Double quantum dots connected in parallel to a single channel, have been studied theoretically in two disparate limits: (I) Systems in which each dot has strong Coulomb interactions, exhibiting an underscreened spin-1 Kondo effect ; (II) An interacting dot 1 and a non-interacting dot 2, showing a quantum phase transition between Kondo phase and non-Kondo local-moment . In this work, we use the numerical renormalization group approach to study a strongly interacting ``quantum dot 1'' and a weakly interacting ``dot 2'' connected in parallel to metallic leads. Gate voltages can drive the system between Kondo-quenched and free-moment phases separated by Kosterlitz-Thouless quantum phase transitions. As interactions in dot 2 become stronger relative to the dot-lead coupling, the free moment evolves from an isolated spin-1/2 in dot 1 to a many-body doublet arising from an underscreened Kondo effect. These limits, which feature very different entanglements between dot and lead electrons, can be distinguished by conductance measurements at finite temperatures. [4pt]  D. E. Logan, C. J. Wright, and M. R. Galpin, PRB 80, 125117 (2009).[0pt]  L. G. G. V. Dias da Silva et al., PRL 97, 096603 (2006).
We propose a topological spin Chern pump using a two-dimensional topological insulator subject to electromagnetic radiations. In each cycle, spin can be continuously pumped into leads, which is attributed to the nonzero spin Chern numbers. In comparison to a previous model (Chen M. N. et al., Phys. Rev. B, 91 (2015) 125117), this system can have a much larger spin pumping conductivity. Moreover, the energy and spin spectra are always gapped in the present system, which makes the spin pumping more stable to perturbations. The spin pumping is an observable effect of the topological invariant spin Chern numbers, which may be useful in spintronic applications. 041b061a72