Abstract
There have recently been several experiments studying induced superconductivity in semiconducting two-dimensional electron gases that are strongly coupled to thin superconducting layers, as well as probing possible topological phases supporting Majorana bound states in such setups. We show that a large band shift is induced in the semiconductor by the superconductor in this geometry, thus making it challenging to realize a topological phase. Additionally, we show that while increasing the thickness of the superconducting layer reduces the magnitude of the band shift, it also leads to a more significant renormalization of the semiconducting material parameters and does not reduce the challenge of tuning into a topological phase.
Highlights
Topological superconductors host zero-energy Majorana bound states at their edges that are highly sought for applications in topological quantum computing [1,2,3]
The two proposals to realize topological superconductivity that have received the most attention to date involve engineering Majorana bound states in either low-dimensional semiconducting systems [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23] or in ferromagnetic atomic chains [24,25,26,27,28,29,30,31,32]
We show that the large band shift that plagues the 1D case persists in two dimensions
Summary
Topological superconductors host zero-energy Majorana bound states at their edges that are highly sought for applications in topological quantum computing [1,2,3]. This large band shift makes it very challenging to realize a topological phase when utilizing thin superconducting layers. Analyzing the self-energy, we find that the induced gap in the presence of only Rashba spin–orbit coupling can be made comparable to the bulk gap of the superconductor only if the tunneling energy scale exceeds the large level spacing of the superconducting layer.
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