Topological columnar nano-SQUID based on a 3D topological insulator

Abstract: Finding an ideal platform to generate non-Abelian Majorana zero-modes (MZMs) is a crucial first step for topological quantum computing. A 3D topological insulator (TI) is promising for this purpose due to the spin-momentum-locked surface state. Here we propose a novel yet simple TI platform that gives rise to a robust topological phase and can realize a well-defined fermion parity necessary for quantum computing. It consists of a bulk-insulating rectangular TI nanowire laterally sandwiched by two superconductors. In this structure, the top and bottom surfaces individually work as SNS line junctions, forming a nanometer-scale columnar SQUID in which the nanowire cross-section defines the threading flux $\Phi$ in axial magnetic fields. We demonstrate that a TI device of this structure indeed presents SQUID-type oscillations of the critical current $I_c$ as a function of $\Phi$ with period $\Phi_{0}^s=\frac{h}{2e}$. It can be tuned by a back gate to attain a full $I_c$ suppression and then a nearly-full recovery as a function of $\Phi$, an indication that the superconductivity is completely surface-dominated. Our theory shows that, when the two junctions are asymmetric, a robust topological phase hosting MZMs occurs periodically for $(n-\frac{1}{2})\Phi_{0}^s < \Phi < (n+\frac{1}{2})\Phi_{0}^s$ with odd-integer $n$.