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

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 betwe...

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Bibliographic Details
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
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Summary: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.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.7.031006