Three-Dimensional Topological Twistronics

Abstract

We introduce a theoretical framework for the new concept of three-dimensional (3D) twistronics by developing a generalized Bloch band theory for 3D layered systems with a constant twist angle $\theta$ between successive layers. Our theory employs a nonsymmorphic symmetry that enables a precise definition of an effective out-of-plane crystal momentum, and also captures the in-plane moiré pattern formed between neighboring twisted layers. To demonstrate the novel topological physics that can be achieved through 3D twistronics, we present two examples. In the first example of chiral twisted graphite, Weyl nodes arise because of inversion-symmetry breaking, with $\theta$-tuned transitions between type-I and type-II Weyl fermions, as well as magic angles at which the in-plane velocity vanishes. In the second example of twisted Weyl semimetal, the twist in the lattice structure induces a chiral gauge field $\mathcal{A}$ that has a vortex-antivortex lattice configuration. Line modes bound to the vortex cores of the $\mathcal{A}$ field give rise to 3D Weyl physics in the moiré scale. We also discuss possible experimental realizations of 3D twistronics.

5+5 pages, 3+1 figures

References in corpus (17)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Tuning superconductivity in twisted bilayer graphene
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Twistronics: Manipulating the Electronic Properties of Two-dimensional Layered Structures through their Twist Angle
• Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
• All "Magic Angles" Are "Stable" Topological
• Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands
• Magic Angle Hierarchy in Twisted Graphene Multilayers
• The pseudo-Landau-level representation of twisted bilayer graphene: band topology and the implications on the correlated insulating phase
• Chiral anomaly from strain-induced gauge fields in Dirac and Weyl semimetals
• Flat bands and perfect metal in trilayer moiré graphene
• Twists and The Electronic Structure of Graphitic Materials
• van der Waals metamaterials

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• Wafer-scale Programmed Assembly of One-atom-thick Crystals
• Why the first magic-angle is different from others in twisted graphene bilayers: interlayer currents, kinetic and confinement energy and wavefunction localization
• Moire Band Structures of the Double twisted Few Layer Graphene
• Twisted multilayer nodal superconductors
• Extended magic phase in twisted graphene multilayers
• Engineering Three Dimensional Moiré Flat Bands
• Doubled Moiré Flat Bands in Double-twisted Few Layer Graphite
• Three-dimensional Moiré Crystal
• Stable Higher-Order Topological Dirac Semimetals with ${\mathbb{Z}}_2$ Monopole Charge in Alternating-twisted Multilayer Graphenes and beyond
• Growth and Properties of Dislocated Two-dimensional Layered Materials
• Resonant interaction in chiral, Eshelby-twisted van der Waals atomic layers
• Spinless topological chirality from Umklapp scattering in twisted 3D structures
• Semimetallic and semiconducting graphene-hBN multilayers with parallel or reverse stacking
• Squeezing Quantum States in Three-Dimensional Twisted Crystals