons with spatially separated electrons and holes is to have a staggered or type-II band alignment across an interface [53][54][55][56] whereby the CBM lies on one side of the interface and the VBM on the other side. In TMD heterostructures with type-II band alignment, an optical excitation initially creates intralayer excitons that then turn into interlayer excitons with electrons and holes separated into different layers via ultra-fast charge transfer process. The Coulomb interaction between the spatially separated electrons and holes can lead to the formation of bound interlayer excitons. [57][58][59] An important characteristic of the interlayer excitons is that they can be tuned in multiple ways such as via external electric fields, interlayer separation thickness, and twist angle. For example, the energy of the interlayer excitons can be tuned by an applied electric field via quantum-confined Stark effect, [1,13,[60][61][62][63] potentially of interest for applications in electrically tunable light emitters. [64] The interlayer exciton lifetime can also be tuned by an electric field by altering the overlap of the electron and hole wavefunctions in the out-of-plane direction. [65] It is also possible to tune the interlayer exciton www.advmatinterfaces.de energy by altering the physical structure of the films: interlayer exciton energies can be tuned by varying the interlayer separation thickness through thermal annealing [66][67][68] or insertion of hexagonal boron nitride (h-BN) layers in between the TMD layers. [69,70] Similarly, pressure tuning of exciton properties has been reported for a WSe 2 -MoSe 2 system. [71][72][73] What is relevant for us is that these electric field effects mean that if the 2D film has a built in electric field (via an intrinsic electrical polarity), then the electrons and holes in a single 2D film can automatically reside on different sides of the 2D film, and we will show that our Mg 2 TiO 4 -MgO heterostructure has this property.
The behavior of an interlayer exciton also depends heavily on the momentum mismatch between the constituent electron and hole, which in TMD systems is influenced by the lattice mismatch and twist angle. [74] The photoluminescence intensity and the energy of interlayer excitons in TMD heterostructures have been reported to show dependence on the twist angle. [68,[75][76][77][78] We note that for TMD heterostructures with small lattice mismatch and/or twist angle, a moiré pattern can be formed. The corresponding moiré potential can lead to localization of interlayer exciton states to local potential minima points. [18,[79][80][81][82][83] Such laterally localized interlayer exciton states can be tuned via an external electric field and have been proposed to be useful as an ordered nanoscale quantum emitter array or artificial excitonic superlattice. [74,80,84] All the above points illustrate the wide range of tunability available in currently researched TMD heterostructures. Thus, any potential interlayer exciton system based on TMOs should also have a degree of tunability to have a competitive advantage compared with TMD based systems. While exciton modulation via the Stark effect would be possible for a TMO system if the interlayer exciton is formed with spatially separated electron and hole, tunability via in-plane structural alteration would be especially challenging for a TMO system, because the epitaxial registry of TMO heterostructures is rigid and thus cannot be altered to introduce tunable parameters such as twist angle. In addition, tuning the interlayer distance in oxides often involves tuning the lattice parameter via strain by growing a different heterostructure or on a different substrate.
We find that the Mg 2 TiO 4 -MgO system satisfies all the aforementioned conditions including tunability and stability against exposure to dry air. MgO has a large bandgap of about 7.9 eV, while Mg 2 TiO 4 is reported to have a bandgap of about 3.7 eV. [85][86][87] Also, Mg 2 TiO 4 has an inverse spinel structure with built-in electrical polarity due to the presence of atomic layers containing only Mg 2+ cations. Thus, when it forms an interface with a non-polar material such as MgO (001), the polar Mg 2 TiO 4 layers near the interface will be displaced to reduce the polar discontinuity which will induce an asymmetric band structure for the different layers of Mg 2 TiO 4 . Structurally, MgO and Mg 2 TiO 4 have a good lattice match, with the lattice constant of Mg 2 TiO 4 (8.4400 Å) being almost exactly twice that of MgO (4.2127 Å). [88,89] The Mg 2 TiO 4 -MgO system is also expected to exhibit a unique characteristic that the electron is localized in the bottom Mg 2 TiO 4 layer and the hole is localized in the top layer (discussed in more detail in Section 2.2.). This allows one to tune the spatial distance between the electron and hole forming the interlayer exciton simply by varying the Mg 2 TiO 4 thickness. This tuning is analogous to varying the interlayer distance in TMD heterostructures by stacking a different number of h-BN layers in between. However, a comparative advantage of Mg 2 TiO 4 -MgO is that it is not necessary to introduce heterolayers such as h-BN in between, thus keeping the growth process simple.
