Review experiments designed in order to observe discrete energy levels in metallic nanoparticles and

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Review experiments designed in order to observe
discrete energy levels in metallic nanoparticles
and other systems
Electrons confined to a small volume, inside a
metallic nanoparticle for example, are expected
to show discreteness of the energy spectrum.
The phenomenon can be understood at a simple
level by solving the usual particle-in-a-box
problem and then assuming that such
single-particle electronic levels are filled
with electrons up to the Fermi level. The
search for experimental demonstration of such
discrete energy levels continues for more than a
decade now. Today we review some of the most
significant experiments in this direction.
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Ralph-Black-Tinkham experiments
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Ralph-Black-Tinkham experiments
-apply voltage V across the junction -measure
current (I) with an ampere-meter (A) -plot I(V)
curves -measure differential conductance dI/dV
versus voltage
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Low-stress SiN Mebranes Fabriaction
Etching process not finished
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Previous experiments Fabrication of bowl-shaped
holes, 3-10 nm in diameter
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Fabrication of RBT devices
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RBT experiments4.2K measurement Applying
Orthodox Theory of SET
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RBT experiments4.2K measurement
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RBT experiments (T0.3K)
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RBT experiments
Illustration of transport through the metal
particle at various values of the sourcedrain
voltage V . Filled singleparticle levels are
indicated by full circles empty ones by open
circles. U is the charging energy, and dE is the
singleparticle mean level spacing. (a) The
system at small voltage bias within the Coulomb
blockade regime (b) V corresponding to the first
resonance. The thin dashed lines indicate the
energy of a level after an electron has tunneled
into the dot
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RBT experiments another illustration of the
resonant tunneling through individual energy
levels
After the first resonance
Just before the first resonance
Empty states
VA
U
U
A
B
VA
A
dE
B
Filled states
CAgtgtCB
U e2/2C 6meV Coulomb charging energy
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RBT experiments
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Fermis golden rule rate of quantum transitions
is proportional to the density of states
BCS density of states
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N(E)-density of states here f(E) is the
Fermi-Dirac distribution
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RBT experiments-Zeeman splitting
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RBT experiments-one more illustration of the
resonant tunneling through individual energy
levels
After the first resonance
Just before the first resonance
Empty states
VA
U
U
A
B
VA
A
dEZ
B
Filled states
CAgtgtCB
U e2/2C 4meV Coulomb charging energy
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RBT experiments-one more illustration of the
resonant tunneling through individual energy
levels
After the first resonance
Just before the first resonance
Empty states
VA
U
U
A
B
VA
A
dEZ
B
Filled states
CAgtgtCB
U e2/2C 4meV Coulomb charging energy