Black Hole on a Chip: Proposal for a Physical Realization of the Sachdev-Ye-Kitaev model in a Solid-State System

• Published in: Physical review. X 2017-07, Vol.7 (3), p.031006, Article 031006
• Main Authors: Pikulin, D. I., Franz, M.
• Format: Article
• Language: English
• Subjects: Black holes; Chaos theory; Chemical potential; Correlators; Dilatons; Fermions; Holography; Information theory; Magnetic flux; Mathematical models; Niobium; Physical properties; Physicists; Quantum mechanics; Quantum physics; Relativity; Solid state; Theory of relativity; Topological insulators
• ISSN: 2160-3308; 2160-3308
• DOI: 10.1103/PhysRevX.7.031006

A system of Majorana zero modes with random infinite-range interactions—the Sachdev-Ye-Kitaev (SYK) model—is thought to exhibit an intriguing relation to the horizons of extremal black holes in two-dimensional anti–de Sitter space. This connection provides a rare example of holographic duality between a solvable quantum-mechanical model and dilaton gravity. Here, we propose a physical realization of the SYK model in a solid-state system. The proposed setup employs the Fu-Kane superconductor realized at the interface between a three-dimensional topological insulator and an ordinary superconductor. The requisite N Majorana zero modes are bound to a nanoscale hole fabricated in the superconductor that is threaded by N quanta of magnetic flux. We show that when the system is tuned to the surface neutrality point (i.e., chemical potential coincident with the Dirac point of the topological insulator surface state) and the hole has sufficiently irregular shape, the Majorana zero modes are described by the SYK Hamiltonian. We perform extensive numerical simulations to demonstrate that the system indeed exhibits physical properties expected of the SYK model, including thermodynamic quantities and two-point as well as four-point correlators, and discuss ways in which these can be observed experimentally.