The structures of an ordered and disordered inverse spinel Mg 2 TiO 4 are shown in Figure 1a. In the ordered inverse spinel, 1/8th of the tetrahedral voids are occupied by Mg 2+ cations (denoted by Mg-tet sites), 1/4th of octahedral voids by Mg 2+ cations (denoted by Mg-oct sites), and 1/4th of octahedral voids by Ti 4+ cations (denoted by Ti-oct sites), while the O 2− sublattice remains similar to that in MgO. In the disordered case, the Mg-oct and Ti-oct sites are mixed. For the ordered inverse spinel structure, different cation orderings are possible at the octahedral sites. Type I and II orderings in Figure 1b are examples of structures in which there are equal numbers of Mg-oct and Ti-oct atoms for each monolayer of Mg 2 TiO 4 . For type III ordering, only two monolayers in a unit cell have equal numbers of Mg-oct and Ti-oct atoms. In the type IV ordered case, the Mg-oct and Ti-oct atoms are segregated into different layers.
We note that the disordered and the type I, II ordered Mg 2 TiO 4 have the same in-plane averaged electron density profile along the c-axis and thus cannot be distinguished from each other through integer-order X-ray diffraction measurements along Q z . However, type III and IV structures in which the Mg-oct and Ti-oct sites are distributed inhomogeneously along the c-axis can be distinguished from disordered or type I, II ordered Mg 2 TiO 4 . The CTR analysis presented below confirms that the Mg 2 TiO 4 structure is of type I, II ordered or disordered. Thus, we choose the type I ordered structure as the basis for DFT calculations, based on the assumption that there is no preferential alignment of Mg-oct and Ti-oct sites either in-plane or out-of-plane. Also, we fit the CTR data to the type I structure over the disordered structure to reduce the computational load.

Electronic Structure of Mg 2 TiO 4 -MgO from DFT Calculations
Using DFT calculations, we confirm that the electronic structure of Mg 2 TiO 4 -MgO is favorable for hosting interlayer excitons. We first consider different ways Mg 2 TiO 4 might grow epitaxially on the MgO (001) surface. Mg 2 TiO 4 can stabilize on MgO with either cation octahedral or tetrahedral sites centered on bulk terminated MgO oxygen sites. The oxygen sublattices of Mg 2 TiO 4 and MgO are matched for the former registry (red arrows in Figure 1c), while they are mismatched for the latter (blue arrows in Figure 1c). Preliminary analysis of the CTR data shows a better fit the with an oxygen sublattice that is continuous from the MgO through the thin film. Thus, the following DFT calculations are based on a continuous oxygen sublattice.
We perform ab initio DFT calculations with the VASP software. [90] We use projector augmented-wave (PAW) pseudopotentials and a plane-wave basis set with a wavefunction energy cutoff of 60 Ry. We perform two stages of calculations: atomic relaxations using a standard DFT functional and projected density of states (PDOS) calculations using a hybrid functional for improved band gap accuracy. For the atomic relaxations, we www.advmatinterfaces.de use the PBE generalized gradient approximation exchange-correlation functional, a 15 × 15 × 1 Monkhorst-Pack k-grid, and 14 meV of Gaussian thermal broadening. [91,92] Having obtained relaxed structures, we compute more accurate energy bands using the HSE06 hybrid functional on a 5 × 5 × 1 k-grid. [93,94] Finally, we generate PDOS data using the non-self-consistent tetrahedron method of Blöchl et al. [95] All calculations used a slab geometry, with four atomic layers of MgO substrate overlaid by four atomic layers of inverse spinel Mg 2 TiO 4 , and at least 10 Å of vacuum above. Figure 1d,e shows the DFT-calculated structures of the relaxed 1 uc Mg 2 TiO 4 on MgO. Results show that two types of interfaces are possible. The first starting layer of Mg 2 TiO 4 at the interface is the Mg-tet layer for the tetrahedral interface (Figure 1d), while it is the Mg-oct/Ti-oct layer for the octahedral interface (Figure 1e). For both the tetrahedral and octahedral

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interfaces, Mg-tet atoms become displaced during the course of DFT optimization of the structure. In the case of the tetrahedral interface, the Mg-tet atoms in the first (innermost) layer of Mg 2 TiO 4 are displaced to fill nearby octahedral vacancies (Figure 1d). For the octahedral interface, Mg-tet atoms in the last (outermost) layer are displaced to fill the nearby octahedral vacancies (Figure 1e).
