From the Kondo box problem to the physics of the Kondo-lattice box

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 effect 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 Kondo-vs.-RKKY competition, where the Kondo effect 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 finite-size 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.