The Sachdev–Ye–Kitaev model is a quantum mechanical model describing a collection of randomly interacting Majorana fermions. Using holographic duality arguments, this model has been shown to have connections and similarities to black holes and quantum chaos, and so may provide a way of exploring the quantum nature of black holes. The quest is therefore on to create such a model experimentally. Dmitry Pikulin and Marcel Franz propose a physical realization of the Sachdev–Ye–Kitaev model in a solid-state system.
The surfaces of three-dimensional topological insulators host quasiparticle excitations that behave like Dirac fermions. If the topological insulator has a thin layer of a conventional superconductor on top of it that contains an irregularly shaped hole with magnetic flux flowing through, proximity effects lead to the formation of bound states that are not Dirac, but Majorana-like. What Pikulin and Franz show is that, with the right ingredients, which all look within experimental reach, these Majorana zero modes can be described by the Sachdev–Ye–Kitaev Hamiltonian, meaning that they would obey the same equations as those describing the horizon of a black hole.
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Fleet, L. The new black. Nature Phys 13, 722 (2017). https://doi.org/10.1038/nphys4236