# Strain engineered higher order topological phases for spin-3/2 Luttinger fermions

## TL;DR

This paper demonstrates how uniaxial strain can induce higher-order topological phases in spin-3/2 fermion systems, leading to hinge and edge modes, with potential applications in materials like HgTe and half-Heusler compounds.

## Contribution

It introduces a method to engineer higher-order topological phases in spin-3/2 fermions via strain, revealing new topological states and boundary modes in specific materials.

## Key findings

- Strain induces HOT Dirac semimetal or insulator phases.
- Insulators exhibit mixed topology with hinge and edge modes.
- Applicable to materials like HgTe, gray-Sn, and half-Heusler compounds.

## Abstract

Recently, the notion of topological phases of matter has been extended to higher-order incarnations, supporting gapless modes on even lower dimensional boundaries, such as corners and hinges. We here identify a collection of cubic spin-3/2 fermions with biquadratic touching of Kramers degenerate valence and conduction bands as a platform to strain-engineer higher-order topological (HOT) phases: external uniaxial strain gives birth to a HOT Dirac semimetal or an insulator, depending on its sign, featuring topological \emph{hinge} modes in the strain direction. The insulator in fact exhibits \emph{mixed} topology, and in addition supports edge modes on orthogonal planes. These outcomes are germane when the external strain is applied along one of the $C_{4v}$ or coordinate axes, as well as $C_{3v}$ or body-diagonal, directions. Our findings place HgTe, gray-Sn, 227 pyrochlore iridates and half-Heusler compounds at the frontier of strain-engineered electronic HOT phases.