Electron-Waves in Strongly-Disordered
Nano-metals
In quantum physics, electrons have wave-like
properties. For example, they can interfere with themselves.
In very small metals and semiconductors, these electron
waves can be measured if the sample size is smaller than the coherence length. The coherence length
is typically 1 micron at very low temperatures (T << 1
Kelvin = -272.15 Celsius). If the temperature increases, the coherence length
decreases, and at room temperatures it is only about few nanometers. So, to
study electron-interference in micron-scale metals, we need to have special
refrigerators, like dilution refrigerators.
Studies of electron interference in weakly-disordered metals are
important in basic and applied sciences, because they open new avenues to
investigate magnetoresistance, decoherence, and spin-flip scattering.
Example: Aharonov-Bohm effect in a metallic ring
The figure above displays a Copper ring, one micron
in diameter, made here in our laboratory at the School of Physics. The
resistance of the ring is measured between points A and B, using the four probe
measurement technique. We study how the resistance of the ring depends on the
magnetic field applied perpendicular to the ring.
At high temperatures, the resistance is found to be
independent of the magnetic field, which is usual. However, at very low
temperatures (<<1 K), the resistance becomes a periodic function with the magnetic field. This behavior can be
explained by electron interference.
An electron in the device can travel from point A to
point B along two paths, 1 and 2. At low temperatures, when the coherence
length is larger than the ring diameter, the resistance depends on the
interference between electron-waves traveling along the two paths. If the phase
difference between the paths is 0, 2p, 4p,…, then the interference will be
constructive and the resistance will be reduced. If the phase difference is p, 3p, 5p, …, the interference will be
destructive and the resistance will be enhanced.
Now, let us apply a magnetic field perpendicular to
the ring and investigate the interference. The magnetic field creates an extra
phase difference between paths 1 and 2, equal to 2pF/F0, where F is the magnetic flux through the ring and F0=h/e is the flux quantum. So, if the applied field varies, the resistance
will vary as a periodic function. This effect is known as the Aharonov-Bohm effect.