Coexistence of quasi-two dimensional electron and hole gas in a single tier Ca0.5TaO3/SrTiO3 oxide heterostructure

Quasi-two-dimensional electron gas has been realized at the polar-nonpolar interface of several insulating oxide heterostructures. However, its hole counterpart remains elusive. In an attempt to find a novel system that exhibits quasi-two-dimensional hole gas (q-2DHG) at the heterointerface, we adopt to materials search, first based on phenomenology followed by a comprehensive set of calculations based on first-principles density functional theory. Our studies show the epitaxial growth of cubic Ca0.5TaO3 on TiO2 terminated substrate display (q-2DHG). The hole gas emanates from the O 2p orbitals of the TiO2 layers of the substrate. On the other hand, an electron gas is formed at the (001) TaO2 top surface, thereby representing the heterostructure as a coupled quantum well system. The partial filling of the Ta 5dt2g conduction band indicates electron reconstruction, in agreement with the polar catastrophe model. Besides, a critical thickness of three monolayers is deduced from the calculations for the formation of q-2DHG in the Ca0.5TaO3/SrTiO3 heterostructure, which is consistent with the model prediction based on the modern theory of polarization. With both cubic systems, Ca0.5TaO3 and SrTiO3, having a similar underlying symmetry and minimal lattice mismatch, epitaxial growth with an abrupt interface can be well anticipated. Such a single-tier oxide heterostructure composed of separated confined hole-electron subsystems is expected to provide a platform to unravel exciting physics and also for functional devices related to oxide electronics. © 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5109631., s The origin of quasi-two-dimensional electron gas at the interface of polar and nonpolar insulating oxides has been attributed to several mechanisms, such as oxygen defects, intersite cation disorder, atomic reconstruction, and electronic reconstruction. Of these, the most fascinating is the electronic reconstruction at the heterointerface due to the polar catastrophe model. In this model, an abrupt heterointerface between polar and nonpolar insulating oxides manifests a polarity discontinuity, thereby resulting in an electric potential which diverges with the increasing thickness of the overlayer polar film. As a result, the heterointerface becomes electronically unstable. To nullify the built-in potential, the polar catastrophe model proposes an electronic reconstruction at the heterointerface. For instance, in case of LaAlO3/SrTiO3, an electronic reconstruction occurs in the vicinity of the TiO2 heterointerface, with an amalgam of Ti and Ti states. The n-type carriers generated are, however, confined to a narrow region, thereby resulting in a quasi-two-dimensional electron gas (q-2DEG). While several such oxide heterostructures exhibiting q2DEG have been tailored successfully, its counterpart, i.e., the quasi-two-dimensional hole gas (q-2DHG), has not been realized in single-tier oxide heterostructures. Rather, such ptype heterointerfaces have been found insulating. However, a q-2DHG has been experimentally discovered in a two-tier SrTiO3/LaAlO3/SrTiO3 heterostructure. Two confined conducting channels with (LaO)/(TiO2) heterointerface exhibiting n-type conductivity and (AlO2)/(SrO) interface showing a p-type conductivity were observed in this system. Realizing that n-type heterointerfaces are more common than the p-type counterparts, we attempt to envisage the latter in a new heterostructure using density functional theory calculations. To look for an appropriate oxide that can be epitaxially grown on SrTiO3, we adhere to the fundamental assumptions of the polar catastrophe model, i.e., the overlayer oxide must be polar and must also have minimal lattice mismatch with the substrate. In this view, we APL Mater. 7, 071108 (2019); doi: 10.1063/1.5109631 7, 071108-1

The origin of quasi-two-dimensional electron gas at the interface of polar and nonpolar insulating oxides has been attributed to several mechanisms, such as oxygen defects, intersite cation disorder, atomic reconstruction, and electronic reconstruction. [1][2][3][4][5][6][7][8][9] Of these, the most fascinating is the electronic reconstruction at the heterointerface due to the polar catastrophe model. In this model, an abrupt heterointerface between polar and nonpolar insulating oxides manifests a polarity discontinuity, thereby resulting in an electric potential which diverges with the increasing thickness of the overlayer polar film. As a result, the heterointerface becomes electronically unstable. To nullify the built-in potential, the polar catastrophe model proposes an electronic reconstruction at the heterointerface. For instance, in case of LaAlO 3 /SrTiO 3 , an electronic reconstruction occurs in the vicinity of the TiO 2 heterointerface, with an amalgam of Ti 4+ and Ti 3+ states. The n-type carriers generated are, however, confined to a narrow region, thereby resulting in a quasi-two-dimensional electron gas (q-2DEG).
