Citation: Kells, Graham, Dganit Meidan, and P. W. Brouwer. "Near-zero-energy end states in topologically trivial spin-orbit coupled superconducting nanowires with a smooth confinement." Physical Review B—Condensed Matter and Materials Physics 86.10 (2012): 100503.
Web: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.100503
Tags: Physical, Majorana-fermions, Spin-chains
In this paper, the authors argue that within the regimes in which people are expecting to create Majorana zero modes there are mechanism whereby one can create near-zero-energy end states to a nanowire. These states might look like Majorana zero modes to many experimental probes, but they do not have the braiding statistics or fusion rules one would expect from Majorana zero modes, or really that one would need to make a quantum computer. By "regime in which people are expecting to create MZMs", I mean a one-dimensional semiconductor with a Rashba spinorbit coupling, subject to a magnetic field and proximity coupled to a standard s-wave spin-singlet superconductor.
These low energy states are called "Andreev states" or "Andreev modes". A lot of the controversy around Microsoft's topological quantum computing efforts come from the difficulty of distinguishing Majorana modes and Andreev modes. For instance, the numerical paper
> Prada, Elsa, Pablo San-Jose, and Ramón Aguado. "Transport spectroscopy of NS nanowire junctions with Majorana fermions." Physical Review B—Condensed Matter and Materials Physics 86.18 (2012): 180503.
simulates a semiconducting nanowire and seems to show convincing evidence of Majorana zero modes, but all of their data is also consistent with Andreev modes. This is very good to be aware of when reasoning about Majorana zero modes in experimental settings. Another good numerical reference:
> Reeg, Christopher, et al. "Zero-energy Andreev bound states from quantum dots in proximitized Rashba nanowires." Physical Review B 98.24 (2018): 245407.