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A road to reality with topological superconductors

Nature Physics volume 12, pages 618–621 (2016)Cite this article

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Topological matter can host low-energy quasiparticles, which, in a superconductor, are Majorana fermions described by a real wavefunction. The absence of complex phases provides protection for quantum computations based on topological superconductivity.

Quantum mechanics is complex. The only way Erwin Schrödinger could get his equation iħdψ/dt = Hψ to work was to multiply the time derivative of the wavefunction ψ by the imaginary unit i. He complained about that in a 1926 letter to Lorentz (as quoted in ref. 1): “What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers — ψ is surely fundamentally a real function.” But the i was there to stay. Freeman Dyson called this apparently illogical step “one of the most profound jokes of nature”2: “Schrödinger put the square root of minus one into the equation, and suddenly it made sense. Suddenly it became a wave equation instead of a heat conduction equation ... and that square root of minus one means that nature works with complex numbers and not with real numbers.”

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Figure 1: Majorana metal in a computer simulation of a chiral p-wave superconductor.
Figure 2: Schematic of the thermal quantum Hall effect.

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Acknowledgements

Our collaboration is supported by an ERC Synergy grant and by the NWO/OCW Nanofront consortium.

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Authors and Affiliations

  1. Carlo Beenakker is at the Instituut-Lorentz of Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands,

    Carlo Beenakker

  2. Leo Kouwenhoven is at QuTech and the Kavli Institute of Nanoscience of Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands,

    Leo Kouwenhoven

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  1. Carlo Beenakker
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Correspondence to Carlo Beenakker or Leo Kouwenhoven.

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Beenakker, C., Kouwenhoven, L. A road to reality with topological superconductors. Nature Phys 12, 618–621 (2016). https://doi.org/10.1038/nphys3778

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