Motivated by experiments on double quantum dots, we study the problem of a single magnetic impurity confined in a finite metallic host. We prove an exact theorem for the ground state spin, and use analytic and numerical arguments to map out the spin structure of the excitation spectrum of the many-body Kondo-correlated state, throughout the weak to strong coupling crossover. These excitations can be probed in a simple tunneling-spectroscopy transport experiment; for that situation we solve rate equations for the conductance.
Motivated by experiments on double quantum dots, we study the problem of a single magnetic impurity confined in a finite metallic host. We prove an exact theorem for the ground state spin, and use analytic and numerical arguments to map out the spin structure of the excitation spectrum of the many-body Kondo-correlated state, throughout the weak to strong coupling crossover. These excitations can be probed in a simple tunneling-spectroscopy transport experiment; for that situation we solve rate equations for the conductance.
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.
The Kondo effect, the screening of the spin of an impurity by the conduction electrons of a metallic host system, is a standard problem in solid state physics. At weak coupling strengths between the host system and a group of impurities, the Kondo competes with indirect (RKKY) exchange, mediated by the conduction electrons, which promotes magnetic order among the impurities.
This work deals with the physics emerging in impurity systems with spatially confined metallic host materials, relevant to the quantum dots and artificial nanostructures created by scanning tunnelling techniques. It is shown that (i) the finite system size leads to an unconventional reentrant competition, where the Kondo prevails at weak couplings in contradiction to the standard Doniach picture. (ii) A novel mechanism is proposed which ferromagnetically correlates the impurities' magnetic moments without any indirect exchange. (iii) In case of degenerate Fermi levels, a multi-channel Kondo effect is observed. (iv) In the regime of strong couplings magnetic ordering is shown to be driven by a novel inverse indirect magnetic exchange (IIME), which is mediated by magnetically inert Kondo singlets.
The evolution of this physics is studied from the single-impurity Kondo box limit via the Kondo-vs.-RKKY quantum box to the regime of the Kondo-lattice box. Key insights are gained analytically by deriving effective low-energy Hamiltonians in the respective regimes by perturbation theory, and numerically by means of density-matrix renormalisation group (DMRG), dynamical mean-field theory (DMFT), and full diagonalisation calculations.
The presented theoretical concept is robust against weak environmental influences. The predicted effects await an experimental confirmation and exploration.
Der Kondo-Effekt, die Abschirmung eines Storstellen-Spins durch Leitungselektronen eines metallischen Wirtssystems, ist ein Standardproblem in der Festkorperphysik. Bei schwachen Kopplungen zwischen dem Wirtssystem und einer Gruppe von Storstellen konkurriert er mit dem indirekten, durch die Leitungselektronen vermittelten (RKKY) Austausch, der magnetische Ordnungen der Storstellen begunstigt.
Die vorliegende Arbeit behandelt die Physik von Storstellensystemen mit raumlich eingeschrankten metallischen Wirtsmaterialien, die von groser Bedeutung ist fur Quantenpunkte und kunstliche Nanostrukturen, die mit Rastertunneltechniken erschaffen werden konnen. Es wird gezeigt, dass (i) die endliche Systemgrose zu einem unkonventionellen Wettstreit fuhrt, in dem der Kondo-Effekt sich entgegen den Standardvorstellungen nach Doniach bei kleinen Kopplungen durchsetzt. (ii) Ein neuartiger Mechanismus wird vorgeschlagen, der die magnetischen Momente von Storstellen ohne jeglichen indirekten Austausch ferromagnetisch korreliert. (iii) Im Fall von entarteten Fermikanten-Zustanden wird ein multi-channel finite-size Kondo-Effekt beobachtet. (iv) Magnetische Ordnung im Regime groser Kopplungen wird durch einen neuartigen inversen indirekten magnetischen Austausch (IIMA) verursacht, der durch magnetisch inerte Kondo-Singlets vermittelt wird.
Die Entwicklung dieser Physik wird untersucht von der Eine-Storstelle-Kondo-Box, uber die Kondo-vs.-RKKY-Quantum-Box, bis hin zum Regime der Kondo-Gitter-Box. Schlusselerkenntnisse werden analytisch gewonnen durch die storungstheoretische Ableitung von effektiven Niedrigenergie-Hamiltonoperatoren in den entsprechenden Grenzfallen und numerisch mithilfe von Dichtematrix-Renormierungsgruppe (DMRG), dynamischer Meanfield-Theorie (DMFT) und voller Diagonalisierung.
Das vorgestellte Konzept ist robust gegen schwache Umgebungseinflusse. Die vorhergesagten Effekte sehen einer experimentellen Bestatigung und Erforschung entgegen.
