Introduction

Following the great success of semiconductors, oxide electronics have recently drawn a lot of attention1,2. The main reason for this growing attraction might be attributed to the versatile ground states of oxide systems that show various type of order parameters3. Moreover, heterostructures of several different oxide perovskites realize artificial composite systems with integrated functionality and accelerate the growth of this field4,5. Introducing a new quantum phase to oxide systems, therefore, has much influence in enriching and developing new physics. In this context, finding an oxide system with non-trivial band topology, so-called topological insulator (TI)6,7 and possibly combining oxide electronics with TI is one of the most intriguing and significant tasks.

However, due to the small spin-orbit coupling (SOC) strength of oxygen atoms, the TI phase is not easily accessible in oxides compared to the heavy chalcogenides8,9. To date, there are only a few predictions of the three-dimensional (3D) TI in oxide systems10,11. Several iridium oxides suggested as TI candidates are still under debate because of the competition with the magnetic instability which is driven by electron-electron interactions and leads to novel phases other than TI such as Weyl semi-metal, axion insulator and so on12,13. The competition among the small energy scales makes those iridates more interesting but less appropriate for practical applications especially in TI-based devices.

Here, we predict YBiO3 to be a new TI candidate, taking a first step toward bridging oxide electronics and TI. The cubic perovskite structure of YBiO3 makes it even more attractive. From the applications point of view, YBiO3 is of great advantage in several aspects: it has a large enough bulk band gap operative at room temperature. Moreover, it showed a high resistivity reported as the order of several MΩ m14, which is hardly achievable in the Bi2Se3-family, the most prevailing 3D TI compounds. The highly resistive insulating phase will greatly help to reveal the fundamental properties of 3D TI through transport experiments by discerning the surface degrees of freedom from bulk. Furthermore, YBiO3 was originally deposited on top of a LaAlO3 substrate and was used as a buffer layer for the high-temperature superconductor YBa2Cu3O7−δ, which acts as a structural template for the epitaxial deposition of the superconductor and a diffusion barrier15. It implies the inborn character of YBiO3 to form interfaces with normal band insulators or superconductors. Considering the state-of-the-art synthesis techniques used in the artificial heterostrucutre of oxide perovskites, YBiO3 might possess great potential to show a rich variety of interface structures with other quantum phases. Probably, the TI phase in an oxide perovskite structure with a large band gap and high resistivity can provide an ideal platform to realize many exotic phenomena emerging at the interfaces, such as topologically protected surface states, giant magnetoelectric effects, Majorana Fermions and so on16,17,18,19.

Results

Basic electronic structure

As a starting point, the basic electronic structure of YBiO3 without SOC is investigated in Fig. 1 where the orbital projections at each k-point are also depicted. It shows a semi-metallic phase with small electron and hole pockets around the Γ and R points in the Brillouin zone, respectively. The valence bands near the Fermi level are mostly composed of oxygen p states, as is usual in conventional oxide perovskites. More precisely, the highest valence band making the hole pocket around the R point has s orbital symmetry originating from the hybridization between Bi 6s and O 2p orbitals (Fig. 1b, c). This s-like singlet, also found in halide perovskite compounds20, is designated as the |l = 0〉 ⊗ |s = 1/2〉 state where l and s are the orbital and spin angular momentum quantum numbers, respectively; in other words, orbital degrees of freedom are quenched. On the other hand, the conduction bands close to the Fermi level consist of Y 5s and 4d orbital components. The Y 5s band has a wide bandwidth forming an electron pocket at the Γ point; the Y 4d bands are narrow and split into the two-fold eg and three-fold t2g levels under the cubic symmetry. Considering the large distance between yttrium and the surrounding twelve oxygen atoms, the cubic crystal field splitting at the Y site is small and opposite to that in the octahedron center. Hence the eg states are lower than t2g at the Γ point by 0.29 eV. But due to the hybridization between Y t2g and Bi 6p states and the opposite sign of hopping parameters between t2g and eg, the t2g bands are located below the eg bands at the R point. As a result, when SOC is excluded, the t2g triplets and s-like singlet construct the low energy spectrum at around the R point and become the main ingredients to determine the topological phase of this system. The t2g triplets are the only SOC active bands and they can be effectively mapped into leff = 1 angular momentum states (|leff = 1〉 ⊗ |s = 1/2〉) which are further split into jeff = 1/2 and jeff = 3/2 states by SOC, where leff and jeff are the effective orbital and total angular momentum quantum numbers explained in detail later.

Figure 1
figure 1

Basic electronic structure of YBiO3.

(a) The electronic band structure of YBiO3 without SOC. The circles at each k-point denote the atomic orbital projection of the Bloch wave-functions. The blowups of the low energy spectrum at around the R point are shown with the orbital contributions highlighted in colors for (b) O 2p, (c) Bi 6s, (d) Y 4d t2g and (e) Bi 6p orbital components, respectively.