While several such oxide heterostructures exhibiting q-2DEG have been tailored successfully, 10,11 its counterpart, i.e., the quasi-two-dimensional hole gas (q-2DHG), has not been realized in single-tier oxide heterostructures. Rather, such ptype heterointerfaces have been found insulating. [12][13][14] However, a q-2DHG has been experimentally discovered in a two-tier SrTiO 3 /LaAlO 3 /SrTiO 3 heterostructure. 15 Two confined conducting channels with (LaO) + /(TiO 2 ) 0 heterointerface exhibiting n-type conductivity and (AlO 2 ) − /(SrO) 0 interface showing a p-type conductivity were observed in this system. 15 Realizing that n-type heterointerfaces are more common than the p-type counterparts, we attempt to envisage the latter in a new heterostructure using density functional theory calculations. To look for an appropriate oxide that can be epitaxially grown on SrTiO 3 , we adhere to the fundamental assumptions of the polar catastrophe model, i.e., the overlayer oxide must be polar and must also have minimal lattice mismatch with the substrate. In this view, we ARTICLE scitation.org/journal/apm carried out a materials objective search using the Crystallography Open Database 16,17 and found Ca 0.5 TaO 3 18 to be a good material to realize q-2DHG. The advantage of Ca 0.5 TaO 3 is that it has a underlying cubic symmetry (space group: Pm-3m) with lattice constant a = 3.875 Å. In comparison to SrTiO 3 (a = 3.905 Å), the lattice mismatch of Ca 0.5 TaO 3 /SrTiO 3 is then estimated to be ≃0.7%. Besides, the Ca vacancies offer an opposite stacking of polar layers in comparison to LaAlO 3 . In LaAlO 3 /SrTiO 3 , the positively charged (LaO) + and the charge neutral (TiO 2 ) 0 layers constitute the heterointerface. On the other hand, in Ca 0.5 TaO 3 /SrTiO 3 , the heterointerface is realized as . . ./(TiO 2 ) 0 /(Ca 0.5 O) − /(TaO 2 ) + . . ., where a negatively charged (Ca 0.5 O) − comes in contact with the (TiO 2 ) 0 layer of the substrate. The negatively charged (Ca 0.5 O) − /(TiO 2 ) 0 layer resembles much like the (AlO 2 ) − /(SrO) 0 , the latter in which a p-type conductivity has been reported. 15 The Ca 0.5 TaO 3 /SrTiO 3 interface is shown schematically in Fig. 1.
Thus, finding that the lattice mismatch is minimal and that a p-type interface can be formed in Ca 0.5 TaO 3 /SrTiO 3 , we performed a comprehensive set of calculations based on first-principles density functional theory. Consistent with the predictions of the polar catastrophe theory, we found an accumulation of p-type charge carriers at the heterointerface of Ca 0.5 TaO 3 /SrTiO 3 . In fact, the onset of conductivity is seen above certain critical thickness of the Ca 0.5 TaO 3 overlayers. The emergence of hole conductivity is charge compensated by an electronic reconstruction of the Ta ions on the TaO 2 surface layer. Therefore, Ca 0.5 TaO 3 /SrTiO 3 represents a p-type oxide heterostructure, the experimental synthesis and characterization of which can lead to a leap in oxide electronics applications. Furthermore, the spatial separation of the nonequilibrium charge carriers can cause nanometer scale variations in the electrostatic potential, thereby having significant impact on the generation, recombination, and transport of charge carriers. All electron full potential linearized augmented plane-wave (FP-LAPW) method as implemented in the Wien2k code 19 was employed to study the structural and electronic structure properties of Ca 0.5 TaO 3 /SrTiO 3 heterostructures. These were modeled using supercells of dimension √ 2a × √ 2a × 2an, where a (=3.905 Å) was taken to be that of cubic SrTiO 3 and n, the number of monolayers (MLs). A monolayer (ML) is defined as a Ca 0.5 O/TaO 2 unit in the Ca 0.5 TaO 3 overlayer film and a SrO/TiO 2 unit in the SrTiO 3 substrate along the crystallographic [001] direction. The TiO 2 terminated SrTiO 3 substrate in our model calculations has five MLs, and the thickness of the Ca 0.5 TaO 3 was varied from 1 to 4 ML. The LAPW sphere radii for Sr/Ca, Ti/Ta, and O were chosen as 2.2, 1.9, and 1.6 a.u., respectively. The internal coordinates of all ions constituting the heterostructure were relaxed. The ground state properties were obtained using well-converged basis sets using the Wien2k parameters: R MT Kmax = 7, Gmax = 24 a.u. −1 , and lmax = 7. 19 The exchange correlation potential to the crystal Hamiltonian was considered in Generalized Gradient Approximation (GGA) as prescribed by Perdew, Burke, and Ernzerhof (PBE). 20 The Brillouin Zone (BZ) integration was carried out using the modified tetrahedron method with a mesh size of 12 × 12 × 2, yielding 98k-points in its irreducible wedge.
