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The presence of topological flat minibands in moiré materials provides an opportunity to explore the interplay between topology and correlation. In this work, we study moiré minibands in topological insulator films with two hybridized surface states under a moiré superlattice potential created by two-dimensional insulating materials. We show the lowest conduction (highest valence) Kramers’ pair of minibands can be$${{\mathbb{Z}}}_{2}$$$Z_2$non-trivial when the minima (maxima) of moiré potential approximately form a hexagonal lattice with six-fold rotation symmetry. Coulomb interaction can drive the non-trivial Kramers’ minibands into the quantum anomalous Hall state when they are half-filled, which is further stabilized by applying external gate voltages to break inversion. We propose the monolayer Sb₂on top of Sb₂Te₃films as a candidate based on first principles calculations. Our work demonstrates the topological insulator based moiré heterostructure as a potential platform for studying interacting topological phases.

 

Abstract For over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. However, the group theory of crystals with commensurate magnetic order has remained incomplete for the past 70 years, due to the complicated symmetries of magnetic crystals. In this work, we complete the 100-year-old problem of crystalline group theory by deriving the small corepresentations, momentum stars, compatibility relations, and magnetic elementary band corepresentations of the 1,421 magnetic space groups (MSGs), which we have made freely accessible through tools on the Bilbao Crystallographic Server. We extend Topological Quantum Chemistry to the MSGs to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids – Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we derive the complete set of symmetry-based indicators of electronic band topology, for which we identify symmetry-respecting bulk and anomalous surface and hinge states. 

The existence of topological hinge states is a key signature for a newly proposed class of topological matter, the second-order topological insulators. In the present paper, a universal mechanism to generate chiral hinge states in the ferromagnetic axion insulator phase is introduced, which leads to an exotic transport phenomenon, the quantum anomalous Hall effect (QAHE) on some particular surfaces determined by both the crystalline symmetry and the magnetization direction. A realistic material system, Sm-doped Bi2Se3, is then proposed to realize such exotic hinge states by combining first-principles calculations and Green’s function techniques. A physically accessible way to manipulate the surface QAHE is also proposed, which makes it very different from the QAHE in ordinary 2D systems. 

Parity‐time symmetry plays an essential role for the formation of Dirac states in Dirac semimetals. So far, all of the experimentally identified topologically nontrivial Dirac semimetals (DSMs) possess both parity and time reversal symmetry. The realization of magnetic topological DSMs remains a major issue in topological material research. Here, combining angle‐resolved photoemission spectroscopy with density functional theory calculations, it is ascertained that band inversion induces a topologically nontrivial ground state in EuCd₂As₂. As a result, ideal magnetic Dirac fermions with simplest double cone structure near the Fermi level emerge in the antiferromagnetic (AFM) phase. The magnetic order breaks time reversal symmetry, but preserves inversion symmetry. The double degeneracy of the Dirac bands is protected by a combination of inversion, time‐reversal, and an additional translation operation. Moreover, the calculations show that a deviation of the magnetic moments from thec‐axis leads to the breaking of C3 rotation symmetry, and thus, a small bandgap opens at the Dirac point in the bulk. In this case, the system hosts a novel state containing three different types of topological insulator: axion insulator, AFM topological crystalline insulator (TCI), and higher order topological insulator. The results provide an enlarged platform for the quest of topological Dirac fermions in a magnetic system.