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It is important to clarify the parities of the basis functions in determining the topological character of the inversion symmetric systems21. Because the inversion is the symmetric operation at the R point, the parity eigenvalue is a good quantum number; in other words, there is no mixing between two eigenfunctions with opposite parities at the R point. Therefore, the wavefunction mixing at the R point in Fig. 1b–e clearly shows that the upper t2g triplets and the lower s-like singlet have opposite parities. More specifically, the Y t2g orbitals couple to Bi 6p states whereas the O 2p orbital couples to Bi 6s. Because Bi 6p and 6s have odd and even parities with respect to the Bi center, respectively, the t2g triplets are odd and the s-like singlet is even.

Non-trivial topological phase

In an attempt to elucidate the topological phase of YBiO3, the evolution of its electronic quasi-particle spectrum with varying SOC up to its full strength was scrutinized. The topological phase of the system can be verified by examining the topological phase transition during this process22. The variation of the SOC strength is designated as the ratio x between the SOC value used in the calculations and in the real system. Figures 2a–d show the 3D plots of the electronic band dispersions on the Γ-X-R-M plane of the Brillouin zone as the SOC ratio x gradually grows. Without SOC, the band topology is identified as the topologically trivial semi-metallic phase (Fig. 2a). When the SOC strength is slightly turned on, triply degenerate t2g bands, the only SOC active ones, split into the lower jeff = 1/2 and the higher jeff = 3/2 states, resulting in the jeff = 1/2 and s-like singlets closer at the R point. When x reaches 0.213, as shown in Fig. 2b, the bottom of the jeff = 1/2 band touches the top of the s-like band, forming a gapless Dirac cone. And by increasing x a little bit larger, the Dirac cone acquires a mass gap again as the two singlet bands are inverted. The emergence of the gapless Dirac cone during the increment of x directly indicates the topological phase transition from the trivial to the non-trivial phase. Due to the preformed electron and hole pockets, the trivial semi-metal is transformed into the topological semi-metallic phase. After the transition point, the non-trivial gap at the R point keeps rising in accordance with the increase of x, getting the volume of the hole pocket smaller and successively opening a real insulating gap. At x = 0.51, the hole pocket shrinks to the point at R and so does the electron pocket at Γ (Fig. 2c). When x exceeds 0.51, the topological semi-metal undergoes a transition to the topological insulating phase. Finally, with the full strength of SOC in Fig. 2d, YBiO3 manifests itself as a 3D TI with an indirect band gap of 0.183 eV between the conduction band minimum at Γ and the valence band maximum at (π, π, 0.58π).

Figure 2
figure 2

Evolution of the electronic structure with varying SOC.

The 3D plots of the band structure on the Γ-X-R-M plane of the Brillouin zone are shown as the SOC ratio x grows: (a) x = 0.0, (b) x = 0.213, (c) x = 0.51 and (d) x = 1.0. The dark blue planes in (a)–(d) indicate the Fermi level.

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YBiO3 has an interesting feature in its indirect band gap; the conduction and valence band edges have different topological character. The conduction band bottom at Γ mainly consists of the Y 5s component, which is not influenced by SOC and does not participate in determining the band topology. On the other hand, the valence band top, the lower part of the non-trivial gap, has the jeff = 1/2 character split-off from the Y t2g bands by SOC, thus governing the topological phase of the system. The upper part of the non-trivial gap, the s-like singlet, is SOC inactive and remains higher than the conduction band minimum. The non-trivial gap is 0.33 eV around the R point, which is larger than the real band gap. Once a 2D surface is introduced, topologically protected surface states are expected to reside inside the non-trivial gap, connecting the inverted bands.

Bulk-boundary correspondence

According to the bulk-boundary correspondence23,24, the topologically protected gapless modes should emerge at the boundary between two different topological phases. The 2D surface of the 3D TI is one of the easily accessible phase boundaries between TI and vacuum, where such gapless states exist. The electronic structures of three conventional surface configurations in cubic perovskite YBiO3, (001), (110) and (111) surfaces, are depicted in Fig. 3. The slab geometries composed of 35 layers were constructed, whose microscopic energy scales related to the electronic degrees of freedom were obtained from the maximally localized Wannier function approach25,26. The topologically protected surface states are shown inside the bulk gap region for all three surface configurations, which connect the inverted conduction and valence bands, present the single 2D Dirac cone and reflect the 3D TI phase of the bulk YBiO3. Apart from the existence of the conducting surface states, details of the surface states are diverse. In case of the (111) surface, the Dirac point of the surface Dirac cone is embedded in the conduction band continuum, whereas the surface Dirac points are isolated from the bulk continuum and appeared inside the band gap in the (001) and (110) surface configurations. The difference originates from the different topological character of the conduction band minimum and valence band maximum and the projection from the bulk to the surface Brillouin zone. More specifically, the Γ and R points of the cubic Brillouin zone project into the same point of the 2D hexagonal Brillouin zone in the (111) surface and consequently the trivial conduction band edge and the non-trivial gap overlap as shown in Fig. 3c.

Figure 3
figure 3

Topologically protected surface states.

The surface geometries and the corresponding electronic band structures containing the topologically protected surface states for (a) (001), (b) (110) and (c) (111) surface configurations of the cubic perovskite YBiO3. The green shaded areas represent the surface-projected bulk continuum bands.