Prelude to understand the properties of the Ca 0.5 TaO 3 /SrTiO 3 heterostructures, we first determined the structural and electronic structure properties of cubic Ca 0.5 TaO 3 . The material was modeled using a cubic unit cell with the underlying Fm-3m (space group 225) symmetry. Ca ions were positioned at the 4a (0, 0, 0) Wyckoff position, Ta ions at 8c ( 1 4 , 1 4 , 1 4 ), and O ions at ( 1 4 , 0, 1 4 ) position of the face centered cubic unit cell. Total energy enroute to determine the equilibrium lattice constant determined the value a 0 = 3.968 Å for Ca 0.5 TaO 3 . In comparison to the experiments, the theoretically determined lattice constant was ≃2.4% overestimated, which can be considered legitimate within the scope of GGA-PBE formalism of treating exchange-correlation effects. The band structure and density of states (DOS) spectra of Ca 0.5 TaO 3 are shown in Fig. 2(a). Generic to all cubic oxide perovskites, the upper valence bands are dominated by the O 2p bands, while the conduction bands were composed of the Ta 5d-bands. An insulating ground state with an electronic gap (Eg) of 2.15 eV was determined using GGA-PBE against the experimental value of 4.0 eV. 21 The overestimation of lattice constant and the underestimation of the electronic gap is quite inherent in GGA-PBE. Therefore, to compare the theoretically obtained values with experiments, we calculated the same physical quantities for cubic SrTiO 3 under a similar set of approximations and computational parameters. We found a 0 for SrTiO 3 to be ≃3.938 Å, which is barely 0.9% overestimated compared to the experimental value of 3.905 Å. The electronic structure calculated at the equilibrium lattice constant for SrTiO 3 is shown in Fig. 2(b). Note that for a direct comparison of the electronic structure of SrTiO 3 with that of Ca 0.5 TaO 3 , we calculated the band structure and DOS spectra for SrTiO 3 using a 2 f.u. unit cell with the underlying Fm-3m cubic symmetry. The Eg for SrTiO 3 was estimated to be ≃1.87 eV. From these sets of calculations, it becomes evident that GGA-PBE consistently underestimates the Eg of band insulators, such as SrTiO 3 and Ca 0.5 TaO 3 , by ≃55%-60%.
Although discrepancies exist between the theoretical and experimental values, the calculations provide qualitatively good results. For instance, the experimental lattice mismatch between Ca 0.5 TaO 3 and SrTiO 3 amounts to 0.7%, while the theoretical values amount to 0.8%. Thus, based on the underlying cubic symmetry and minimal lattice mismatch between Ca 0.5 TaO 3 and SrTiO 3 , we predict that the epitaxial growth of Ca 0.5 TaO 3 films is possible on the SrTiO 3 substrate. Also, consistent with the experiments, the GGA-PBE calculations predict Eg(Ca 0.5 TaO 3 ) > Eg(SrTiO 3 ). This infers that the electronic gap of SrTiO 3 would completely lie within the gap of Ca 0.5 TaO 3 . As a result, the charge carriers if generated at the heterointerface can be anticipated to reside in the SrTiO 3 side of the heterointerface, similar to LaAlO 3 /SrTiO 3 oxide heterostructures.
