Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry

TL;DR

This paper introduces a new class of three-dimensional intertwined Weyl phases that combine unconventional Weyl semimetallic and higher-order topological phases, revealing unique bulk distributions and surface phenomena driven by crystalline symmetry.

Contribution

It develops a theory to create intertwined topological phases by combining gapped and gapless phases protected by the same symmetry, enabling the design of novel Weyl phases with distinctive properties.

Findings

Intertwined Weyl phases feature unconventional Weyl semimetallic and higher-order topological characteristics.

Surface Fermi-arc topology exhibits periodic changes with surface orientation.

Guidelines for material search and cold-atom emulation of these phases are provided.

Abstract

We discover three-dimensional intertwined Weyl phases, by developing a theory to create topological phases. The theory is based on intertwining existing topological gapped and gapless phases protected by the same crystalline symmetry. The intertwined Weyl phases feature both unconventional Weyl semimetallic (monopole charge>1) and higher-order topological phases, and more importantly, their exotic intertwining. While the two phases are independently stabilized by the same symmetry, their intertwining results in the specific distribution of them in the bulk. The construction mechanism allows us to combine different kinds of unconventional Weyl semimetallic and higher-order topological phases to generate distinct phases. Remarkably, on 2D surfaces, the intertwining causes the Fermi-arc topology to change in a periodic pattern against surface orientation. This feature provides a characteristic and feasible signature to probe the intertwining Weyl phases. Moreover, we provide guidelines for searching candidate materials, and elaborate on emulating the intertwined double-Weyl phase in cold-atom experiments.