片上黑洞：固态系统中物理实现SYK模型的建议
Black hole on a chip: proposal for a physical realization of the SYK model in a solid-state system
摘要：
具有随机无限程相互作用的Majorana零模系统--Sachdev-Ye-Kitaev（SYK）模型--被认为与二维反de Sitter（AdS $_2$）空间中极端黑洞的视界有着有趣的关系。这种联系为可解量子力学模型和量子引力之间的全息对偶提供了一个罕见的例子。在这里，我们提出了一个物理实现的SYK模型在固态系统。所提出的装置采用Fu-Kane超导体实现在三维拓扑绝缘体（TI）和普通超导体之间的界面。必要的$N$马约拉纳零模被束缚在超导体中制造的纳米级孔中，该纳米级孔由磁通量的$N$量子穿过。我们表明，当系统被调谐到表面中性点（即化学势与狄拉克点的TI表面状态）和孔具有足够的不规则形状，马约拉纳零模式所描述的SYK哈密顿量。我们进行了广泛的数值模拟，以证明该系统确实表现出预期的SYK模型的物理特性，包括热力学量和两点，以及四点蒸发器，并讨论了这些可以通过实验观察到的方式。
英文摘要：
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.
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