We study the low-temperature physics arising in models of a strongly correlated, tunnel-coupled double quantum dot (DQD), particularly the two-impurity Anderson model (2AIM) and the two-impurity Kondo model (2IKM), employing a combination of physical arguments and the Numerical Renormalisation Group. These models exhibit a rich range of Kondo physics. In the regime with essentially one electron on each dot, there is a competition between the Kondo effect and the interdot exchange interaction. This competition gives rise to a quantum phase transition (QPT) between local singlet and Kondo singlet phases in the 2IKM, which becomes a continuous crossover in the 2AIM as a result of the interlead charge transfer present. The 2IKM is known to exhibit two-channel Kondo (2CK) physics at the QPT, and we investigate whether this is also the case for the 2AIM at the crossover. We find that while in principle 2CK physics can be observed in the 2AIM, extremely low temperatures are required, such that it is unlikely that 2CK physics will be observed in an experimental DQD system in the near future. We have studied the effect of a magnetic field on the 2AIM and the 2IKM, finding that both the zero-field QPT in the 2IKM and the zero-field crossover in the 2AIM, persist to finite field. This presents the possibility of observing 2CK physics in an experimental DQD at finite field, but we find that the temperatures required to do so are extremely low. We show that longer even-numbered chains of spins also exhibit QPTs at finite field, and argue that a 2N-spin chain should undergo N QPTs as field is increased (starting deep in the local singlet phase at zero field). We have also carried out a joint theoretical-experimental study of a carbon nanotube based DQD, in collaboration with Dr. Mark Buitelaar et al. The agreement between experimental and theoretical results is good, and the experiments are able to access the crossover present in the 2AIM at finite field. Furthermore, the experiments show the wide range of physics exhibited by DQD systems, and illustrate the utility of such systems in probing correlated electron physics.
We present an extensive study of the two-impurity Kondo problem for spin-1 adatoms on a square lattice using an exact canonical transformation to map the problem onto an effective one-dimensional system that can be numerically solved using the density matrix renormalization group method. We provide a simple intuitive picture and identify the different regimes, depending on the distance between the two impurities, Kondo coupling JK, longitudinal anisotropy D, and transverse anisotropy E. In the isotropic case, two impurities on opposite (the same) sublattices have a singlet (triplet) ground state. However, the energy difference between the triplet ground state and the singlet excited state is very small and we expect an effectively fourfold-degenerate ground state, i.e., two decoupled impurities. For large enough JK the impurities are practically uncorrelated forming two independent underscreened states with the conduction electrons, a clear nonperturbative effect. When the impurities are entangled in an RKKY-like state, Kondo correlations persist and the two effects coexist: the impurities are underscreened, and the dangling spin-1/2 degrees of freedom are responsible for the interimpurity entanglement. We analyze the effects of magnetic anisotropy in the development of quasiclassical correlations.
The splitting of the Kondo resonance in the density of states of an Anderson impurity in a finite magnetic field is calculated from the exact Bethe-ansatz solution. The result gives an estimate of the electron spectral function for a nonzero magnetic field and the Kondo temperature, with consequences for transport experiments on quantum dots in the Kondo regime. The strong correlations of the Kondo ground state cause a significant low-temperature reduction of the peak splitting. Explicit formulas are found for the shift and broadening of the Kondo peaks. A likely cause of the problems of large- N approaches to spin- 1 / 2 impurities at finite magnetic field is suggested.
In this work we consider several exactly solvable models of magnetic impurities in critical quantum antiferromagnetic spin chains and multichannel Kondo impurities. Their ground-state properties are studied, and the finite set of nonlinear integral equations which exactly describe the thermodynamics of the models is constructed. We obtain several analytical low-energy expressions for the temperature, magnetic field, and frequency dependences of important characteristics of exactly solvable disordered quantum spin models and disordered multichannel Kondo impurities with essential many-body interactions. We show that the only low-energy parameter that gets renormalized is the velocity of the low-lying excitations (or the effective crossover scale connected with each impurity); the others appear to be universal. In our study several kinds of strong disorder important for experiments were used. Some of them produce low divergences in certain characteristics of our strongly disordered critical systems (compared with finite values for the homogeneous case or a single impurity). For weak disorder, or for narrow distributions of the local Kondo temperatures, our exact results reveal the presence of Kondo screening of disordered ensembles of magnetic impurities by low-lying excitations of the host. We point out that our results qualitatively coincide with the data of experiments on real disordered quasi-one-dimensional antiferromagnetic systems and with the similar behavior of some heavy metallic alloys.