Having realized that Ca 0.5 TaO 3 can be modeled as alternating negative (Ca 0.5 O) − and positive (TaO 2 ) + layers on TiO 2 terminated SrTiO 3 substrate and epitaxial growth with an abrupt interface is possible, polar catastrophe theory anticipates conductivity at the heterointerface. Nevertheless, one of the important predictions of the model is that there exists an overlayer film thickness threshold for heterointerface conductivity to emerge. 26 Hence, we have modeled heterostructures with varying thickness (1-4 ML) of Ca 0.5 TaO 3 on TiO 2 terminated SrTiO 3 . Also, since the interplay of electrostatic effects and local lattice distortions is crucial in determining the electronic structure properties of oxide heterostructures, we first present the structural relaxation effects in the 1-4 ML Ca 0.5 TaO 3 /SrTiO 3 oxide heterostructures. Figure 3 graphically summarizes the results of the structural relaxation effects in Ca 0.5 TaO 3 /SrTiO 3 heterostructures for the overlayer film thickness ranging from 1 to 4 ML. By large, the effect

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scitation.org/journal/apm of structural relaxation is mostly seen in the Ca 0.5 TaO 3 overlayers. In the substrate, the distortion is largely contained in the TiO 6 octahedra which is in the immediate vicinity of the heterointerface. The interplanar distance between the TiO 2 and SrO layers of the substrate in its interior corresponds to that of the bulk value, i.e., d STO = 1.952 Å. However, the TiO 2 -SrO interplanar distance which constitutes the heterointerface ML shows a systematic change in their separation with increasing overlayer thickness. While for 1 ML Ca 0.5 TaO 3 its separation decreases by −0.8% from that of d STO , it steadily increases to +0.9% for 4 ML Ca 0.5 TaO 3 . Thus, we find that increasing the Ca 0.5 TaO 3 film thickness above 2 ML leads to an inversion of the TiO 6 distortion pattern at the heterointerface. Such distortions, which result in the elongation of the TiO 6 octahedra at the heterointerface, have been argued to facilitate conductivity. 22,23 Besides, we find that planes along the [001] crystallographic direction are alternately compressed and elongated. For the 4 ML Ca 0.5 TaO 3 /SrTiO 3 heterostructure, as large as 5% change in the interplanar distances has been estimated for the surface and subsurface TaO 2 layer with the adjacent Ca 0.5 O layer. The in-plane and out-of-plane Ta-O bond distances range between 1.88 Å and 2.01 Å. On the contrary, the Ti-O distortion in the substrate is found very minimal within a value of ≃0.01 Å or smaller. Furthermore, the deviation of the Ti-O-Ti bond angle from 180 ○ is found to be <1.5 ○ , whereas the Ta-O-Ta bond angle in the surface TaO 2 layer deviates by ≃3 ○ . Thus, the structural relaxation of the heterostructure shows significant distortion in the TaO 6 octahedra, which is then expected to lift the degeneracy of the Ta 5dt 2g orbitals.
The elongation and compression of alternate layers in the Ca 0.5 TaO 3 /SrTiO 3 heterostructures, irrespective of the ML thickness, partly validates the polar catastrophe model. This can be interpreted as a response to the built-in electric field due to the polarnonpolar interface. This electric field polarization vector is directed perpendicular to the surface. Along this field direction, the internal field between the (Ca 0.5 O) − → (TaO 2 ) + layers is then oppositely directed to the polarization, while that of (TaO 2 ) + → (Ca 0.5 O) − is parallel. As a result, the interplanar distance between the (Ca 0.5 O)-(TaO 2 ) layers along the crystallographic c-axis is elongated and the (TaO 2 )-(Ca 0.5 O) is compressed. Such effects have also been observed in LaAlO 3 /SrTiO 3 heterostructures. 24,25 The interplanar distances shown in Fig. 3 represent averaged quantities.
