First Principles Assessment of CdTe as a Tunnel Barrier at the $\mathbf{\alpha}$-Sn/InSb Interface

Majorana zero modes, with prospective applications in topological quantum computing, are expected to arise in superconductor/semiconductor interfaces, such as $\beta$-Sn and InSb. However, proximity to the superconductor may also adversely affect the semiconductor's local properties. A tunnel barrier inserted at the interface could resolve this issue. We assess the wide band gap semiconductor, CdTe, as a candidate material to mediate the coupling at the lattice-matched interface between $\alpha$-Sn and InSb. To this end, we use density functional theory (DFT) with Hubbard U corrections, whose values are machine-learned via Bayesian optimization (BO) [npj Computational Materials 6, 180 (2020)]. The results of DFT+U(BO) are validated against angle resolved photoemission spectroscopy (ARPES) experiments for $\alpha$-Sn and CdTe. For CdTe, the z-unfolding method [Advanced Quantum Technologies, 5, 2100033 (2022)] is used to resolve the contributions of different $k_z$ values to the ARPES. We then study the band offsets and the penetration depth of metal-induced gap states (MIGS) in bilayer interfaces of InSb/$\alpha$-Sn, InSb/CdTe, and CdTe/$\alpha$-Sn, as well as in tri-layer interfaces of InSb/CdTe/$\alpha$-Sn with increasing thickness of CdTe. We find that 16 atomic layers (3.5 nm) of CdTe can serve as a tunnel barrier, effectively shielding the InSb from MIGS from the $\alpha$-Sn. This may guide the choice of dimensions of the CdTe barrier to mediate the coupling in semiconductor-superconductor devices in future Majorana zero modes experiments.