Helical Liquids and Majorana Bound States in Quantum Wires

TLDR

Zero‑energy Majorana bound states arise when a helical quantum wire is proximitized by an s‑wave superconductor. The study examines the experimental signatures of helical liquids and Majorana bound states in quantum wires. The formation of Majorana states is driven by spatial variations of magnetic field, superconducting gap, or chemical potential along the wire. Spin‑orbit coupling and Zeeman field or interactions create a helical electron liquid with spin‑velocity correlation, enabling zero‑energy Majorana bound states that do not require vortices.

Abstract

We show that the combination of spin-orbit coupling with a Zeeman field or strong interactions may lead to the formation of a helical electron liquid in single-channel quantum wires, with spin and velocity perfectly correlated. We argue that zero-energy Majorana bound states are formed in various situations when such wires are situated in proximity to a conventional $s$-wave superconductor. This occurs when the external magnetic field, the superconducting gap, or, most simply, the chemical potential vary along the wire. These Majorana states do not require the presence of a vortex in the system. Experimental consequences of the helical liquid and the Majorana states are also discussed.