To confirm whether the electronic structure of Mg 2 TiO 4 -MgO can host interlayer excitons, we calculate the PDOS for each layer in the relaxed Mg 2 TiO 4 on MgO. We first consider the tetrahedral interface structure. We employ the HSE06 hybrid functional in the DFT calculations to account better for the effect of electron-electron interactions and obtain a bandgap of 3.88 eV, which is slightly larger than the reported bulk Mg 2 TiO 4 bandgap. Figure 2b) shows the PDOS associated with the Mg 2 TiO 4 top and bottom layers, as well as the MgO interface layer. The PDOS plot shows an electric field between the top and bottom layers of the tetrahedral interface Mg 2 TiO 4 as an out-of-plane gradient of the CBM and VBM. This internal electric field is expected to lead to localization of photoexcited holes in the top layer and electrons in the bottom layer, promoting the formation of interlayer exciton states (Figure 2a).
The PDOS plot for all 4 layers of Mg 2 TiO 4 and 4 layers of MgO substrate considered in the calculations (Figure 3a top) shows that the VBM of the system is in the top Mg 2 TiO 4 layer, while the CBM is in the bottom Mg 2 TiO 4 layer. The VBM states are localized to oxygen p-states in the top layer, and the CBM states are localized to Ti d-states in the bottom layer ( Figure 3c). Also, from the calculated band structure, we determine the bandgap to be indirect. The VBM is located at the Y point of the Brillouin zone, whereas the CBM is located at the Γ point (Figure 3b). This implies that a band-edge electronic transition will require momentum transfer. Thus, we expect optical excitation and recombination to be weak. Essentially, an exciton consisting of the VBM and CBM states will not only be an interlayer exciton but also an indirect exciton, with the electron and hole separated in both real space and momentum space. We also note that the VBM of the Mg 2 TiO 4 bottom and the MgO interface layers are very close in energy. This is attributed to the Mg-tet sites in the bottom Mg 2 TiO 4 layer filling nearby Mg-oct sites and bringing the net charge of the bottom Mg 2 TiO 4 layer close to that of MgO interface. At the same time, the CBM of the Mg 2 TiO 4 bottom layer is at significantly lower energy compared to the MgO interface. This is due to the presence of Ti atoms in the Mg 2 TiO 4 layer and is confirmed by the calculated Bloch functions for the CBM states (Figure 3c).
It is important to note that the above band structure is unique to the tetrahedral interface. DFT+HSE06 calculations show that the octahedral interface structure has a direct bandgap of 3.53 eV, with VBM and CBM both at the Γ point. Also, the PDOS plot for the octahedral interface shows that the VBM is in the MgO substrate, with the CBM in the Mg 2 TiO 4 interior and top layers (Figure 3a bottom). Such band structure is not desirable for hosting long-lived excitons, since the excitons cannot be confined to the film layer and the electrons and holes are not spatially separated. This illustrates the importance of precisely controlling and characterizing the oxide interface. According to the DFT calculations, the desirable relaxed tetrahedral interface structure is 0.24 eV uc -1 more stable than the relaxed octahedral interface structure. In the following parts, we confirm experimentally that the tetrahedral interface is indeed achieved.

Mg 2 TiO 4 Growth Using Reactive MBE
We grow a single unit cell of Mg 2 TiO 4 on MgO (001) using a reactive MBE process. The growth was carried out in the oxide MBE chamber at beamline 33-ID-E at the Advanced Photon Source (APS) to allow in situ CTR measurements before and after growth. We deposit TiO 2 on MgO using Ti flux from an effusion cell and molecular oxygen. Prior to growth, the MgO substrates are annealed at over 700 °C at an oxygen partial pressure of about 6 × 10 −9 Torr to obtain a clean surface. The growth temperature is maintained at about 800 °C. Inter-diffusion of Mg and Ti atoms at the MgO surface leads to formation of epitaxial Mg 2 TiO 4 at these high growth temperatures. Reflection high-energy electron diffraction (RHEED) images show epitaxial growth of the films on MgO (Figure 4). Additional diffraction peaks appearing in the RHEED images (white arrows) are attributed to the surface structure of an ordered inverse spinel Mg 2 TiO 4 (Figure 4e,f). The Mg 2 TiO 4 surface unit cell is a centered c(2 × 2) reconstructed version of the underlying MgO unit cell (Figure 4g). Extra half-order rods in RHEED along both [100] and [110] directions agree with such surface reconstruction. We also note that the reconstruction appears only when TiO 2 is deposited at temperatures above 700 °C or when the film is annealed at elevated temperatures following a lower temperature growth. This is consistent with previously reported formation mechanisms of Mg 2 TiO 4 . [96][97][98] Based on the above observations, we conclude that the deposition of TiO 2 on MgO at high temperatures results in the epitaxial growth of thin Mg 2 TiO 4 on MgO, down to the single unit cell limit.