We also observe a trend in the interlayer separation between the ⟨(Ca 0.5 O) − − (TaO 2 ) + ⟩ layers and ⟨(TaO 2 ) + − (Ca 0.5 O) − ⟩ layers along the growth direction, i.e., the crystallographic c-axis. For instance, in the 4 ML heterostructure, the ⟨(Ca 0.5 O) − − (TaO 2 ) + ⟩ separation decreases steadily from 1.923 Å (near to the heterointerface) to 1.873 Å (the surface layer), i.e., a decrease by −2.7%. On the other hand, the ⟨(TaO 2 ) + − (Ca 0.5 O) − ⟩ layer separation increases by 0.8% i.e., from 1.999 Å to 2.015 Å (the subsurface layer). Similarly, for the 2 ML heterostructure, the relative decrease in the two ⟨(Ca 0.5 O) − − (TaO 2 ) + ⟩ layer separations is estimated to be −1.1%. These observations are consistent with the assumptions of the polar catastrophe model that the layers of such polar-nonpolar oxide heterostructures can be approximated as parallel plate capacitors. The relative increase (decrease) in the interplanar distances between the charged layers along the c-axis with increasing film thickness is clearly a manifestation of a proportional increase in the built-in potential with increasing ML thickness. Thus, we find that density functional based calculations capture the essential model characteristics pertained to the polar catastrophe theory. The interplay of electrostatic effects and local lattice distortions is evident from the calculations.
The electronic structures of the Ca 0.5 TaO 3 /SrTiO 3 heterostructures for 1-4 ML overlayers are studied in terms of DOS, charge, and orbital populations. In Figs. 4(a)-4(d), we show the thickness dependent evolution of the electronic structure of the Ca 0.5 TaO 3 /SrTiO 3 heterostructure. The 1 ML Ca 0.5 TaO 3 /SrTiO 3 heterostructure is insulating with Eg ≃ 0.72 eV, and the 2 ML heterostructure is found barely insulating. For Ca 0.5 TaO 3 overlayers ≥3 ML, there appears finite density of states at the Fermi energy, rendering a metallic ground state. The valence band of all four heterostructure systems is composed of the O 2p bands, while the conduction band is composed of the transition metal d states. However, the 3d states of the Ti ions of the substrate were found to be 0.5 eV above the surface Ta 5d bands.

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Evidently, a substantial band bending is manifested in the electronic structure by a layer wise change in the position of the valence band maximum (VBM) and conduction band minimum (CBM). In fact, this variation reflects the electrostatic potential which rigidly shift the bands with respect to the Fermi energy. Together with the changes observed in the interlayer separation and the band bending effects, a strong correlation of the electrostatic effects with that of the electronic structure becomes evident as a function of increasing film thickness. In particular, it may be followed from the above discussion that the TaO 2 surface layer is significantly compressed along the c-axial direction of the heterostructure. This enhances the hybridization between the Ta 5d and O 2p orbitals of adjacent layers, thereby increasing the covalency associated with the surface chemical bonds.
We now calculate the critical thickness (tC) of the Ca 0.5 TaO 3 films which will introduce charge carriers at the heterointerface. The potential divergence resulting in band bending equates with the Eg of Ca 0.5 TaO 3 , which for bulk is ≃4.0 eV. 21 Besides, the potential difference between the surface and interface can be approximated as ea 0 E pol tC, with the polar field E pol = 2πe/ a 2 0 , a 0 being the lattice constant and being the dielectric constant of Ca 0.5 TaO 3 . Thus, given Eg = 4.0 eV and assuming ≃ 25, tC is estimated to be ≃3 ML. Note that varying for Ca 0.5 TaO 3 in the range 20-30 changes tC( ) to 2.5-3.5. Thus, the value of tC, i.e., ≃3 ML of Ca 0.5 TaO 3 , obtained from the present GGA calculations is found to be consistent with the phenomenological model which is based on the modern theory of polarization. In fact, we also note that tC for the LaAlO 3 /SrTiO 3 heterostructures was estimated to be ≃4 ML using GGA, 27 despite theoretical calculations underestimating the electronic gap for both LaAlO 3 and SrTiO 3 .
