Efficient prediction of topological superlattice bands with spin-orbit coupling

Abstract

We develop a symmetry indicator framework to efficiently predict the topology of superlattice-induced minibands with spin-orbit coupling. Our algorithm requires input only from the parent material before the superlattice is applied. The simplification arises by assuming a perturbatively weak superlattice potential; however, our results extend beyond the perturbative regime as long as the superlattice-induced gaps remain open. We first consider a time-reversal- and inversion-symmetric system subject to a weak superlattice potential and derive a compact formula for the ${\mathbb{Z}}_2$ invariant of the lowest miniband. We then extend to time-reversal breaking systems and compute the Chern number. We apply our theory to selected transition metal dichalcogenides, HgTe/CdTe quantum wells, and thin films of three-dimensional topological insulators and Dirac semimetals. We find topological superlattice bands can arise even from non-topological materials, broadening the pool of candidates for realizing topological flat bands. Our theory predicts which geometry and periodicity of superlattice will yield topological bands for a given material, providing a clear guiding principle for designing topological superlattice heterostructures.

15 pages, 4 figures

References in corpus (63)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides
• Topological Insulators with Inversion Symmetry
• Moire bands in twisted double-layer graphene
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Three Dimensional Dirac Semimetal and Quantum Transports in Cd3As2
• Topological quantum chemistry
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• Crossover of Three-Dimensional Topological Insulator of Bi2Se3 to the Two-Dimensional Limit
• k.p theory for two-dimensional transition metal dichalcogenide semiconductors
• Origin of Magic Angles in Twisted Bilayer Graphene
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Topological insulators in twisted transition metal dichalcogenide homobilayers
• Hubbard model physics in transition metal dichalcogenide moiré bands
• Observation of Fractionally Quantized Anomalous Hall Effect
• Topological classification of crystalline insulators through band structure combinatorics
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Twistronics: Manipulating the Electronic Properties of Two-dimensional Layered Structures through their Twist Angle
• Oscillatory crossover from two dimensional to three dimensional topological insulators
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene
• Nearly Flat Chern Bands in Moiré Superlattices
• Effective continuous model for surface states and thin films of three dimensional topological insulators
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Observation of fractional Chern insulators in a van der Waals heterostructure
• Ab-Initio Theory of Moiré Superlattice Bands in Layered Two-Dimensional Materials
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• Band Structure Engineering of 2D Materials using Patterned Dielectric Superlattices
• Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii-Moriya interaction in twisted bilayer WSe${}_2$
• Gate-Tunable Topological Flat Bands in Trilayer Graphene-Boron Nitride Moiré Superlattices
• A Microscopic Perspective on Moiré Materials
• Topological Bloch Bands in Graphene Superlattices
• Band Representations and Topological Quantum Chemistry
• Electronic structures, charge transfer and charge orders in twisted transition metal dichalcogenide bilayers
• Anisotropic band flattening in graphene with 1D superlattices
• Topological and stacked flat bands in bilayer graphene with a superlattice potential
• Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
• Topological Phases in AB-Stacked MoTe${}_2$/WSe${}_2$: ${\mathbb{Z}}_2$ Topological Insulators, Chern Insulators, and Topological Charge Density Waves
• Band structures of bilayer graphene superlattices
• A moiré superlattice on the surface of a topological insulator
• Engineering high quality graphene superlattices via ion milled ultra-thin etching masks
• Two-dimensional topological insulator state in cadmium arsenide thin films
• Gate-tunable flat bands in van der Waals patterned dielectric superlattices
• Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
• Multilayer graphene with a superlattice potential
• Gate-tunable topological phases in superlattice modulated bilayer graphene
• Designer Meron Lattice on the Surface of a Topological Insulator
• Signature of Correlated Insulator in Electric Field Controlled Superlattice
• Engineering the in-plane anomalous Hall effect in Cd${}_3$As${}_2$ thin films
• Chiral model of twisted bilayer graphene realized in a monolayer
• Twist-angle evolution of the intervalley-coherent antiferromagnet in twisted WSe${}_2$
• Spinon pairing induced by chiral in-plane exchange and the stabilization of odd-spin Chern number spin liquid in twisted ${\mathrm{MoTe}}_2$
• ${\mathbb{Z}}_2$-Nontrivial Moiré Minibands and Interaction-Driven Quantum Anomalous Hall Insulators in Topological Insulator Based Moiré Heterostructures
• Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
• Attractive Haldane bilayers for trapping non-Abelian anyons
• An $O(N)$ $Abinitio$ Calculation Scheme for Large-Scale Moiré Structures
• Two-dimensional Dirac fermions in a mass superlattice
• Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices
• Low-energy modeling of three-dimensional topological insulator nanostructures
• Artificial moiré engineering for an ideal BHZ model