Suppression of symmetry-breaking correlated insulators in a rhombohedral trilayer graphene superlattice.

Counterintuitive temperature dependence of isospin flavor polarization has recently been found in twisted bilayer graphene, where unpolarized electrons in a Fermi liquid become a spin-valley polarized insulator upon heating. So far, the effect has been limited to v = +/-1 (one electron/hole per superlattice cell), leaving open questions such as whether it is a general property of symmetry-breaking electronic phases. Here, by studying a rhombohedral trilayer graphene/boron nitride moiré superlattice, we report that at v = -3 a resistive peak emerges at elevated temperatures or in parallel magnetic fields.

Molecular Pairing in Twisted Bilayer Graphene Superconductivity.

We propose a theory for how the weak phonon-mediated interaction (J_{A}=1-4  meV) wins over the prohibitive Coulomb repulsion (U=30-60  meV) and leads to a superconductor in magic-angle twisted bilayer graphene (MATBG). We find the pairing mechanism akin to that in the A_{3}C_{60} family of molecular superconductors: Each AA stacking region of MATBG resembles a C_{60} molecule, in that optical phonons can dynamically lift the degeneracy of the moiré orbitals, in analogy to the dynamical Jahn-Teller effect. Such induced J_{A} has the form of an intervalley anti-Hund's coupling and is less suppressed than U by the Kondo screening near a Mott insulator.

Correlated Charge Density Wave Insulators in Chirally Twisted Triple Bilayer Graphene.

Electrons residing in a flat-band system can play a vital role in triggering spectacular phenomenology due to relatively large interactions and spontaneous breaking of different degeneracies. In this work, we demonstrate chirally twisted triple bilayer graphene, a new moiré structure formed by three pieces of helically stacked Bernal bilayer graphene, as a highly tunable flat-band system. In addition to the correlated insulators showing at integer moiré fillings, commonly attributed to interaction induced symmetry broken isospin flavors in graphene, we observe abundant insulating states at half-integer moiré fillings, suggesting a longer-range interaction and the formation of charge density wave insulators which spontaneously break the moiré translation symmetry.

Engineering the Band Topology in a Rhombohedral Trilayer Graphene Moiré Superlattice.

Moiré superlattices have become a fertile playground for topological Chern insulators, where the displacement field can tune the quantum geometry and Chern number of the topological band. However, in experiments, displacement field engineering of spontaneous symmetry-breaking Chern bands has not been demonstrated. Here in a rhombohedral trilayer graphene moiré superlattice, we use a thermodynamic probe and transport measurement to monitor the Chern number evolution as a function of the displacement field.

Catalog of topological phonon materials.

Phonons play a crucial role in many properties of solid-state systems, and it is expected that topological phonons may lead to rich and unconventional physics. On the basis of the existing phonon materials databases, we have compiled a catalog of topological phonon bands for more than 10,000 three-dimensional crystalline materials. Using topological quantum chemistry, we calculated the band representations, compatibility relations, and band topologies of each isolated set of phonon bands for the materials in the phonon databases.

Evolution of the flat band and the role of lattice relaxations in twisted bilayer graphene.

Magic-angle twisted bilayer graphene exhibits correlated phenomena such as superconductivity and Mott insulating states related to the weakly dispersing flat band near the Fermi energy. Such a flat band is expected to be sensitive to both the moiré period and lattice relaxations. Thus, clarifying the evolution of the electronic structure with the twist angle is critical for understanding the physics of magic-angle twisted bilayer graphene.

Anderson critical metal phase in trivial states protected by average magnetic crystalline symmetry.

Transitions between distinct obstructed atomic insulators (OAIs) protected by crystalline symmetries, where electrons form molecular orbitals centering away from the atom positions, must go through an intermediate metallic phase. In this work, we find that the intermediate metals will become a scale-invariant critical metal phase (CMP) under certain types of quenched disorder that respect the magnetic crystalline symmetries on average. We explicitly construct models respecting average CT, m, and CT and show their scale-invariance under chemical potential disorder by the finite-size scaling method.

Interacting topological quantum chemistry in 2D with many-body real space invariants.

The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained from momentum space. Recently, Real Space Invariants (RSIs) have provided a spatially local description of the global momentum space indices. The present work generalizes this real space classification to interacting 2D states.

Audio-Visual Fusion Based on Interactive Attention for Person Verification.

