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.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.

arXiv:0801.4166Physical Review BMar 19, 200831 citations

Kondo lattice on the edge of a two-dimensional topological insulator

Joseph Maciejko

We revisit the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and show that the zero-temperature phase diagram contains a large local moment region for antiferromagnetic Kondo coupling, which was missed by previous poor man's scaling treatments. The combination of an exact solution at the so-called decoupling point and a renormalization group analysis \`a la Anderson-Yuval-Hamann allows us to access the regime of strong electron-electron interactions on the edge and strong Kondo coupling. We apply similar methods to the problem of a regular one-dimensional array of quantum impurities interacting with the edge liquid. When the edge electrons are at half-filling with respect to the impurity lattice, the system remains gapless unless the Luttinger parameter of the edge is less than $1/2$ in which case two-particle backscattering effects drive the system to a gapped phase with long-range Ising antiferromagnetic order. This is in marked contrast with the gapped disordered ground state of the ordinary half-filled one-dimensional Kondo lattice.We revisit the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and show that the zero-temperature phase diagram contains a large local moment region for antiferromagnetic Kondo coupling, which was missed by previous poor man's scaling treatments. The combination of an exact solution at the so-called decoupling point and a renormalization group analysis \`a la Anderson-Yuval-Hamann allows us to access the regime of strong electron-electron interactions on the edge and strong Kondo coupling. We apply similar methods to the problem of a regular one-dimensional array of quantum impurities interacting with the edge liquid. When the edge electrons are at half-filling with respect to the impurity lattice, the system remains gapless unless the Luttinger parameter of the edge is less than $1/2$ in which case two-particle backscattering effects drive the system to a gapped phase with long-range Ising antiferromagnetic order. This is in marked contrast with the gapped disordered ground state of the ordinary half-filled one-dimensional Kondo lattice.

arXiv:1204.0017Physical Review BJun 11, 201248 citations

Kondo effect in a many-electron quantum ring

K. Ensslin

Bulletin of the American Physical SocietyMar 25, 20050 citations

Coulomb interaction effects and electron spin relaxation in the one-dimensional Kondo lattice model

Sebastian Smerat, Herbert Schoeller, Ian P. McCulloch +1 more

We study the effects of the Coulomb interaction in the one-dimensional Kondo lattice model on the phase diagram, the static magnetic susceptibility, and electron spin relaxation. We show that onsite Coulomb interaction supports ferromagnetic order and nearest-neighbor Coulomb interaction drives, depending on the electron filling, either a paramagnetic or a ferromagnetic order. Furthermore, we calculate electron quasiparticle lifetimes, which can be related to electron spin relaxation and decoherence times, and explain their dependence on the strength of interactions and the electron filling in order to find the sweet spot of parameters where the relaxation time is maximized. We find that effective exchange processes between the electrons dominate the spin relaxation and decoherence rate.We study the effects of the Coulomb interaction in the one-dimensional Kondo lattice model on the phase diagram, the static magnetic susceptibility, and electron spin relaxation. We show that onsite Coulomb interaction supports ferromagnetic order and nearest-neighbor Coulomb interaction drives, depending on the electron filling, either a paramagnetic or a ferromagnetic order. Furthermore, we calculate electron quasiparticle lifetimes, which can be related to electron spin relaxation and decoherence times, and explain their dependence on the strength of interactions and the electron filling in order to find the sweet spot of parameters where the relaxation time is maximized. We find that effective exchange processes between the electrons dominate the spin relaxation and decoherence rate.

arXiv:1011.3404Physical Review BFeb 25, 20116 citations

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.

1/2

in which case two-particle backscattering effects drive the system to a gapped phase with long-range Ising antiferromagnetic order. This is in marked contrast with the gapped disordered ground state of the ordinary half-filled one-dimensional Kondo lattice.