Emergent topological states via digital (001) oxide superlattices

Complex oxides display diverse phenomena like Mott insulators, long-range orders, multiferroics, and high-temperature superconductivity. The search for topological states in various systems, including solid-state, photonic, and acoustic crystals, is a significant area of research. Topological insulating and metallic states, characterized by Dirac points and Dirac node lines, have been extensively studied in narrow-gap semiconductors dominated by s and p orbitals. However, complex oxides with d orbitals have been less explored, with previous studies focusing on candidates like YiBiO3 and electron-doped BaBiO3 exhibiting s-p band inversion. Crystal symmetry has also been leveraged to find Dirac points and lines in oxides such as SrNbO3 and SrIrO3. Recent work highlights high-mobility and giant magnetoresistance in Dirac semi-metal CaIrO3. Advances in thin-film deposition techniques allow the creation of digital oxide superlattices and heterostructures, offering an alternative approach to induce non-trivial topological states in complex oxides. Oxide superlattices can provide engineered electronic structures absent in bulk materials. While (111) perovskite oxide bilayers have been proposed, their polar terminations pose synthesis challenges. In contrast, (001) perovskite oxide heterostructures, particularly those with non-polar terminations, are readily synthesized and precisely controlled at the atomic scale. This research proposes inducing non-trivial topological states in (001) oxide superlattices by exploiting band inversion between d orbitals of dissimilar transition metals, the parity properties of the (001) superlattice geometry, oxygen octahedral rotation patterns, and d orbital occupancy. The study utilizes first-principles methods and model Hamiltonian calculations to demonstrate the principles through concrete examples.

The introduction thoroughly reviews existing literature on topological insulators and semi-metals in both conventional semiconductors and complex oxides. It highlights the challenges and limitations of previous approaches, particularly those involving (111) oriented perovskite oxide heterostructures due to their polar nature and difficulties in precise thickness control. The review contrasts this with the advantages of using (001) oriented structures which are easier to synthesize and control, setting the stage for the novel approach proposed in the paper. The literature review also emphasizes the importance of band inversion, spin-orbit coupling, and crystal symmetry in the emergence of topological states, providing the theoretical background for the subsequent analysis and findings.

The research methodology combines first-principles density functional theory (DFT) calculations using the Vienna Ab Initio Simulation Package (VASP) with tight-binding Hamiltonian modeling. DFT calculations, employing the generalized gradient approximation with PBEsol exchange-correlation functional, were performed to determine the electronic structure of the superlattices. A high energy cutoff (600 eV) and a dense k-mesh were used to ensure accuracy. Spin-orbit coupling was included self-consistently. Atomic relaxations were conducted to obtain the equilibrium structure, and bi-axial strain calculations were performed by fixing in-plane lattice constants and allowing out-of-plane relaxation. The Wannier90 package was utilized to construct maximally localized Wannier functions (MLWF) for two purposes: first, to fit the band structure with spin-orbit coupling included, enabling the calculation of surface bands using the Green function method as implemented in WannierTools. Second, to fit the band structure without spin-orbit coupling, thus constructing a tight-binding model where the effects of atomic spin-orbit coupling could be explicitly analyzed. The tight-binding Hamiltonian, incorporating Ta-dxz, dyz, dy²-y² orbitals and all five Ir-d orbitals, was used to investigate the origin of topological properties. The Z2 topological index was calculated using the parity rule, exploiting the inversion symmetry of the superlattice structure. The study also included analysis of Dirac points (DP) and Dirac node lines (DNL) and their topological properties (mirror Chern numbers) using constant energy contours and the surface band structure.

The study identifies key design principles for inducing topological states in (001) oxide superlattices: band inversion between d orbitals of dissimilar transition metals, parity properties of the (001) superlattice geometry, oxygen octahedral rotation patterns, and d orbital occupancy. Specifically, the (SrTaO3)1/(SrIrO3)1 superlattice, a d1 + d5 system, is identified as a strong topological insulator with a Z2 index of (1;001). This strong TI state is robust against epitaxial strain and weak structural distortions. A tight-binding model confirms these findings, showing a direct gap of ~20 meV that increases monotonically with increasing spin-orbit coupling constant. The (SrMoO3)1/(SrIrO3)1 superlattice, a d2 + d5 system, exhibits multiple coexisting topological states: a topological insulator (TI) and a topological Dirac semi-metal (TDS). The TDS state features a pair of type-II Dirac points near the Fermi level and symmetry-protected Dirac node lines. The type-II Dirac points are stabilized by time-reversal, inversion, and C4 rotation symmetries, and their mirror Chern number is 2. The Dirac node lines are protected by the non-symmorphic space group. The number of Dirac points can be tuned by epitaxial strain. The surface TDS Dirac cone is sandwiched by two surface TI Dirac cones. The study shows that the strong TI state in (SrTaO3)1/(SrIrO3)1 doesn't depend critically on inversion symmetry or C4 rotation. The origin of non-trivial topology in both superlattices is linked to the special atomic positions of the transition metals, causing different phase shifts in their wavefunctions under inversion operation. The analysis of the (SrMoO3)1/(SrIrO3)1 superlattice shows that the Dirac points are of type-II with a mirror Chern number of 2, exhibiting two Fermi arcs. The Dirac node lines are protected by non-symmorphic space group symmetry. Epitaxial strain is shown to control band inversion and the number of Dirac point pairs.

The findings demonstrate the emergence of topological states in artificially designed oxide heterostructures that are absent in their bulk constituents. This offers a new route to creating topological phenomena, beyond relying solely on naturally occurring topological materials. The study highlights the tunability of topological properties, particularly in the (SrMoO3)1/(SrIrO3)1 superlattice where epitaxial strain can control the number of Dirac points. The co-existence of TI and TDS states in (SrMoO3)1/(SrIrO3)1 leads to a unique 'sandwich' structure of surface bands with potential for TI-TDS-TI topological phase transitions through chemical doping or electric field gating. The robustness of the topological properties against canted antiferromagnetism is established through DFT+U+SOC calculations. The limitations of DFT calculations in underestimating p-d separation are acknowledged, but the focus on d-d band inversion is deemed less affected by these limitations. The study also addresses the accessibility of (100) surfaces, which exhibit similar topological surface states, and discusses the separation of topological surface bands from bulk spectra using techniques like ARPES and exploiting Anderson localization.

The research successfully demonstrates the induction of multiple topological states, namely strong topological insulator and topological Dirac semi-metal states, in (001) oxide superlattices via rational design. The key is exploiting the band inversion between d orbitals of different transition metal atoms, combined with specific d orbital occupancy and crystal symmetries. Future work could explore the emergence of other topological states, such as quantum anomalous Hall states and Weyl semi-metal states, in (001) superlattices with stronger correlation effects on transition metal d orbitals.

The study acknowledges the inherent limitations of DFT calculations using semi-local exchange-correlation functionals, primarily the underestimation of p-d separation. However, the primary focus on d-d band inversion minimizes the impact of this limitation on the main conclusions. While the (001) surface is naturally formed in these superlattices, the study points out that other surfaces, (100) and (010), could also be prepared experimentally, possessing similar topological properties. The potential for surface states to overlap with bulk spectra presents a challenge for experimental observation, but the study suggests ways to overcome this, like using ARPES in conjunction with manipulation of surface conditions.