How small is mesoscopic?
The same small metal ring can show a different resistance trace when it is cooled and a magnetic field is swept. Its diameter stays fixed. What can change is the distance over which electrons retain phase information.
Compare three lengths
Take the spacing between two voltage probes as the device length L. The elastic mean free path ℓ describes how far an electron typically travels before scattering changes its direction. The phase-coherence length Lφ describes the distance over which waves following different paths retain the relative phase needed for observable interference.
To assess interference, compare the relevant device dimension, such as the length of a ring arm, with Lφ. In a diffusive conductor, Lφ is the characteristic spatial extent of diffusion during the coherence time. The total distance travelled through successive scattering events can be much longer. Material, temperature and disorder all matter.
Scattering can coexist with interference
When L is much shorter than ℓ, an electron can traverse the device with little scattering: transport is ballistic. When ℓ is much shorter than L, repeated changes of direction lead to diffusive transport. Elastic scattering from static disorder can redirect an electron while preserving coherence.
A sample can satisfy both ℓ ≪ L and L ≲ Lφ. Electrons then scatter many times, yet waves travelling different paths may still interfere. Cooling often weakens some sources of dephasing and makes the interference easier to see.
Measurement schematic and relation
For single-electron h/e oscillations in a uniform perpendicular field, A is the effective enclosed area, h is Planck’s constant and e is the elementary charge. An illustrative area of 1.0 µm² gives a field period of about 4.14 mT; this is a worked example, not a value measured in the cited paper.
Read an experiment: flux through a metal ring
Webb and colleagues observed magnetoresistance oscillations in submicrometre gold rings. Electron waves can travel along the two arms and meet at the exit; magnetic flux through the ring changes their relative phase. To test the single-electron, one-winding interpretation, estimate the effective ring area from a micrograph and compare the predicted and measured periods. Oscillations alone do not establish the mechanism.
Open the original experiment ↗