Emergent topological states via digital (001) oxide superlattices

The study addresses how to induce non-trivial topological phases (topological insulators and topological semimetals) in complex oxides using artificial (001) superlattices. While topological phases have been widely explored in s- and p-orbital dominated semiconductors, d-orbital oxides remain less explored. Prior efforts in oxides focused on bulk candidates or (111) bilayers with honeycomb lattices, but (111) growth poses challenges due to polarity. In contrast, (001) oxide heterostructures with non-polar terminations (e.g., Sr-based perovskites) are routinely synthesized with atomic-layer precision. The authors propose design principles leveraging d–d band inversion between dissimilar transition metals, specific parity properties inherent to (001) superlattice geometry, oxygen octahedral rotations, and d-electron occupancy to realize strong topological insulating and Dirac semimetal states. They aim to demonstrate, via first-principles and model calculations, that carefully chosen (SrMO3)1/(SrM′O3)1 superlattices can host strong TI phases [Z2 = (1;001)] and, in certain cases, coexisting TI and TDS phases near the Fermi level.

Topological insulating and semimetallic states in time-reversal-invariant crystals have been extensively explored in systems with s/p orbitals, e.g., Bi2Se3-family TIs and Dirac semimetals (Na3Bi, Cd3As2). In oxides, proposed TIs such as YBiO3 and doped BaBiO3 rely on s–p band inversion and SOC-induced gaps. Crystalline symmetries have been used to identify Dirac points and node lines in non-magnetic oxides like SrNbO3 and SrIrO3; Dirac semimetal behavior has also been observed in CaIrO3. Heterostructuring enables engineered electronic structures absent in bulk, with (111)-oriented bi-layers predicted to host quantum spin Hall and related phases due to honeycomb lattices and SOC, though their polar terminations hinder precise growth. Conversely, (001) perovskite heterostructures with non-polar terminations are widely accessible and can precisely control octahedral rotations and symmetry, offering a practical platform to engineer topological states.

First-principles calculations: Density functional theory (DFT) calculations were performed with VASP using the PBEsol exchange-correlation functional. Plane-wave cutoff: 600 eV. k-mesh: 10×10×8 Monkhorst-Pack for the superlattice Brillouin zone. Spin–orbit coupling (SOC) included self-consistently unless noted. Self-consistent convergence threshold: 1e-6 eV. Structural relaxations to forces < 0.01 eV/Å and residual pressure < 0.5 kbar. For biaxial strain, in-plane lattice constants were fixed (to simulate substrates) while the out-of-plane constant relaxed fully; strain ε = ((a − a0)/a0) × 100%, where a0 is the DFT-optimized pseudo-tetragonal lattice constant, and a is the substrate lattice constant. Wannierization and surface calculations: Maximally localized Wannier functions (Wannier90) were constructed. One set (including SOC) was used with Green-function methods (WannierTools) to compute semi-infinite slab surface spectra. A second set (without SOC) was used to build tight-binding (TB) models with SOC added explicitly as atomic λ L·S terms. Model Hamiltonians: For (SrTaO3)1/(SrIrO3)1, a TB model on alternating Ta and Ir square layers along z included Ta {dxz, dyz, d(x2−y2)} and all five Ir d orbitals on two layers per period, totaling 16 orbitals (doubled by spin). H0(k) (no SOC) was fitted to DFT bands via MLWF; SOC was added as Hsoc = λ L·S (common λ used for simplicity). Parity at TRIM points and Z2 indices were derived using inversion symmetry and verified by Wilson loop when inversion/C4 were artificially broken. Surface spectra for (100)/(001) terminations were obtained via Green-function methods. Structural/symmetry considerations: Combining cubic (Pm3m) early transition-metal perovskites (e.g., SrTaO3, SrMoO3) with orthorhombic (Pnma) late transition-metal perovskites (e.g., SrIrO3) in (001) superlattices yields a tetragonal P4/mbm structure with out-of-phase in-plane octahedral rotations (a0a0c0), enforcing cell doubling, C4 symmetry, and a non-symmorphic space group crucial for Dirac points (DP) and Dirac nodal lines (DNL). Electronic fillings considered: d1+d5 (total 12 d electrons per doubled cell) and d2+d5 (total 14 = 3×4+2), constraining possible insulating vs. necessarily semimetallic fillings by symmetry.

