= Solution
One suitable platform is a monolayer \b[<molybdenum disulfide>] <semiconductor>. An electrostatic accumulation gate supplies conduction electrons whose motion is confined to the atomic sheet; source and drain contacts act as reservoirs. A clean insulating substrate and dielectric or encapsulation reduce disorder and prevent gate leakage. Two split gates deplete the adjacent sheet and leave a narrow conducting gap, thereby confining the in-plane transverse direction while retaining transport along the gap.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2017/paper-2-split-gate-device.png]
{title=Split gates narrow a gated two-dimensional semiconductor sheet between source and drain reservoirs}
{source=paper-2-split-gate-device.py}
Apply a small source-drain <voltage>, measure the current and determine linear-response conductance while tuning the split-gate <voltage> and carrier <density>. A <graphene> sheet is another two-dimensional carrier system, but its lack of an ordinary gap complicates purely electrostatic confinement; etched boundaries or a suitable gapped architecture may be needed. A two-dimensional material does not by itself guarantee ballistic transport or resolved subbands.<Split-gated point-contact in MoS2-hBN structures by Chithra H. Sharma and Madhu Thalakulam>[Electrostatic confinement in a two-dimensional <semiconductor> platform]{ref}
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