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arXiv:0901.0016 · Physical Review B

Ground state and excitations of quantum dots with magnetic impurities

Ribhu K. Kaul, Denis Ullmo, Gergely Zaránd, Shailesh Chandrasekharan A, Harold U. Baranger

Published Jul 24, 2009• 10 citations
arXivHTMLPDF

Abstract

We consider an ``impurity'' with a spin degree of freedom coupled to a finite reservoir of noninteracting electrons, a system which may be realized by either a true impurity in a metallic nanoparticle or a small quantum dot coupled to a large one. We show how the physics of such a spin impurity is revealed in the many-body spectrum of the entire finite-size system; in particular, the evolution of the spectrum with the strength of the impurity-reservoir coupling reflects the fundamental many-body correlations present. Explicit calculation in the strong- and the weak-coupling limits shows that the spectrum and its evolution are sensitive to the nature of the impurity and the parity of electrons in the reservoir. The effect of the finite-size spectrum on two experimental observables is considered. First, we propose an experimental setup in which the spectrum may be conveniently measured using tunneling spectroscopy. A rate equation calculation of the differential conductance suggests how the many-body spectral features may be observed. Second, the finite-temperature magnetic susceptibility is presented, both the impurity and the local susceptibilities. Extensive quantum Monte Carlo calculations show that the local susceptibility deviates from its bulk scaling form. Nevertheless, for special assumptions about the reservoir---the ``clean Kondo box'' model---we demonstrate that finite-size scaling is recovered. Explicit numerical evaluations of these scaling functions are given, both for even and odd parities and for the canonical and the grand-canonical ensembles.

DOI
10.1103/physrevb.80.035318

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We consider an impurity'' with a spin degree of freedom coupled to a finite reservoir of noninteracting electrons, a system which may be realized by either a true impurity in a metallic nanoparticle or a small quantum dot coupled to a large one. We show how the physics of such a spin impurity is revealed in the many-body spectrum of the entire finite-size system; in particular, the evolution of the spectrum with the strength of the impurity-reservoir coupling reflects the fundamental many-body correlations present. Explicit calculation in the strong- and the weak-coupling limits shows that the spectrum and its evolution are sensitive to the nature of the impurity and the parity of electrons in the reservoir. The effect of the finite-size spectrum on two experimental observables is considered. First, we propose an experimental setup in which the spectrum may be conveniently measured using tunneling spectroscopy. A rate equation calculation of the differential conductance suggests how the many-body spectral features may be observed. Second, the finite-temperature magnetic susceptibility is presented, both the impurity and the local susceptibilities. Extensive quantum Monte Carlo calculations show that the local susceptibility deviates from its bulk scaling form. Nevertheless, for special assumptions about the reservoir---the clean Kondo box'' model---we demonstrate that finite-size scaling is recovered. Explicit numerical evaluations of these scaling functions are given, both for even and odd parities and for the canonical and the grand-canonical ensembles.
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Abstract We investigate the boundary phenomena that arise in a finite-size XX spin chain interacting through an XX interaction with a spin − 1 2 impurity located at its edge. Upon Jordan–Wigner transformation, the model is described by a quadratic Fermionic Hamiltonian. Our work displays, within this ostensibly simple model, the emergence of the Kondo effect, a quintessential hallmark of strongly correlated physics. We also show how the Kondo cloud shrinks and turns into a single particle bound state as the impurity coupling increases beyond a critical value. In more detail, using both Bethe Ansatz and exact diagonalization techniques, we show that the local moment of the impurity is screened by different mechanisms depending on the ratio of the boundary and bulk coupling J imp J . When the ratio falls below the critical value 2 , the impurity is screened via the Kondo effect. However, when the ratio between the coupling exceeds the critical value 2 an exponentially localized bound mode is formed at the impurity site which screens the spin of the impurity in the ground state. We show that the boundary phase transition is reflected in local ground state properties by calculating the spinon density of states, the magnetization at the impurity site in the presence of a global magnetic field, and the finite temperature susceptibility of the impurity. We find that the spinon density of states in the Kondo phase has the characteristic Lorentzian peak that moves from the Fermi level to the maximum energy of the spinon as the impurity coupling is increased and becomes a localized bound mode in the bound mode phase. Moreover, the impurity magnetization and the finite temperature impurity susceptibility behave differently in the two phases. When the boundary coupling J imp exceeds the critical value 2 J , the model is no longer boundary conformal invariant as a massive bound mode appears at the impurity site.