Electrons crossing a device without bumping into anything on the way. Usually electrons in a conductor scatter off impurities, vibrations and each other many times, and resistance grows with length. If the device is shorter than the distance an electron travels between collisions – its mean free path – electrons fly straight through, like balls rolling across an empty hall. In graphene sealed in boron nitride that distance reaches micrometres even at room temperature, and the shortest are approaching this limit.
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Few-layer InSe reached room-temperature mobilities around 1,000 cm2/(V·s) and showed the quantum Hall effect – among the best of any 2D semiconductor – and has since been used for ballistic transistors.
Hamiltonians taken from semilocal DFT inherit gap errors that shift barriers, and ballistic simulations ignore the phonon scattering that sets room-temperature performance.
In an ordinary conductor electrons scatter again and again and resistance grows with length. In a channel shorter than the mean free path they fly straight through. In clean graphene this shows as negative bend resistance: electrons sent round a corner overshoot it, and the voltage changes sign.
Diffusive and ballistic
In an ordinary conductor an electron is knocked off course every few tens of nanometres or less, by impurities, defects, lattice vibrations and other electrons. Its path is a random walk, the current flows by diffusion, and resistance grows in proportion to length – the regime in which and are the right quantities.
When a device is shorter than the mean free path, electrons cross it without scattering. Resistance then stops depending on length; what limits the current is how many electron modes fit through the narrowest point and how well the contacts inject them. Each perfectly transmitted mode contributes a fixed conductance, 2e2/h – about 77 microsiemens for -degenerate electrons – so even a perfect ballistic channel has a resistance, one reason contacts matter so much in short devices.
Seen in clean graphene
Graphene sealed between layers of hexagonal boron nitride is clean enough for electrons to travel micrometres without scattering, even at room temperature. In a cross-shaped device this shows as a negative bend resistance: current sent round a corner overshoots into the opposite arm instead of turning, so the measured voltage changes sign (Mayorov and colleagues, 2011).
In a narrow ballistic constriction the number of modes that fit through becomes countable, and the conductance should rise in steps as a gate adds modes. Graphene constrictions showed evenly spaced, reproducible kinks rather than clean steps: scattering at their rough edges blurs the quantisation (Terrés and colleagues, 2016).
Devices at the limit
Ballistic motion can be put to work. An asymmetric cross junction in graphene, with a room-temperature mobility around 200,000 cm2/(V·s), steers electrons by its shape alone and rectifies: it reached a of 23,000 mV per milliwatt, with noise low enough to compare with bolometers that need cryogenic cooling (Auton and colleagues, 2016).
In transistors, the shortest 2D channels approach the ballistic limit; InSe transistors with short gates reported in 2023 were described as ballistic. Calculations of the ballistic limit give an upper bound: they leave out the scattering that sets real room-temperature performance.
For specialists
Transport over distances shorter than the momentum-relaxation mean free path, where conductance is set by the transmitted modes rather than by scattering, G = (2e2/h) ΣTn for spin-degenerate modes (4e2/h per mode in graphene, with its degeneracy), so a resistance remains even without scattering. In hBN-encapsulated graphene, negative bend resistance shows micrometre-scale ballistic transport at room temperature; narrow constrictions show the size quantisation of modes, blurred by edge roughness. Ballistic geometries make rectifiers of high responsivity, while device simulations that assume ballistic transport give upper bounds that phonon scattering lowers.
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