Structural Characterization Using CTR Measurements
We employ in situ CTR measurements to characterize the physical structure of the interface as predicted by theory. CTR measurements are done immediately after the growth in ultrahigh vacuum (UHV) without exposing the films to atmosphere. The structure of the films is obtained by fitting the measured CTR spectra with calculated spectra using the surface X-ray diffraction (SXRD) analysis program GenX. [99,100] Since we use the integer-order diffraction rods along the Q z direction, information contained in the CTR data is the in-plane averaged electron

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density profile along the c-axis. Therefore, we use a simplified structure of Mg 2 TiO 4 ( Figure S1, Supporting Information) to fit the CTR data, a complete set of which is shown in Figures S2-S4, Supporting Information. The simplified structure has the same unit cell as MgO, but the occupancy of the Mg/Ti-oct sites is 0.25 Ti + 0.25 Mg occupancy, and the Mg-tet sites have 0.125 Mg occupancy. Such a structure has the same in-plane averaged electron density profile along the c-axis as the full type I, II ordered or disordered Mg 2 TiO 4 structure. Figure 5a shows the calculated and measured specular CTR spectra of the annealed MgO before growth, 1 uc Mg 2 TiO 4 and 2 uc Mg 2 TiO 4 (see the Supporting Information for the full set of the CTR data). The film structure derived from the CTR data indicates that the reactive MBE process continues to form Mg 2 TiO 4 up to at least 8 monolayers (ML) or 2 uc, without formation of remnant TiO 2 layers. This demonstrates the ability to grow 2D Mg 2 TiO 4 films with precisely controlled thickness.

Polarity-Driven Displacements at the Interface
A closer look at the Mg 2 TiO 4 -MgO interface structure confirms the displacement of Mg-tet atoms as predicted by the DFT calculations in Figure 1d. If the Mg-tet atoms in the first layer are displaced to fill nearby Mg/Ti-oct vacancies, the electron density of the first layer Mg/Ti-oct sites will be increased by the amount corresponding to the electron density of the Mg-tet sites. Also, one would observe no electron density for the Mg-tet sites immediately above the last atomic layer of MgO. Figure 5b and the dashed red circles in Figure 6a highlight such displacement of Mg-tet atoms observed for the experimentally determined Mg 2 TiO 4 on MgO structures. This observation also agrees with the DFT calculation that predicts the tetrahedral interface to be energetically more favorable than the octahedral interface. In the case of the octahedral interface, one would expect finite electron density for the Mg-tet sites immediately above the last MgO oxygen layer and increased electron densities for the Mg/Ti-oct sites in the top Mg 2 TiO 4 layer (Figure 1e), both of which disagree with the experimentally determined structure.
Another feature that distinguishes 2D Mg 2 TiO 4 on MgO from bulk Mg 2 TiO 4 is the picometer scale displacements of Mg-tet sites within the Mg 2 TiO 4 region. In bulk Mg 2 TiO 4 , the Mg-tet sites are in the plane midway between the Mg/Ti-oct and oxygen planes. In 2D Mg 2 TiO 4 films, the Mg-tet atoms are vertically displaced away from the midpoint. (Figure 6a). We extract the displacement δ of Mg-tet sites away from their bulk positions. Figure 6b shows the off-center displacement δ of the Mg-tet sites measured for 1 uc and 2 uc Mg 2 TiO 4 (orange and yellow points respectively), as well as the theoretically calculated values for 1 uc Mg 2 TiO 4 (blue points). Positive values of δ indicate that the Mg-tet sites are displaced upward toward the surface whereas negative values indicate the sites are displaced downward toward the MgO.
