= Solution
With <ballistic conductance quantization>, as a gate opens the channel, \b[conductance plateaux at $G=N_b(2e^2/h)$] appear; successive transverse modes add one quantum, approximately $77.5\,\mu\mathrm S$ per spin-degenerate subband. Their appearance is the key low-temperature electrical signature.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2019/paper-2-conductance-steps.png]
{title=Ideal conductance plateaux sharpen as thermal and disorder broadening become small compared with subband spacing}
{source=paper-2-conductance-steps.py}
Require transverse confinement with separated subbands, $k_BT$ and measurement-bias <energy> well below the subband spacing, a <mean free path> exceeding the channel length, and smooth low-reflection coupling to reservoirs. Correct for appreciable external series resistance. Phase coherence is needed for additional interference oscillations, but perfect phase coherence across an entire macroscopic circuit is not a separate requirement for the basic mode-counting result. A field that resolves spin splitting can produce $e^2/h$ increments.<Quantized conductance of point contacts by B. J. van Wees and others>[Gate-controlled ballistic GaAs-AlGaAs point contacts and conductance steps]{ref}
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