Engineering topological phases in the Luttinger semimetal $\alpha$-Sn

TL;DR

This paper demonstrates how to induce and control various topological phases, including insulators and semimetals, in the Luttinger semimetal $ ext{α}$-Sn using external stimuli like strain, magnetic fields, and light.

Contribution

It reveals that multiple topological phases, including type-II Weyl and double-Weyl nodes, can be engineered in $ ext{α}$-Sn through external perturbations, expanding the potential for topological material applications.

Findings

Multiple topological phases can be induced in $ ext{α}$-Sn.

Type-II Weyl and double-Weyl nodes can be generated.

External stimuli effectively control topological states.

Abstract

$\alpha$-Sn is well known as a typical Luttinger semimetal with a quadratic band touching at the $\Gamma$ point. Based on the effective $k\cdot p$ analysis as well as first-principles calculations, we demonstrate that multiple topological phases with a rich diagram, including topological insulator, Dirac semimetal, and Weyl semimetal phases, can be induced and engineered in $\alpha$-Sn by external strains, magnetic fields, and circularly polarized light (CPL). Intriguingly, not only the conventional type-I Weyl nodes, but also type-II Weyl nodes and double-Weyl nodes can be generated directly from the quadratic semimetal by applying a magnetic field or CPL. Our results apply equally well to other Luttinger semimetals with similar crystal and electronic structures, and thus open an avenue for realizing and engineering multiple topological phases on a versatile platform.