Abstract
Hybrid superconductor-semiconductor devices are currently one of the most promising platforms for realizing Majorana zero modes. Their topological properties are controlled by the band alignment of the two materials, as well as the electrostatic environment, which are currently not well understood. Here, we pursue to fill in this gap and address the role of band bending and superconductor-semiconductor hybridization in such devices by analyzing a gated single Al-InAs interface using a self-consistent Schrodinger-Poisson approach. Our numerical analysis shows that the band bending leads to an interface quantum well, which localizes the charge in the system near the superconductor-semiconductor interface. We investigate the hybrid band structure and analyze its response to varying the gate voltage and thickness of the Al layer. This is done by studying the hybridization degrees of the individual subbands, which determine the induced pairing and effective $g$-factors. The numerical results are backed by approximate analytical expressions which further clarify key aspects of the band structure. We find that one can obtain states with strong superconductor-semiconductor hybridization at the Fermi energy, but this requires a fine balance of parameters, with the most important constraint being on the width of the Al layer. In fact, in the regime of interest, we find an almost periodic dependence of the hybridization degree on the Al width, with a period roughly equal to the thickness of an Al monolayer. This implies that disorder and shape irregularities, present in realistic devices, may play an important role for averaging out this sensitivity and, thus, may be necessary for stabilizing the topological phase.
Highlights
Metal-semiconductor interfaces is a well-established field in the context of semiconducting electronics for implementing either Schottky diodes or Ohmic contacts, cf. Refs. [1,2,3]
We must restrict ourselves to back-gate voltages where the valence band edge of the semiconductor stays below the Fermi level of the metal, otherwise the band bending would lead to the formation of an unwanted hole pocket near the semiconductor dielectric interface
The strongest deviation for the latter appears at the metal-semiconductor interface, where the Thomas-Fermi result approaches the value predicted by Eq (2), while the value obtained using the Schrödinger method rises steeply due to the hybridization with the Al layer
Summary
Metal-semiconductor interfaces is a well-established field in the context of semiconducting electronics for implementing either Schottky diodes or Ohmic contacts, cf. Refs. [1,2,3]. It has been theoretically predicted that the induced superconducting pairing combined with spin-orbit coupling (SOC) and an applied magnetic field can drive the system into the topological superconducting (p-wave) [4,5,6,7,8] state This topologically nontrivial state supports charge-neutral zeroenergy end states which obey non-Abelian exchange statistics. The sensitivity to the Al width found here implies that a fine balance of parameter values may be required to obtain Majorana zero modes This sensitivity appears even for Al thicknesses much larger than the ones routinely employed in experiments, e.g., ∼10 nm. The dependence of the hybridization degree on the Al width, for the bands with mixed character, exhibits an alternating pattern ranging from high to low values The period of this pattern is approximately equal to the thickness of a single atomic Al layer. We expect that the combination of the above disorder sources could average out the periodically varying degree of hybridization
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