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

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