It is evident from Fig. 4 that as the ML thickness increases, the VBM of the heterointerface TiO 2 layer of the substrate moves toward lower energy and subsequently holes are introduced in its O 2p bands. By requirement of charge neutrality, the holes in the interface TiO 2 layer are compensated by electrons in the surface TaO 2 layer, resulting in a n-type film-vacuum interface. However, the Ta 5d of the overlayers and the Ti 3d bands of the substrate do not mix with the O 2p bands of the respective layers. That is, the p-d hybridization gap in the layers remain intact, irrespective of the Ca 0.5 TaO 3 thickness. For instance, in the 3 ML heterostructure, the O 2p-Ta 5d energy separation in the surface layer is ≃2.4 eV, and for subsequent two subsurface TaO 2 layers, it is found to be 1.6 eV. Similarly, the O 2p-Ti 3d energy separation in the substrate layers also shows variation with the heterointerface TiO 2 layer showing a gap of 1.4 eV. The subsequent TiO 2 layers into the interior of the substrate show a gap of 1.9 eV. It also needs to be mentioned that the CBM of the substrate layers remains more or less pinned at 1.7 eV above EF.
In the 4 ML Ca 0.5 TaO 3 /SrTiO 3 heterostructure, the layer wise resolved DOS spectra show a finite contribution to the EF from both the film and the substrate. In order to understand the dominant orbital states responsible for the hole and electron conduction, we show the layer wise decomposed orbital density of states in Fig. 5. It becomes clear from Fig. 5 that the electron gas at the surface TaO 2 layer is predominantly of Ta 5dt 2g in nature, while the hole gas formed at the heterointerface TiO 2 is of O 2p in character. Thus, the Ca 0.5 TaO 3 /SrTiO 3 heterostructure represents itself as a unique single-tier oxide heterostructure system, where both electron and hole gas are realized.
Furthermore, to obtain the contribution of hole carriers in the conduction process, we integrate the layer projected density of states of the substrate with the integration limits set from Fermi energy to the lower conduction band edge. Note that the integration is carried out within the LAPW spheres and therefore does not account the contributions from the interstitial region. For 2 ML, we find ≃0.01 holes residing in the TiO 2 heterointerface, which increases to 0.29 holes and 0.32 holes for the 3 ML and 4 ML Ca 0.5 TaO 3 /SrTiO 3 heterostructures, respectively. Also, we find from layer wise analysis ( Fig. 5; the sixth and seventh panels from the top) that the hole concentration in the SrTiO 3 substrate decreases exponentially into its interior. For the TiO 2 layer below the heterointerface, the hole concentration decreases by an order of magnitude. Similarly, we also estimated the electron concentration in the conduction process by integrating the layer wise density of states from the bottom of the Ta 5d band edge to the Fermi energy. For the 2 ML thickness heterostructure, we found 0.04 electrons in the surface layer, which In (a), the blue, red, and green curves represent the orbital resolved dxy, dxz, and dyz partial density of states, respectively, while in (b) the red and green curves represent the orbital resolved px(py) and pz partial DOS, respectively. The top panel represents the surface TaO 2 layer, and the second to fourth panels from the top represent the subsequent TaO 2 layers. The fifth panel from the top represents the TiO 2 heterointerface, whereas the sixth and seventh panels represent the TiO 2 layers of the SrTiO 3 substrate interior. The vertical broken line through energy zero represents the reference Fermi energy.

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scitation.org/journal/apm increased to 0.19 electrons and 0.22 electrons in the 3 ML and 4 ML heterostructures, respectively. However, the surface electron gas was found to decay at a lesser rate into the film interior, in comparison to the hole gas. Our analysis shows that the electron concentration in the subsurface TaO 2 amounts to one-fourth of the concentration determined in the surface TaO 2 layer. Thus, it becomes evident that in the Ca 0.5 TaO 3 /SrTiO 3 heterostructure, hole conduction occurs at the TiO 2 heterointerface and electron conduction occurs at the surface TaO 2 layers. The partial filling of the Ta 5dt 2g bands thus leads to the formation of mixed valence states associated with the Ta ions, such as Ta 5+ , Ta 4+ , and/or Ta 3+ states. Note that charge neutrality conditions applied to bulk Ca 0.5 TaO 3 render the Ta ions to exist in +5 formal valence state. However, the theoretical observation of charge disproportionation in TaO 2 surface layers should be explored experimentally. To strictly quantify the Ta mixed valence states in the overlayers, one useful analysis may be the core level spectra obtained from the photoemission experiments.
