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Observation of the Multi-channel ‘charge’ Kondo Effect

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

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Abstract

This chapter is divided in three sections. The first one gives an introduction to the multi-channel Kondo effect, which occurs when a local spin is antiferromagnetically coupled with multiple electron continua. It has become central to study non-Fermi liquid physics, but its experimental observations remained mostly elusive. A powerful implementation called ‘charge’ Kondo effect will be explained in the second section. The charge model involves ‘charge’ degrees of freedom instead of ‘spin’.

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Notes

  1. 1.

    The first observations were made in the 30’s, for a review see [2].

  2. 2.

    Everything happens as if the value of J was changing; but note that the true value of the exchange coupling never changes, it is only effectively renormalized. We will then distinguish the ‘bare’ value \(J_\infty \) from ‘renormalized’ value J (both are equal before renormalization).

  3. 3.

    It flows to zero in the ferromagnetic case, this case can be solved easily [4, 5].

  4. 4.

    The shape of the peak is modified by a Coulomb interaction, but this is well understood [12].

  5. 5.

    In the underscreened case \(N<2S\), the residual effective weak coupling to \(S'\) is ferromagnetic, the fixed point \(J_\mathrm {underscreened} \longrightarrow \infty \) is therefore stable. This case has been realized in recent experiments [19, 20], however it is not supposed to lead to a non-Fermi liquid ground state (but rather to a ‘singular’ Fermi liquid one [21]).

  6. 6.

    Private discussion with A.K. Mitchell; the proposal is from L. Fritz.

  7. 7.

    Matveev considers a metallic island, which therefore contains a macroscopic number of electrons. The charge Q we are considering is the charge in excess.

  8. 8.

    With our practical implementation in the QHE regime, a single channel is transmitted through the junction below \(\tau = 1\). In the tunnel regime, one can identify the transmission with the tunneling probability in this problem \(\tau = t^2 \ll 1\).

  9. 9.

    In this chapter, we will consider the individual conductance G of each QPC and not the serial conductance \(G_\mathrm {SET}\) through the whole device as in Chap. 2. For instance, with two symmetric channels \(G \triangleq G_1 = G_2\), the serial conductance is \(G_\mathrm {SET} = G_1 G_2/(G_1 + G_2) = G/2\).

  10. 10.

    In practice realized with a QPC in the QHE regime.

  11. 11.

    The case \(N=2\) is special because the fixed point is reached at an extremal value of \(\tau (\rho J) = 1\) (see Fig. 3.8).

  12. 12.

    We have only adjusted the position of the maximum of the peak at \(\delta V_g = 0\).

  13. 13.

    This initial renormalization occurs at energies of order of \(E_C\).

  14. 14.

    The NRG curves also present a minimum, this is a numerical artifact. The minimum occurs at \(T=E_C/k_B\) and the part of the curve with \(T \geqslant E_C/k_B\) should not be considered.

  15. 15.

    More generally \(k_B T_\mathrm {uni} \approx \min (E_C,D)/20\).

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    Zubair Iftikhar

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Iftikhar, Z. (2018). Observation of the Multi-channel ‘charge’ Kondo Effect. 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_3

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