Charge Quantization and Kondo Quantum Criticality in Few-Channel Mesoscopic Circuits by Zubair Iftikhar

Author:Zubair Iftikhar
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(3.5)

where h is a magnetic field along the z-axis. Let us emphasize here that the ‘spin’ involved in this mapping is not the true spin discussed in the previous Kondo models (the original and the multi-channel). We call this a ‘pseudo-spin’: it can take only two values as it refers to the position of the electron (either on the island or outside). The impurity and location pseudo-spins are thus necessarily equal to .

A simple picture based on pseudo-spins explains this mapping. Indeed, an electron that enters the island flips both the location pseudo-spin and the impurity pseudo-spin . This implements the Kondo process quite naively, with an exchange coupling J directly related to the tunneling amplitude t of the Coulomb blockade model.

This implementation of the Kondo effect will be called the ‘charge’ Kondo model, in contrast to the original (which we be referred as the ‘spin’ Kondo model). The degrees of freedom involved in each model are of different nature (charge and spin), but both describe the same Kondo effect. The major advantage of this implementation is the natural access it gives to the multi-channel Kondo model as explained below.

A natural implementation of the multi-channel Kondo model

So far we have considered a single-mode junction between the electrode and the island. However, several electronic channels could participate. There are basically three ways to increase the number of channels: (i) to consider the true spin of the electron and say that two identical channels are connecting the island, (ii) to use a wider junction that allows more transverse modes, (iii) to add more electrodes with single-mode junctions.

All these options are modeled identically because electronic channels are assumed independent in the Landauer-Büttiker formalism. One has just to sum over the number N of channels to get the Coulomb blockade or the ‘charge’ Kondo Hamiltonian:

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