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Discussion

All the above evidence say in unison that YBiO3 belongs to 3D TI via inverting the band character between the jeff = 1/2 state split-off from Y t2g orbital and the s-like state at the R point. However, there remains an unanswered question on what is the driving force for the nontrivial phase of YBiO3. The strong candidate is SOC only within the t2g orbital of Y 4d, but it is inappropriate to explain the topological phase transition appearing in Fig. 2b because of the following two reasons. The SOC strength of Y 4d is relatively small to induce the non-trivial phase. And more importantly, the leff = 1 triplet of the t2g manifold is known to split into the higher jeff = 1/2 singlet and the lower jeff = 3/2 doublet by SOC; the sign of the SOC strength is effectively opposite to that of the original l = 1 manifold (p-orbital)27,28. The effective orbital angular momentum operator (Leff) is defined within the t2g subspace in connection with the original angular momentum operator (L) by

where is the projection operator to the t2g manifold. Accordingly, Jeff = Leff + S is the effective total angular momentum operator and the effective SOC term is written as

Therefore, SOC only in the Y t2g orbital tends to form the jeff = 3/2 and s = 1/2 states as the low energy spectrum near the R point rather than the jeff = 1/2 and s = 1/2 singlets, which is inconsistent with the current situation.

In order to solve the contradiction, we vary the SOC strength of the Bi atom (λBi) only, while maintaining the full SOC strength of other elements, envisaging the largest SOC of Bi 6p states to play a crucial role. When we turn off λBi, the Y t2g bands split into the lower jeff = 3/2 doublet and the higher jeff = 1/2 singlet by 50 meV at the R point (Fig. 4a), which agrees well with the previous description and indicates the bare possibility of the topological insulating phase by SOC solely in Y 4d. As λBi increases, the splitting between the jeff = 1/2 and jeff = 3/2 states turns out to be reversed (Fig. 4b–e); λBi substantially makes the jeff = 1/2 and s = 1/2 singlets as constituents of the low energy spectrum and finally induces an inversion between them, changing the band topology from trivial to non-trivial. Under the influence of the Bi 6p orbital, the Y t2g states follow the SOC splitting of the original l = 1 states. All the behaviors of the Y 4d t2g orbital states related to the topological phase of YBiO3 are driven by the SOC of the Bi 6p orbital states through the strong d-p hybridization.

Figure 4
figure 4

SOC of the Bi 6p orbital.

The bulk band structure of YBiO3 with varying xBi, the SOC ratio of the Bi atom, with xBi = (a) 0.0, (b) 0.25, (c) 0.5, (d) 0.75 and (e) 1.0. The red, green and grey arrows correspond to s = 1/2, jeff = 1/2 singlets and jeff = 3/2 doublet, respectively. The SOC values of other elements are maintained with their full strength. (f) The schematic diagram shows the evolution of the low energy spectrum as a function of the SOC strength of each atom, describing the topological phase of YBiO3.

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YBiO3, used as a buffer layer for the cuprate superconductor, is suggested as a new TI candidate. Combining the present theoretical results with the previous experimental facts and the future potentiality, its finding has more meaning than merely adding one more material in the TI catalogue. YBiO3 can provide a new platform for TI applications in terms of the large band gap, high resistivity and an oxide perovskite material. The high residual bulk carrier density of conventional 3D TIs, although being improved29,30, mostly hampers the practical use of TI and fails to meet the original goal of TI, insulating bulk and conducting surface. This material with its high bulk resistivity, which may stem from the chemical and structural integrity of oxide systems, can achieve the original goal. It is presumably useful for room temperature applications, feasible for the utilization of advanced fabrication techniques and accessible for the various interface geometries with other quantum phases. These features are essential requirements for making better TI-based devices and convincingly entitle YBiO3 as a promising TI material that assumes importance for future development.

Methods

First-principles calculations

To investigate the electronic structure and topological phase of YBiO3, first-principles calculations were performed using the full-potential linearized augmented plane wave (FLAPW) method31 with the generalized gradient approximation for the exchange-correlation functional. For the momentum space integrations, a 10 × 10 × 10 mesh of special k-points was used in the 3D irreducible Brillouin zone wedge. We used a wave-vector cutoff of the basis set equal to Kmax = 3.8 a.u. and an angular momentum expansion up to lmax = 8 for both the potential and charge density. The muffin-tin radii of Y, Bi and O were 2.8, 2.9 and 1.8 a.u., respectively. The relativistic SOC was included self-consistently by a second variational procedure. The SOC contribution to the Hamiltonian is decomposed to that from atomic spheres and interstitial following the standard way in the LAPW method. When the SOC strength was adjusted, the spherical part of the SOC interaction of each sphere is multiplied by a simple constant x. A maximally localized Wannier function approach25,26 was employed for extracting the electronic energy scales and constructing the tight-binding Hamiltonian of the slab geometries. The projectors, as an aid to describing the low energy spectrum properly, consist of Bi p, O p and Y s, p, d orbitals. The calculations were carried out with the experimental cubic lattice constant, 5.428 Å15. Even though we adopted the simple cubic perovskite structure which might be feasible in the real growth condition, the structural properties of this compound need a further investigation.