With the rapid development of multimedia technology, personnel verification systems have become increasingly important in the security field and identity verification. However, unimodal verification systems have performance bottlenecks in complex scenarios, thus triggering the need for multimodal feature fusion methods. The main problem with audio-visual multimodal feature fusion is how to effectively integrate information from different modalities to improve the accuracy and robustness of the system for individual identity.

Chemical Potential Characterization of Symmetry-Breaking Phases in a Rhombohedral Trilayer Graphene.

Rhombohedral trilayer graphene has recently emerged as a natural flat-band platform for studying interaction-driven symmetry-breaking phases. The displacement field () can further flatten the band to enhance the density of states, thereby controlling the electronic correlation that tips the energy balance between spin and valley degrees of freedom. To characterize the energy competition, chemical potential measurement─a direct thermodynamic probe of Fermi surfaces─is highly demanding to be conducted under a constant .

Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries.

Adding magnetic flux to a band structure breaks Bloch's theorem by realizing a projective representation of the translation group. The resulting Hofstadter spectrum encodes the nonperturbative response of the bands to flux. Depending on their topology, adding flux can enforce a bulk gap closing (a Hofstadter semimetal) or boundary state pumping (a Hofstadter topological insulator).

Magic-Angle Twisted Bilayer Graphene as a Topological Heavy Fermion Problem.

Magic-angle (θ=1.05°) twisted bilayer graphene (MATBG) has shown two seemingly contradictory characters: the localization and quantum-dot-like behavior in STM experiments, and delocalization in transport experiments. We construct a model, which naturally captures the two aspects, from the Bistritzer-MacDonald (BM) model in a first principle spirit.

Obstructed Surface States as the Descriptor for Predicting Catalytic Active Sites in Inorganic Crystalline Materials.

The discovery of new catalysts that are efficient and sustainable is a major research endeavor for many industrial chemical processes. This requires an understanding and determination of the catalytic origins, which remains a challenge. Here, a novel method to identify the position of active sites based on searching for crystalline symmetry-protected obstructed atomic insulators (OAIs) that have metallic surface states is described.

Catalogue of flat-band stoichiometric materials.

Topological electronic flattened bands near or at the Fermi level are a promising route towards unconventional superconductivity and correlated insulating states. However, the related experiments are mostly limited to engineered materials, such as moiré systems. Here we present a catalogue of the naturally occuring three-dimensional stoichiometric materials with flat bands around the Fermi level.

Efficient Method for Prediction of Metastable or Ground Multipolar Ordered States and Its Application in Monolayer α-RuX_{3} (X=Cl, I).

Exotic high-rank multipolar order parameters have been found to be unexpectedly active in more and more correlated materials in recent years. Such multipoles are usually dubbed "hidden orders" since they are insensitive to common experimental probes. Theoretically, it is also difficult to predict multipolar orders via ab initio calculations in real materials.

Magnetic topological quantum chemistry.

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.

Dynamical symmetry indicators for Floquet crystals.

Various exotic topological phases of Floquet systems have been shown to arise from crystalline symmetries. Yet, a general theory for Floquet topology that is applicable to all crystalline symmetry groups is still in need. In this work, we propose such a theory for (effectively) non-interacting Floquet crystals.

Delocalization Transition of a Disordered Axion Insulator.

The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that, under quenched disorder respecting inversion symmetry on average, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction.

Fragile Topology and Flat-Band Superconductivity in the Strong-Coupling Regime.

In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of the superfluid weight D_{s}, does not draw from the curvature of the band but has a purely band-geometric origin. In a mean-field description, a nonzero Chern number or fragile topology sets a lower bound for D_{s}, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG).

Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices.

Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this Letter, we introduce a generic approach to construct two-dimensional (2D) topological quasiflat bands from line graphs and split graphs of bipartite lattices. A line graph or split graph of a bipartite lattice exhibits a set of flat bands and a set of dispersive bands.

Hofstadter Topology: Noncrystalline Topological Materials at High Flux.

The Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding ∼10^{4}  T magnetic fields to a trivial band structure. In this Letter, we show that when a magnetic field is added to an initially topological band structure, a wealth of possible phases emerges.

High-throughput calculations of magnetic topological materials.

The discoveries of intrinsically magnetic topological materials, including semimetals with a large anomalous Hall effect and axion insulators, have directed fundamental research in solid-state materials. Topological quantum chemistry has enabled the understanding of and the search for paramagnetic topological materials. Using magnetic topological indices obtained from magnetic topological quantum chemistry (MTQC), here we perform a high-throughput search for magnetic topological materials based on first-principles calculations.