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arXiv:cond-mat/0603168 · Physical Review B

Quantum dot with ferromagnetic leads: A density-matrix renormalization group study

C. J. Gazza, M. E. Torio, José A. Riera

Published May 31, 2006• 14 citations
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Abstract

A quantum dot coupled to ferromagnetically polarized one-dimensional leads is studied numerically using the density-matrix renormalization group method. Several real space properties and the local density of states at the dot are computed. It is shown that this local density of states is suppressed by the parallel polarization of the leads. In this case we are able to estimate the length of the Kondo cloud, and to relate its behavior to that suppression. Another important result of our study is that the tunnel magnetoresistance as a function of the quantum dot on-site energy is minimum and negative at the symmetric point.

DOI
10.1103/physrevb.73.193108

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A quantum dot coupled to ferromagnetically polarized one-dimensional leads is studied numerically using the density-matrix renormalization group method. Several real space properties and the local density of states at the dot are computed. It is shown that this local density of states is suppressed by the parallel polarization of the leads. In this case we are able to estimate the length of the Kondo cloud, and to relate its behavior to that suppression. Another important result of our study is that the tunnel magnetoresistance as a function of the quantum dot on-site energy is minimum and negative at the symmetric point.
Measurements of the persistent current in a ring containing a quantum dot would afford a unique opportunity to finally detect the elusive Kondo screening cloud. We present the first large-scale numerical results on this controversial subject using exact diagonalization and density matrix renormalization group (RG). These extremely challenging numerical calculations confirm RG arguments for weak to strong coupling crossover with varying ring length and give results on the universal scaling functions. We also study, analytically and numerically, the important and surprising effects of particle-hole symmetry breaking.
We investigate electronic transport through a parallel double quantum dot (DQD) system with strong on-site Coulomb interaction, as well as the interdot tunnelling. By applying numerical renormalization group method, the ground state of the system and the transmission probability at zero temperature are obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit (2 e 2 / h ) due to the Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to anti-ferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.
We investigate the quench dynamics of a quantum dot strongly coupled to spin-polarized ferromagnetic leads. The real-time evolution is calculated by means of the time-dependent density-matrix numerical renormalization group method implemented within the matrix product states framework. We examine the system's response to a quench in the spin-dependent coupling strength to ferromagnetic leads as well as in the position of the dot's orbital level. The spin dynamics is analyzed by calculating the time-dependent expectation values of the quantum dot's magnetization and occupation. Based on these, we determine the time dependence of a ferromagnetic-contact-induced exchange field and predict its nonmonotonic buildup. In particular, two timescales are identified, describing the development of the exchange field and the dot's magnetization sign change. Finally, we study the effects of finite temperature on the dynamical behavior of the system.
A magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. For several mechanisms---the gate potential and a magnetic field---which destroy the Kondo effect, we investigate the behavior of the screening cloud induced by these perturbations.
A recently proposed density-matrix renormalization group is used to investigate the ground-state properties of the Kondo-necklace Hamiltonian. It represents a chain of XY interacting pseudospins that are Kondo coupled (J) to localized spins. The spin gap as well as the short- and long-range spin correlation functions are consistent with the existence of a smooth crossover at J\ensuremath{\approxeq}0.5. For J\ensuremath{\le}0.5, the gap depends exponentially on ${\mathit{J}}^{\mathrm{\ensuremath{-}}1/2}$ and the in-plane correlation function of the localized spins shows RKKY oscillations while the z one falls monotonically in contrast to the XY behavior. The correlation length diverges at J=0. For J\ensuremath{\ge}0.5, the gap is linearly increasing with J, and the system is made of nearly independent singlets.
A new application of the density matrix renormalization group (DMRG) method to a system composed of an interacting dot coupled to a infinite one dimensional lead is presented. This method enables one to study the influence of the coupling to an external lead on the thermodynamical properties of the dot. It is shown that this method reproduces known results for a non-interacting dot coupled to a lead, i.e., that for strong coupling discrete states remain in the dot. We show that these states are robust and do not disappear once interactions in the dot are considered. Moreover, due to these discrete states, Coulomb blockade affects the charging of the dot even though its strongly coupled to a lead.