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System of Majorana zero modes with random infinite range interactions -- theSachdev-Ye-Kitaev (SYK) model -- is thought to exhibit an intriguing relationto the horizons of extremal black holes in two-dimensional anti-de Sitter(AdS$_2$) space. This connection provides a rare example of holographic dualitybetween a solvable quantum-mechanical model and dilaton gravity. Here wepropose a physical realization of the SYK model in a solid state system. Theproposed setup employs the Fu-Kane superconductor realized at the interfacebetween a three dimensional topological insulator (TI) and an ordinarysuperconductor. The requisite $N$ Majorana zero modes are bound to a nanoscalehole fabricated in the superconductor that is threaded by $N$ quanta ofmagnetic flux. We show that when the system is tuned to the surface neutralitypoint (i.e. chemical potential coincident with the Dirac point of the TIsurface state) and the hole has sufficiently irregular shape, the Majorana zeromodes are described by the SYK Hamiltonian. We perform extensive numericalsimulations to demonstrate that the system indeed exhibits physical propertiesexpected of the SYK model, including thermodynamic quantities and two-point aswell as four-point correlators, and discuss ways in which these can be observedexperimentally.

Black hole on a chip: proposal for a physical realization of the SYK model in a solid-state system