- (SrTaO3)1/(SrIrO3)1 (d1 + d5 case) is a strong topological insulator with Z2 index (1;001). SOC opens a full direct gap between the highest valence and lowest conduction bands throughout the Brillouin zone; DFT and TB models agree. The parity analysis shows all TRIM points even except Z (odd), yielding a strong TI. The minimum direct gap increases monotonically with SOC strength λ; the most promising candidate combination (e.g., Ta–Ir) exhibits a direct gap of about 20 meV. Topological surface states traverse the gap on (100) and (001) surfaces, with the (100) surface Dirac crossing near EF. - Origin of topology: Non-trivial topology arises from d–d band inversion between dissimilar transition metals (Ta and Ir) and a special parity property due to their distinct positions in the (001) superlattice. Inversion induces different phase factors for Ta-d vs. Ir-d states at Γ and Z, causing a parity switch at Z upon inversion and yielding the strong TI. - (SrMoO3)1/(SrIrO3)1 (d2 + d5 case) hosts coexisting topological phases: • Topological Dirac semi-metal (TDS): A pair of type-II Dirac points along Γ–Z, stabilized by time-reversal, inversion, and C4 rotation symmetries. The crossing lies about 87 meV below EF and occurs between predominantly Ir-d (valence) and Mo-d (conduction) bands with different C4 eigenvalues. Constant-energy contours show touching electron and hole pockets at the DP, confirming type-II character. The mirror Chern number nM at kz = 0 is 2, implying two Fermi arcs emanating from each projected DP on the (010) surface. • Dirac node lines (DNL): Along U–R (and symmetry-related lines) due to nonsymmorphic P4/mbm symmetry combined with T and inversion; with total filling 14 (3×4+2), the Fermi level must cross a DNL, enforcing semimetallicity. • Coexisting TI gaps: Between the top valence and second valence band, and between the bottom conduction and second conduction band, global gaps are topologically non-trivial with Z2 = (1;001), analogous in origin to the Ta/Ir case. - Strain tunability of Dirac points in (SrMoO3)1/(SrIrO3)1: Epitaxial strain modulates band inversion and the number/positions of DP along Γ–Z: • 2% tensile to 1.7% compressive: one DP pair. • 1.7% to 2.7% compressive: two DP pairs. • 2.7% to 4% compressive: no DP. On KTaO3 (negligible mismatch): one DP pair; on SrTiO3 (~2.3% compressive): two DP pairs. DNL persist across strain due to symmetry and filling. - Surface band topology: On the (010) surface, two Fermi arcs connect the projections of the DP pair, consistent with nM = 2. The TDS surface Dirac cone is sandwiched in energy-momentum space between two TI surface Dirac cones; the upper TI surface Dirac cone crosses EF, enabling potential TI–TDS–TI transitions via hole doping or gating.

The work demonstrates a practical route to engineer non-trivial topology in (001) oxide superlattices by combining dissimilar transition metals to achieve d–d band inversion, leveraging parity properties set by atomic positions and crystal symmetries (inversion, C4, nonsymmorphic operations). For d1+d5 fillings, SOC opens a full gap yielding a robust strong TI [Z2 = (1;001)], with topological surface states accessible on (100)/(010) surfaces. For d2+d5 fillings, symmetry protects Dirac points and nodal lines at EF, while adjacent band manifolds retain non-trivial TI gaps, producing a rich coexistence of TDS and TI states and multiple surface Dirac cones near EF. Strain control provides an external knob to tune the number and position of DP, while DNL are symmetry-enforced and robust. The predicted momentum-space separation between topological surface states and bulk bands near EF facilitates spectroscopic detection (e.g., ARPES). The absence of canted AFM up to UIr = 4 eV in DFT+U+SOC suggests robustness of the predicted topological features against moderate correlations. The principles are broadly applicable and suggest pathways to additional correlated topological phases (e.g., QAHE, Weyl semimetals) in oxide superlattices by tuning orbital filling, symmetry, and interactions.

By combining first-principles and tight-binding analyses, the authors establish design rules for realizing multiple topological phases in (001) perovskite oxide superlattices. (SrTaO3)1/(SrIrO3)1 is a strong TI with Z2 = (1;001), originating from d–d inversion and parity switching at Z. (SrMoO3)1/(SrIrO3)1 hosts coexisting TDS (type-II DP with mirror Chern number 2 and symmetry-protected DNL) and TI gaps, yielding characteristic surface states where a TDS Dirac cone is sandwiched between two TI Dirac cones. Epitaxial strain tunes Dirac points while preserving DNL, and the surface electronic structure near EF is amenable to experimental detection. The demonstrated approach opens a route to engineer emergent topological phenomena in oxide heterostructures; future work may extend to strongly correlated 3d systems to realize QAHE and Weyl semimetals via the same principles.

- Computational approximations: Semi-local DFT functionals underestimate oxygen p–metal d separation; although the study focuses on d–d inversion (less sensitive), quantitative gaps and band positions may shift with more advanced methods. - Correlation effects: While DFT+U+SOC finds no canted AFM up to UIr = 4 eV, real materials may exhibit additional correlation-driven phases or disorder not captured here. - Experimental realization: Predicted surface states often overlap in energy with bulk states; separation relies on momentum-space resolution and specific surface orientations [(100)/(010) preparation by cleaving/polishing]. Precise epitaxial strain control is required to tune Dirac points; maintaining nonsymmorphic symmetry and C4 is essential for DP/DNL protection. - Fermi level tuning: Accessing TI–TDS–TI transitions may require chemical doping or gating to align EF with the targeted surface/bulk features, which can introduce disorder or band bending. - Model simplifications: TB models use a common SOC constant for different elements and neglect potential subtle structural distortions; inversion/C4 breaking cases were tested, but full surface/defect reconstructions are not explored.