Quantum Transport: Atom to Transistor - Questions & Answers
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Lecture 4: Charging/Coulomb Blockade, slide 6
Q: Why is the broadening in G vs Vg plot equal to "gamma + kT + 2*Uo ". My question is about the 2*Uo part. With your reasoning that the electronic level cannot raise its own energy by coulombic means it should end up being just Uo.
A: This is a somewhat subtle point - slide 6 refers to the limit when the broadening is large (far from the Coulomb blockade limit) - in this limit since gamma is large it is probably hard to tell experimentally whether the remainder is U0 or 2*U0 - so I am not sure if the answer is known experimentally.
Conceptually I am inclined to vote for 2*U0 for the following reason: A large broadening means that one could view the entire broadened level, not as two levels, but as a collection of 2N closely spaced levels with only (1/N) of each wavefunction residing on the dot (N is a very large number, say a thousand or a million). Filling up the entire broadened level adds 2N electrons to the entire system (dot + contact), but only two to the dot.
You are arguing that since there are only two electrons on the dot, each should feel the charging due to 2-1 = 1 electron. I would argue that we are adding 2N electrons to the system and each electron should feel the charging due to (1/N) of (2*N - 1) electrons which is = 2 - (1/N) ~ 2.
As I said, this is somewhat subtle, hard to convey by email...
Researchers should cite this work as follows:
Supriyo Datta (2005), "Quantum Transport: Atom to Transistor - Questions & Answers," https://nanohub.org/resources/97.