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arXiv:0801.4166 · Physical Review B

Kondo screening cloud and charge staircase in one-dimensional mesoscopic devices

Rodrigo G. Pereira, Nicolas Laflorencie, Ian K. Affleck, Bertrand I. Halperin

Published Mar 19, 2008• 31 citations
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Abstract

We propose that the finite size of the Kondo screening cloud, ${\ensuremath{\xi}}_{K}$, can be probed by measuring the charge quantization in a one-dimensional system coupled to a small quantum dot. When the chemical potential $\ensuremath{\mu}$ in the system is varied at zero temperature, one should observe charge steps whose locations are at values of $\ensuremath{\mu}$ that are controlled by the Kondo effect when the system size $L$ is comparable to ${\ensuremath{\xi}}_{K}$. We show that, if the standard Kondo model is used, the ratio between the widths of the Coulomb blockade valleys with odd or even number of electrons is a universal scaling function of ${\ensuremath{\xi}}_{K}∕L$. If we take into account electron-electron interactions in a single-channel wire, this ratio also depends on the parameters of the effective Luttinger model; in addition, the scaling is weakly violated by a marginal bulk interaction. For the geometry of a quantum dot embedded in a ring, we show that the dependence of the charge steps on a magnetic flux through the ring is controlled by the size of the Kondo screening cloud.

DOI
10.1103/physrevb.77.125327

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We study finite-size effect of the Kondo screening cloud in a double quantum dot setup via a large-NNN slave-boson mean-field theory. In this setup, one of the dots is embedded in a close metallic ring with a finite size LLL and the other dot is side coupled to the embedded dot via an antiferromagnetic spin-spin-exchange coupling with a strength KKK. The antiferromagnetic coupling favors local spin-singlet state and suppresses the Kondo screening. The mean-field phase diagram as a function of 1/L1/L1/L and KKK shows a crossover to the local spin-singlet ground state from the Kondo phase to occur at K<KcK<{K}_{c}K<Kc​ (L=4n,4n+1,4n+3)(L=4n,4n+1,4n+3)(L=4n,4n+1,4n+3) and at K>KcK>{K}_{c}K>Kc​ (L=4n+2)(L=4n+2)(L=4n+2). The effective Kondo temperature Tk{T}_{k}Tk​ (proptotional to inverse of the Kondo screening cloud size) shows the Kosterlitz-Thouless (KT) scaling at finite sizes for L=4n,4n+2L=4n,4n+2L=4n,4n+2, indicating quantum transition of the KT type between the Kondo screened phase for $K\ensuremath{\le}{K}_{c}$ and a local spin-singlet phase for $K\ensuremath{\ge}{K}_{c}$ in the thermodynamic limit with Kc{K}_{c}Kc​ being the critical value. The local density of states on the embedded quantum dot and the persistent current at finite sizes with different values of KKK are calculated in the crossover region.
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Abstract The screening of an impurity spin in the Kondo model occurs over a characteristic length scale ξ K , that defines the size of the Kondo screening cloud or ‘mist’. The presence of such a length scale in experimental and numerical results is rather subtle. A consistent way to show the presence of the screening cloud is to demonstrate scaling in the spatial correlations in terms of the single variable, r / ξ K instead of the correlations depending on r and ξ K separately. Here we study the paradigmatic one channel Kondo model using a spin chain representation, with an impurity spin at one end of the chain coupled with a strength J K ′ . Using Fermi liquid theory combined with numerical results, we obtain new high precision estimates of the non-universal terms in the entanglement entropy which leads to a verification of the expected non-integer ground-state degeneracy, g. This then allows us to study the impurity contribution to the entanglement in detail. If the impurity coupling J K ′ is varied, a precise determination of ξ K can then be obtained. The length scale, ξ K , is then shown to characterize the scaling of both the uniform and alternating part of a measure of the magnetization of part of an odd length chain.