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The [111]-oriented InAs/GaSb and GaSb/InAs core-shell nanowires have beenstudied by the $8\times 8$ Luttinger-Kohn $\vec{k}\cdot\vec{p}$ Hamiltonian tosearch for non-vanishing fundamental gaps between inverted electron and holebands. We focus on the variations of the topologically nontrivial fundamentalgap, the hybridization gap, and the effective gap with the core radius andshell thickness of the nanowires. The evolutions of all the energy gaps withthe structural parameters are shown to be dominantly governed by quantum sizeeffects. With a fixed core radius, a topologically nontrivial fundamental gapexists only at intermediate shell thicknesses. The maximum gap is $\sim 4.4$meV for GaSb/InAs and $\sim 3.5$ meV for InAs/GaSb core-shell nanowires, andfor the GaSb/InAs core-shell nanowires the gap persists over a wider range ofgeometrical parameters. The intrinsic reason for these differences between thetwo types of nanowires is that in the shell the electron-like states of InAs ismore delocalized than the hole-like state of GaSb, while in the core thehole-like state of GaSb is more delocalized than the electron-like state ofInAs, and both features favor stronger electron-hole hybridization. Sincesimilar features of the electron- and hole-like states have been found innanowires of other materials, it could serve as a common rule to put thehole-like state in the core while the electron-like state in the shell of acore-shell nanowire to achieve better topological properties.

Topological energy gaps in the [111]-oriented InAs/GaSb and GaSb/InAs core-shell nanowires