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

TL;DR

This work proposes a tangible solid-state realization of the Sachdev-Ye-Kitaev (SYK) model using Majorana zero modes at a Fu-Kane TI/SC interface, where a nanoscale irregular hole threaded by N flux quanta binds N Majorana modes. By tuning the surface to the Dirac neutrality point the two-fermion couplings vanish, leaving random four-fermion interactions among all Majorana modes, yielding an SYK-like Hamiltonian with couplings $J_{ijkl}$. The authors derive the effective low-energy theory, compute the expected coupling statistics, and perform extensive numerical simulations on both the noninteracting lattice model and the interacting many-body problem, demonstrating thermodynamic quantities, Green’s functions, level statistics, and scrambling behavior consistent with SYK physics. They discuss realistic material parameters, device geometries, and experimental detection methods (notably tunneling spectroscopy and flux counting) to observe the SYK phenomenology and its connection to holography. The work thus bridges mesoscopic TI/SC physics, quantum chaos, and AdS/CFT-inspired ideas, offering a concrete path to explore non-Fermi-liquid and fast-scrambling dynamics in a laboratory setting.

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.

Figures (9)

• Figure 1: The proposed setup for a solid-state realization of the SYK model.
• Figure 2: a) Spectral functions, measurable in a tunneling experiment, in the conformal (strongly interacting) limit (red) and free-fermion limit (blue). b) Numerically evaluated large-$N$ Matsubara Green's functions for $J=1.0$, $T=0.001$ and different values of $K$. Red dashed line shows the conformal limit behavior Eq. (\ref{['prop7']}) while the thick green and brown lines correspond to free-fermion result (\ref{['prop4']}) with $K=0.1$ and $0.5$, respectively.
• Figure 3: Band structure (\ref{['latt2']}) of the lattice model Eq. (\ref{['latt1']}) for $\lambda=1$ and $m=0$ (blue dashed) and $m=0.5$ (red solid line). $X$ and $M$ denote the $(0,\pi)$ and $(\pi,\pi)$ points of the Brillouin zone, respectively.
• Figure 4: Numerical simulations of the BdG Hamiltonian Eq. (\ref{['latt5']}). a) Stadium-shaped hole geometry employed in the simulations. $R$ parametrizes the hole size whereas $R_B$ denotes the radius inside which the magnetic field is nonzero. b) Energy levels $E_n$ of the BdG Hamiltonian (\ref{['latt5']}) calculated for $N=0$ and $N=24$. Energies have been sorted in ascending order and plotted as a function of their integer index $n$. The shaded band represents the SC gap region. c-f) Density plots of the typical zero mode wavefunction amplitudes for $N=24$. The dashed circle in panel (c) has radius $R_B$. The following parameters have been used to obtain these results: $\lambda=1$, $m=0.5$, $\Delta_0=0.3$, $\mu=w_\mu=0$, $w_\lambda=w_\Delta=0.1$, $L=42$, $R=10$ and $R_B=15$.
• Figure 5: Thermodynamic properties of the many-body Hamiltonian (\ref{['heff2']}), a) thermal entropy per particle and b) heat capacity per particle. Dashed lines show the expected behavior for the SYK model with random independent couplings, solid lines show results for the couplings obtained from the giant vortex system. In all panels the same parameters have been used as in Fig. \ref{['fig4']} with $V_0$ adjusted so that $J=1$.