Three-Dimensional Topological Twistronics

TL;DR

This paper develops a theoretical framework for 3D twistronics, revealing new topological phenomena in layered materials with twist angles, including Weyl nodes, topological phase transitions, and vortex-like gauge fields.

Contribution

It introduces a generalized Bloch band theory for 3D twisted layered systems, enabling the study of novel topological effects and phase transitions in 3D twistronics.

Findings

Weyl nodes emerge in twisted graphite due to inversion symmetry breaking.

Transitions between type-I and type-II Weyl fermions are tunable by the twist angle.

Vortex-antivortex lattice configurations of gauge fields induce line modes in twisted Weyl semimetals.

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 moir\'e 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 $\boldsymbol{\mathcal{A}}$ that has a vortex-antivortex lattice configuration. Line modes bound to the vortex cores of the $\boldsymbol{\mathcal{A}}$ field give rise to 3D Weyl physics in the moir\'e scale. We also discuss possible experimental realizations of 3D twistronics.