Evolution of the surface states of the Luttinger semimetal under compressive strain and broken inversion symmetry*

Luttinger semimetal, the quadratic-node semimetal for $j=3/2$ electrons under full cubic symmetry, is the parent highest-symmetry minimal model for a variety of topological and/or strongly correlated materials, such as HgTe, $\alpha$-Sn, and iridate compounds. Recently, Luttinger semimetal has been demonstrated [1] to exhibit surface states of topological origin that can be attributed to approximate chiral symmetry. In the present work, we theoretically study the effect of the symmetry-lowering perturbations on these surface states within an analytical model. Under compressive strain lowering rotational symmetry, Luttinger semimetal becomes a Dirac semimetal with a pair of double-degenerate linear nodes. Breaking further inversion symmetry, the system turns into a Weyl semimetal, with each Dirac node split into four Weyl nodes. We analyze the corresponding evolution of the surface states,and its relation to the surface states of the full Kane model.
[1] M. Kharitonov, J.-B. Mayer, and E. M. Hankiewicz, Phys. Rev. Lett., 119, 266402 (2017)