For the first Mg-tet site that displaces significantly into the nearby Mg/Ti-oct vacant sites immediately above, theory predicts displacement of about 10 pm, which is close to the measured values of 11 and 13 pm for 1 uc and 2 uc samples, respectively. However, for other Mg-tet sites in 1 uc samples, the theoretical values deviate from the experimental values. While the theory predicts positive displacement, the 1 uc sample shows negative displacement. One possible reason for differences in sign and magnitude compared to theory is roughness

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or disorder of the film surface. The root mean squared (rms) roughness of the 2uc Mg 2 TiO 4 film is 0.752 nm over a 5 um by 5 um area as measured by atomic force microscopy (AFM), which is about 90% of the Mg 2 TiO 4 unit cell thickness. Supporting this hypothesis is the fact that the Mg-tet displacement values for 2 uc sample agree well with the theory in regions more remote from the surface (up to 80 pm above the MgO layer), which indicate that surface disorder and factors not included in the theory can play a role in the experimental measurements. Since the experimentally observed atomic positions deviate from the atomic positions used in the DFT calculations, it is reasonable to expect the real band structures to also deviate from the calculated band structures to some extent. However, as discussed in Section 2.2., the critical component for the Mg 2 TiO 4 -MgO to host interlayer excitons is the stabilization of the tetrahedral interface (Figure 3a), which is observed experimentally.
The displacements of the first Mg-tet layer atoms that result in the tetrahedral interface are clearly observed, and the formation of such an interface is crucial to hosting interlayer exciton states. As discussed above, the displacement of Mg-tet atoms into nearby Mg/Ti-oct vacancies brings the net charge of the bottom Mg 2 TiO 4 layer to 0. Such polarity-driven atomic displacements strongly affect the electrostatics of the film and interface, resulting in localization of holes in the VBM of the top Mg 2 TiO 4 layer and electrons in the CBM of the bottom layer. We attribute this reconstruction to the tendency of the polar 2D Mg 2 TiO 4 to reduce polarity near a non-polar interface such as MgO (001). Unlike MgO (001) layers, which have a net charge of 0, Mg 2 TiO 4 (001) layers have net charges alternating between  (Figure 6a). This polarity drives displacements at the interface with MgO, at which the Mg-tet site (Mg 2 ) 4+ migrates to fill nearby vacant Mg/Ti-oct sites, so that the charge of the interface Mg 2 TiO 4 tends toward zero.

Conclusion
We propose that a single unit cell Mg 2 TiO 4 on MgO (001) can serve as an oxide platform for exploring interlayer excitons. This materials system may also host energy-tunable interlayer excitons: in the few unit cell limit, Mg 2 TiO 4 hosts an electric field between the top and bottom layers. By controlling the distance between the top and bottom layers of Mg 2 TiO 4 , one may be able to control the radius of the interlayer exciton state, thus controlling the binding energy. This could be achieved by varying the thickness of the Mg 2 TiO 4 film, which we have demonstrated is feasible. From this perspective, the Mg 2 TiO 4 -MgO system has a major advantage of potentially being a tunable interlayer exciton system, while maintaining stability against exposure to dry air. Also, thin film Mg 2 TiO 4 may be interfaced with functional oxides such as ferroelectric BTO or 2D electron gas (2DEG) systems including LaAlO 3 -STO so that the interlayer excitons may be coupled to various degrees of freedom in the functional oxides. In such cases, the interlayer excitons in Mg 2 TiO 4 may serve as a probe for investigating correlated states in oxide heterostructures, similar to the excitonic probe of correlated states in TMD moiré heterostructures. [16,[101][102][103] One area for potential materials improvement is growing Mg 2 TiO 4 through co-deposition of Mg and Ti on MgO. As mentioned in the previous section, reactive MBE growth may be responsible for the observed surface roughness, which amounts to about 90% of the 1 uc Mg 2 TiO 4 thickness. Co-deposition may reduce the surface roughness and result in higher quality films. Since the binding energy of a potential interlayer exciton is expected to be related to the thickness of the Mg 2 TiO 4 film, large surface roughness can lead to large variations in the binding energies of the observed excitons. Also, rough surfaces with a large density of atomic steps can reduce the diffusion length of potential interlayer excitons, as they recombine at the step edges where the top layer is abruptly terminated. [1] It would be ideal to achieve large terraces with small surface roughness through improved growth techniques.
A key enabling factor for obtaining interlayer excitons in Mg 2 TiO 4 -MgO is the internal electric field supported by polarity-driven atomic displacements. Such displacements at an inverse spinel interface have been observed for the first time in this work. Since these displacements are driven by polar discontinuity at the polar/non-polar interface, we posit that other polar spinel/non-polar host material interfaces will also exhibit similar atomic displacements. This implies the above scheme for hosting interlayer excitons in oxides can be generalized to other interesting spinel oxides, such as Mg 2 SnO 4 and MgGa 2 O 4 , which show persistent luminescence. [104][105][106] This may lead to the development of other 2D spinel oxide interfaces as a new class of materials for which exciton physics might be explored.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.