Surprises in the Phase Diagram of an Anderson Impurity Model for a Single C60n- Molecule

Abstract

We find by Wilson numerical renormalization group and conformal field theory that a three-orbital Anderson impurity model for a C n− 60 molecule has a very rich phase diagram which includes non-Fermi-liquid stable and unstable fixed points with interesting properties, most notably high sensitivity to doping n. We discuss the implications of our results to the conductance behavior of C60-based single-molecule transistor devices. PACS numbers: 71.10.Hf,72.15.Qm, The characteristic behavior of an Anderson impurity model (AIM) emerges often unexpectedly in physical contexts which are apparently faraway from magnetic alloys. The typical example is the conductance behavior of nano-scale devices, e.g. quantum dots and single-molecule transistors (SMT), where Kondo-assisted tunneling may lead to nearly perfect transmission at zero bias in spite of a large charging energy [1]. Usually the two conduction leads are bridged by a single quantum dot or molecular level, which therefore behaves effectively as a one-orbital AIM. Less common is the case when several levels happen to be nearby degenerate thus realizing in practice a multi-orbital AIM. This may be achieved for instance in SMTs built with high-symmetry molecules. Recently a zero-bias anomaly has been reported for a C 60 based SMT[2], which has been proven to be of the Kondo-type by its splitting under the action of a magnetic field or magnetic leads[3]. Fullerene's large electron affinity is known to yield to electron transfer into C 60 when adsorbed on metallic substrates. The actual number of doped electrons depends on the substrate[4], but may also be controlled by attaching alkali atoms to the molecule [5]. In this case a variety of conductance behavior has been reported depending on the number of K-atoms attached to C 60 [5], ranging from Kondo-like resonances to Fano-like anti-resonances.Motivated by this opportunity, in this Letter we study the behavior of an AIM for C n− 60 by Wilson Numerical Renormalization Group (NRG) [6] and Conformal Field Theory (CFT) [7]. We obtain a phase diagram which includes Fermiand non-Fermi-liquid phases, with a doping dependence qualitatively in agreement with experiments. In particular we find a Kondo-like zero-bias anomaly for doping n = 1, likely the case of C 60 on Au[4], as found in Refs. [2,3]. For n = 2, which should correspond to pure or slightly K-doped C 60 on Ag[4], we predict instead a conductance-minimum at zerobias, compatible with actual observations [5]. Finally, for n = 3 we find a conductance minimum with a non-analytic voltage behavior G(V ) − G(0) ∼ |V | 2/5 . The LUMO's of C 60 are three-fold degenerate t 1u orbitals [8]. The electron-electron interaction acts as if these orbitals were effectively p-orbitals. Therefore the Coulomb energy of a C n− 60 molecule with n valence electrons into a configuration with total spin S and angular momentum L is. The reference valency, n 0 , is controlled in SMTs by the gate voltage, the metal substrate and the alkali doping. The Coulomb exchange, J > 0, favoring high-de...

Universal transport signatures in two-electron molecular quantum dots: gate-tunable Hund’s rule, underscreened Kondo effect and quantum phase transitions

“…One crucial question is thus to understand what classes of universal behaviors can be expected in such a complicated situation. Going one step further, we also mention that three-orbital models show even more complex and interesting physics, such as non-Fermi liquid fixed points, a topic that goes far beyond the present review (see [34,[57][58][59][60][61] for a few recent theoretical studies and [62] for a review).…”

Numerical renormalization group for impurity quantum phase transitions: structure of critical fixed points

“…Impurity phase transitions are of relevance for impurities in correlated bulk systems (e.g. superconductors [6]), for multilevel impurities like fullerene molecules [7], as well as for nanodevices like coupled quantum dots [8] or point contacts under the influence of dissipative noise [9,10]. In addition, impurity phase transitions have been argued to describe aspects of so-called local quantum criticality in correlated lattice systems.…”