The goal of this book is the investigation of physical effects at low energies caused by magnetic impurity adatoms, coupled to a small non-magnetic metallic substrate surface. Such systems can be understood with help of multi-impurity Kondo models, describing the substrate as a tight-binding model of finite-size and the impurities as quantum spins, which are antiferromagnetically coupled locally to their respective substrate sites. Focusing on one-dimensional finite-size systems with open boundary conditions at half-filling numerical exact diagonalisation and the variation of matrix product states (VMPS) method are used for the investigation. It is the aim to study finite-size effects in different regimes of the magnetic exchange interaction. For example due to the finite size of the system, the interplay of the Kondo effect and the indirect magnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between impurity spins is site dependent and non-trivial for at least three impurity Kondo systems. Furthermore evidence for an unconventional and novel magnetic coupling mechanism, causing magnetic order in the actually non-magnetic substrate, due to inverse indirect magnetic exchange, will be given.
The goal of this book is the investigation of physical effects at low energies caused by magnetic impurity adatoms, coupled to a small non-magnetic metallic substrate surface. Such systems can be understood with help of multi-impurity Kondo models, describing the substrate as a tight-binding model of finite-size and the impurities as quantum spins, which are antiferromagnetically coupled locally to their respective substrate sites. Focusing on one-dimensional finite-size systems with open boundary conditions at half-filling numerical exact diagonalisation and the variation of matrix product states (VMPS) method are used for the investigation. It is the aim to study finite-size effects in different regimes of the magnetic exchange interaction. For example due to the finite size of the system, the interplay of the Kondo effect and the indirect magnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between impurity spins is site dependent and non-trivial for at least three impurity Kondo systems. Furthermore evidence for an unconventional and novel magnetic coupling mechanism, causing magnetic order in the actually non-magnetic substrate, due to inverse indirect magnetic exchange, will be given.
The competition between the Kondo screening and indirect magnetic exchange in systems with two magnetic impurities coupled to a conventional s-wave superconductor gives rise to a nontrivial ground-state phase diagram. Here, we utilize the density matrix renormalization group (DMRG) method and exploit the non-Abelian spin-SU(2) symmetry to study the phase diagram for two quantum spin-21 impurities locally exchange coupled to large one-dimensional chains. The nonlocal interimpurity exchange is treated as an emergent Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling. We find qualitatively different phase diagrams for impurity spins coupled to sites with odd or even distances d on the chain and a partial Kondo-screened spin-doublet phase that extends over the whole range of local exchange couplings J in the limit of weak superconducting pairing strength $\mathrm{\ensuremath{\Delta}}$. Our numerical DMRG studies are complemented by exact diagonalization of small (quantum-box) systems and by perturbative-in-J computations of the d- and $\mathrm{\ensuremath{\Delta}}$-dependent RKKY interaction. It is thereby demonstrated that the specific system geometry is essential for our understanding of magnetic impurity interactions in superconducting hosts, and thus for insights into the control of quantum-state properties in nanoparticle systems and topological superconductivity.
To analyze the physical properties arising from indirect magnetic exchange between several magnetic adatoms and between complex magnetic nanostructures on metallic surfaces, the real-space extension of dynamical mean-field theory (R-DMFT) appears attractive as it can be applied to systems of almost arbitrary geometry and complexity. While R-DMFT describes the Kondo effect of a single adatom exactly, indirect magnetic (RKKY) exchange is taken into account on an approximate level only. Here, we consider a simplified model system consisting of two magnetic Hubbard sites (``adatoms'') hybridizing with a noninteracting tight-binding chain (``substrate surface''). This two-impurity Anderson model incorporates the competition between the Kondo effect and indirect exchange but is amenable to an exact numerical solution via the density-matrix renormalization group (DMRG). The particle-hole symmetric model at half filling and zero temperature is used to benchmark R-DMFT results for the magnetic coupling between the two adatoms and for the magnetic properties induced in the substrate. In particular, the dependence of the local adatom and the nonlocal adatom-adatom static susceptibilities as well as the magnetic response of the substrate on the distance between the adatoms and on the strength of their coupling with the substrate is studied. We find excellent agreement with the DMRG data even on subtle details of the competition between RKKY exchange and the Kondo effect but also complete failure of the R-DMFT, depending on the parameter regime considered. R-DMFT calculations are performed using the Lanczos method as impurity solver. With the real-space extension of the two-site DMFT, we also benchmark a simplified R-DMFT variant.
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.
Quantum dots exhibit a variety of strongly correlated effects, e.g., they can emulate localized magnetic impurities that form a Kondo singlet with their surrounding environment. Interestingly, in double-dot setups, such magnetic impurities couple to each other by direct Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which wins over the Kondo physics. In this work, we investigate a double-dot device where the dots are coupled via off-resonant ballistic modes, dubbed electronic cavity modes. Within this cavity-double-dot system, we study, using variational matrix product state techniques, the competition between Kondo formation and the combined coherent orbital hybridization and RKKY-like interaction that the cavity facilitates. Specifically, we find that Kondo can form on each dot individually whereby the cavity can either (i) destroy the Kondo via the RKKY that mediates a singlet state on the two dots, or (ii) lead to an exotic orbital macrsoscopic superposition of the Kondo forming on each of the dots. We dub the latter “Kondo cat”. En route to this key finding, we rigorously study the many-body phase diagram of the system, as well as compare it with the case of coupling the dots via an incoherent RKKY channel. The realization of a Kondo cat can facilitate applications in metrology, and reveal the spin coherence length in mesoscopic devices. Published by the American Physical Society 2024
Quantum dots exhibit a variety of strongly correlated effects, e.g., when tuned to emulate localized magnetic impurities that form a Kondo singlet with their surrounding environment. Interestingly, in double-dots setups, the magnetic impurities couple to each other by direct Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which wins over the Kondo physics. In this work, we investigate a double-dot device where the dots are coupled via off-resonant ballistic whispering gallery modes, dubbed electronic cavity modes. Within this cavity-double-dot system, we study, using variational matrix product state techniques, the competition between Kondo formation and the coherent RKKY-like interaction that the cavity facilitates. Specifically, we find that (i) Kondo can win and form on each dot individually, or (ii) the cavity can win and mediate between the two dots either a singlet or a novel nonlocal Kondo-like effect phase, which we call "cat Kondo". We systematically study the quantum phase transitions between the different many-body states. Our discoveries lay the foundation for the experimental observation of unconventional nonlocal magnetic impurities.
The (111) surface of noble metals is usually treated as an isolated two-dimensional (2D) triangular lattice completely decoupled from the bulk. However, unlike in topological insulators, bulk bands also cross the Fermi level. We here introduce an effective tight-binding model that accurately reproduces results from first-principles calculations, accounting for both surface and bulk states. We numerically solve the many-body problem of two quantum impurities sitting on the surface by means of the density matrix renormalization group. By performing simulations in a star geometry, we are able to study the nonperturbative problem in the thermodynamic limit with machine precision accuracy. We find that there is a nontrivial competition between Kondo and RKKY physics and as a consequence, ferromagnetism is never developed, except at short distances. The bulk introduces a variation in the period of the RKKY interactions, and therefore the problem departs considerably from the simpler 2D case. In addition, screening and the magnitude of the effective indirect exchange are enhanced by the contributions from the bulk states.