To have an insight of the relative bandwidth associated with the electron and hole bands, as shown in Fig. 6, we show the band structure of the 4 ML Ca 0.5 TaO 3 /SrTiO 3 heterostructure. We find that the Fermi energy crosses the highly dispersive bands of Ta 5d character, thereby illustrating a smaller effective mass. On the other hand, the O 2p hole states emanating from the TiO 2 heterointerface appear to be lesser dispersive. The states derived from the O 2px (y) bands are spread over the energy range 0.3 ≤ E (eV) ≤ −0.4, while the O 2pz bands are very much localized with their energy spread being 0.03 ≤ E (eV) ≤ −0.03. The relatively larger bandwidth of the O 2px (y) bands, i.e., ≃0.7 eV, in comparison to the out-of-plane O 2pz bands, shows a greater degree of covalent bonding characteristics within the plane, attributing to spatially confined hole gas at the interface.
Finally, in Fig. 7, we show the schematic diagram of band alignment before and after electronic reconstruction in the  Ca 0.5 TaO 3 /SrTiO 3 heterostructure. The experimental electronic gap of SrTiO 3 in bulk is 3.3 eV, while that of Ca 0.5 TaO 3 is 4 eV. As evident from DOS spectra in the Ca 0.5 TaO 3 /SrTiO 3 heterostructure, the conduction band offset is small. The conduction band is mainly composed of the Ta 5d and Ti 3d states, with the latter being only 0.5 eV above the Ta 5d band edge. Thus, the upper edge of these states can be considered as almost aligned. For the electronic reconstruction to occur, a large band bending with the CBM of Ca 0.5 TaO 3 at the surface aligning with the VBM of SrTiO 3 is required, which is consistent with the observation made in the density functional based calculations presented above. Overall, we find that ML dependent hole and electron conductivity at the TiO 2 heterointerface layer and TaO 2 surface layer in the Ca 0.5 TaO 3 /SrTiO 3 heterostructure is mediated by a rigid band shift of the substrate SrTiO 3 valence and overlayer Ca 0.5 TaO 3 conduction band, toward the Fermi energy. The calculations, which are based on an abrupt interface/surface, devoid of any oxygen defects, intersite disorder and/or surface adsorbents, relate the underlying conducting mechanism in the Ca 0.5 TaO 3 /SrTiO 3 heterostructure to the polar catastrophe model.
The occurrence of q-2DHG at the interface of insulating oxides heterostructures is rare. In pursuit to look for q-2DHG in single-tier oxide heterostructures, we adhere to the postulates of polar catastrophe theory, i.e., to look for a oxide material which would have a negatively charged layer in contact with the TiO 2 layer of the substrate SrTiO 3 and also that the lattice mismatch be minimal. We find Ca 0.5 TaO 3 as a good candidate material to exhibit q-2DHG. Modeling the heterostructures by means of supercells, first-principles density functional theory calculations were performed. The electronic structure of the heterostructures shows an evolution of q-2DHG with increasing Ca 0.5 TaO 3 overlayer thickness on TiO 2 terminated SrTiO 3 . The critical thickness of Ca 0.5 TaO 3 for the existence of q-2DHG was determined to be 3 ML from the GGA-PBE calculations, which is consistent with the empirical model based on the modern theory of polarization. Furthermore, the systematic variations in the interplanar distances between the (Ca 0.5 O) − and (TaO 2 ) + charged layers clearly manifest as the response of the built-in electric field, as ARTICLE scitation.org/journal/apm predicted by the polar catastrophe theory. The q-2DHG is found to be highly confined to the TiO 2 heterointerface and is derived from the O 2p bands. On the other hand, the charge compensated electron carriers are found to reside at the TaO 2 surface layer. The partial filling of the Ta 5dt 2g manifold indicates an electronic reconstruction at the surface, thereby inducing the mixed valence state of the Ta ions. Our argument of charge disproportionation in surface TaO 2 layer in Ca 0.5 TaO 3 /SrTiO 3 heterostructures, however, should be explored experimentally. To the best of our knowledge, the Ca 0.5 TaO 3 /SrTiO 3 appears as the first single-tier oxide heterostructure in which hole gas exists at its heterointerface. In fact, in heterostructures representing the coupled quantum well system, the interaction between the interface and surface confined charges is expected to drive several novel properties.