Page 100 - Principles and Applications of NanoMEMS Physics

88 Chapter 3

3.1.3 Quantum Interference
While the RTD I-V characteristics are the result of constructive and
destructive interference between the barriers, as a one-dimensional device
these are really function of the degree of resonance with the energy levels in
the well. When transport occurs in two dimensions, we may have
constructive and destructive interference as a result of waves traveling
thorough different paths that converge at one point.

3.1.3.1 Aharonov-Bohm Effect

The quintessential example of this type of interference, which also
exposes the wave nature of electrons, is the Aharonov-Bohm (AB) effect
[125], Figure 3-7. The essence of the AB effect, see Fig. 3-7, is that an
electron beam, with wavefunction ψ , split at point A into two waves, ψ 1
in
and ψ , which subsequently follow paths ABF and ACF, around a solenoid
2
establishing a magnetic flux φ strictly in its interior, will gain respective
0
phases S and S so that at F the wavefunction is,
1
2
ψ = ψ e − iS 1 = + ψ e − iS 2 = , (25)
F 1 2
or, in other words, there is a phase difference (S − S ) = between them. In
1 2
particular, the phase shift is given by,
B B

Interferen
Electro Solenoid id Interference ce
Electron n
Soleno
Region n
Beam m
Bea A A F F Regio
Shadow w
Shado
R adius, R
R adius, R
Metal l
Meta
Foil il
Fo
C C
(a)
t ~e
t ~e ik L L
ik
1 1
1 1
φ φ φ
O
In In Out ut
0 0 0
ik
t ~e ik L L
t ~e
2 2
2 2
(b)
Figure 3-7. (a) Aharonov-Bohm-effect electron wave interference setup. (After [125].) (b)
Sketch of metallic ring implementation.