Scaling of sub-gap excitations in a superconductor-semiconductor   nanowire quantum dot
  A quantum dot coupled to a superconducting contact provides a tunable artificial analogue of a magnetic atom in a superconductor, a paradigmatic quantum impurity problem. We realize such a system with an InAs semiconductor nanowire contacted by an Al-based superconducting electrode. We use an additional normal-type contact as weakly coupled tunnel probe to perform tunneling spectroscopy measurements of the elementary sub-gap excitations, known as Andreev bound states or Yu-Shiba-Rusinov states. We demonstrate that the energy of these states, $\zeta$, scales with the ratio between the Kondo temperature, $T_K$, and the superconducting gap, $\Delta$. $\zeta$ vanishes for $T_K/\Delta \approx 0.6$, denoting a quantum phase transition between spin singlet and doublet ground states. By further leveraging the gate control over the quantum dot parameters, we determine the singlet-doublet phase boundary in the stability diagram of the system. Our experimental results show remarkable quantitative agreement with numerical renormalization group calculations. 
Eduardo J. H. Lee, Xiaocheng Jiang, Rok Zitko, Ramon Aguado, Charles   M. Lieber and Silvano De Franceschi
cond-mat.mes-hall