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Delocalization Transition of Disordered Axion Insulator
Zhi-Da Song, Biao Lian, Raquel Queiroz +3
The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that under quenched disorder respecting inversion symmetry {\it on average}, th…
Fragile topology in line-graph lattices with two, three, or four gapped flat bands
Christie S. Chiu, Da-Shuai Ma, Zhi-Da Song +2
The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicial…
Evidence for a Monolayer Excitonic Insulator
Yanyu Jia, Pengjie Wang, Cheng-Li Chiu +19
The interplay between topology and correlations can generate a variety of quantum phases, many of which remain to be explored. Recent advances have identified monolayer WTe2 as a p…
Magnetic Topological Quantum Chemistry
Luis Elcoro, Benjamin J. Wieder, Zhida Song +3
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 gr…
Twisted bilayer graphene.VI. An Exact Diagonalization Study of Twisted Bilayer Graphene at Non-Zero Integer Fillings
Fang Xie, Aditya Cowsik, Zhi-Da Song +3
Using exact diagonalization, we study the projected Hamiltonian with Coulomb interaction in the 8 flat bands of first magic angle twisted bilayer graphene. Employing the U(4) (U(4)…
Twisted Bilayer Graphene V: Exact Analytic Many-Body Excitations in Twisted Bilayer Graphene Coulomb Hamiltonians: Charge Gap, Goldstone Modes and Absence of Cooper Pairing
B. Andrei Bernevig, Biao Lian, Aditya Cowsik +3
We find exact analytic expressions for the energies and wavefunctions of the charged and neutral excitations above the exact ground states (at rational filling per unit cell) of pr…
Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
Biao Lian, Zhi-Da Song, Nicolas Regnault +3
We derive the exact insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and s…
Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
B. Andrei Bernevig, Zhi-Da Song, Nicolas Regnault +1
We derive the explicit Hamiltonian of twisted bilayer graphene (TBG) with Coulomb interaction projected into the flat bands, and study the symmetries of the Hamiltonian. First, we…
Twisted bilayer graphene. II. Stable symmetry anomaly
Zhi-Da Song, Biao Lian, Nicolas Regnault +1
We show that the entire continuous model of twisted bilayer graphene (TBG) (and not just the two active bands) with particle-hole symmetry is anomalous and hence incompatible with…
Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a 2-Band model
B. Andrei Bernevig, Zhi-Da Song, Nicolas Regnault +1
We investigate the Twisted Bilayer Graphene (TBG) model to obtain an analytic understanding of its energetics and wavefunctions needed for many-body calculations. We provide an app…
Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
Da-Shuai Ma, Yuanfeng Xu, Christie S. Chiu +4
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 transpor…
Fragile topology and flat-band superconductivity in the strong-coupling regime
Valerio Peri, Zhida Song, B. Andrei Bernevig +1
In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of the superfluid weight , does not draw from the curvature o…
Symmetry broken Chern insulators and magic series of Rashba-like Landau level crossings in magic angle bilayer graphene
Ipsita Das, Xiaobo Lu, Jonah Herzog-Arbeitman +5
Flat-bands in magic angle twisted bilayer graphene (MATBG) have recently emerged as a rich platform to explore strong correlations, superconductivity and mag-netism. However, the p…
Discovery of a quantum limit Chern magnet TbMn6Sn6
Jia-Xin Yin, Wenlong Ma, Tyler A. Cochran +23
The quantum level interplay between geometry, topology, and correlation is at the forefront of fundamental physics. Owing to the unusual lattice geometry and breaking of time-rever…
Hofstadter Topology: Non-crystalline Topological Materials at High Flux
Jonah Herzog-Arbeitman, Zhi-Da Song, Nicolas Regnault +1
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 Hofsta…
Universal Approach to Magnetic Second-Order Topological Insulator
Cong Chen, Zhida Song, Jian-Zhou Zhao +4
We propose a universal practical approach to realize magnetic second-order topological insulator (SOTI) materials, based on properly breaking the time reversal symmetry in conventi…
Gapless Criterion for Crystals from Effective Axion Field
Jiabin Yu, Zhi-Da Song, Chao-Xing Liu
Gapless criteria that can efficiently determine whether a crystal is gapless or not are particularly useful for identifying topological semimetals. In this work, we propose a suffi…
High-throughput calculations of magnetic topological materials
Yuanfeng Xu, Luis Elcoro, Zhida Song +6
The discoveries of intrinsically magnetic topological materials, including semimetals with a large anomalous Hall effect and axion insulators, have directed fundamental research in…
Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
Luis Elcoro, Zhida Song, B. Andrei Bernevig
The electronic properties in a solid depend on the specific form of the wave-functions that represent the electronic states in the Brillouin zone. Since the discovery of topologica…