| The quantum phase transition (QPT) from a singlet to a doublet ground state has been observed in transport measurements through a C60 quantum dot [Roch et al., Nature 453, 633 (2008)]. We show that the minimal model to understand this transition is the singlet-triplet Anderson model (STAM) in which a singlet and a triplet are hybridized with a doublet, promoting an electron from the conducting leads in effectively a one-channel fashion. Using the non-crossing approximation (NCA), we calculate the spectral densities and conductance through the system as a function of temperature and bias voltage, and determine the changes that take place at the QPT. The separation of the spectral density into a singlet and a triplet part allows us to shed light on the underlying physics and to explain the shoulder observed in the zero-bias conductance as a function of temperature. We also explain the structure with three peaks observed in the conductance as a function of applied bias voltage on one side of the transition. The fact that the transition is driven by an applied bias voltage is understood from the different magnitude of the tunneling elements of the triplet and the singlet, as shown in detail in a recent collaboration with the experimental group and S. Florens [S. Florens et al, submitted]. We also report on another collaboration with experimentalists for a system in which the singlet is absent, but a QPT is driven by stretching a molecule, inducing a splitting of the triplet [Parks et al., Science 328, 1370 (2010)]. |
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