Abstract
In this chapter, we address the very basic problem of how the quantization of the charge as a multiple of the elementary electron charge.
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Notes
- 1.
The value given by the NIST (http://physics.nist.gov/cgi-bin/cuu/Value?e) for this constant is: \(e =- (1.602 176 6208 \pm 0.000 000 0098)\times {10}^{-19}C\).
- 2.
The metallic character of the island is of great importance as it will be explained below.
- 3.
We have verified numerically that \(\dfrac{1}{4T} \displaystyle \int _{-\infty }^\infty \mathrm {d}E \dfrac{1}{\cosh ^2(E/(2k_BT))} \dfrac{\Gamma _+^2(\tau _L,\tau _R,N_g)}{E^2 + \Gamma _+^2(\tau _L,\tau _R,N_g)} = \dfrac{\Gamma _+(\tau _L,\tau _R,N_g)}{2 \pi k_BT} \psi '\left( 1/2 + \dfrac{\Gamma _+(\tau _L,\tau _R,N_g)}{2 \pi k_BT}\right) \).
- 4.
Probably because of the large fluctuations of the phase at low temperature and \(\sqrt{1-\tau } \ll 1\) that makes the instanton technique less accurate (private discussion with our collaborators).
- 5.
The shown sample is actually not the one used for the experiment but both belong to the same batch and are essentially the same. Indeed, the relatively important electron beam required to acquire such a high-resolution image might change the properties of the sample and introduce possible artifacts.
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Iftikhar, Z. (2018). Charge Quantization. In: Charge Quantization and Kondo Quantum Criticality in Few-Channel Mesoscopic Circuits. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-94685-6_2
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