Engineering long ballistic single mode electrostatically defined quantum wires for future detection of Majorana zero modes*

A key challenge to realising and detecting Majorana Zero Modes is the need to form low disorder, single mode 1D systems: If the quantum wire is too short the Majorana modes will annihilate each other. In transport measurements a short 1D wire length also leads to a high energy uncertainty, which masks the signature of the spin-gap (a prerequisite for Majorana Zero Modes). Split gate devices on high mobility 2D systems are a potential ultra-low disorder alternative to physically etched or self-assembled nanowires for probing Majorana Zero Modes. However it is non-trivial to create long single mode wires electrostatically as even in the absence of disorder the length of the single mode region is usually much shorter than the physical gate dimensions.

Here we introduce a new elliptical split-gate design simulated to allow longer electrostatic 1D channel lengths in low disorder 2D GaAs electron systems. We report low temperature transport measurements and source drain bias spectroscopy measurements from elliptical gate quantum point contacts with a range of different ellipticities to determine the actual 1D channel length, and compare with numerical finite-element calculations.