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

## TL;DR

This paper proposes a solid-state experimental setup using Majorana zero modes in a topological insulator-superconductor interface to realize the SYK model, connecting quantum chaos, holography, and black hole physics.

## Contribution

It introduces a feasible physical realization of the SYK model in a solid-state system using Majorana modes in a topological insulator-superconductor heterostructure.

## Key findings

- Numerical simulations confirm SYK-like thermodynamic behavior.
- The setup exhibits characteristic two-point and four-point correlators.
- Potential experimental methods for observing SYK physics are discussed.

## Abstract

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 (AdS$_2$) 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 (TI) 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 TI 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.