No abstract

We generalize Nozières' Fermi-liquid theory for the low-energy behavior of the Kondo model to that of the single-impurity Anderson model. In addition to the electrons' phase shift at the Fermi energy, the low-energy Fermi-liquid theory is characterized by four Fermi-liquid parameters: the two given by Nozières that enter to first order in the excitation energy, and two additional ones that enter to second order and are needed away from particle-hole symmetry. We express all four parameters in terms of zero-temperature physical observables, namely the local charge and spin susceptibilities and their derivatives w.r.t. the local level position. We determine these in terms of the bare parameters of the Anderson model using Bethe Ansatz and Numerical Renormalization Group (NRG) calculations. Our low-energy Fermi-liquid theory applies throughout the crossover from the strong-coupling Kondo regime via the mixed-valence regime to the empty-orbital regime. From the Fermi-liquid theory, we determine the conductance through a quantum dot symmetrically coupled to two leads in the regime of small magnetic field, low temperature and small bias voltage, and compute the coefficients of the ∼ B 2 , ∼ T 2 , and ∼ V 2 terms exactly in terms of the Fermiliquid parameters. The coefficients of T 2 , V 2 and B 2 are found to change sign during the Kondo to empty-orbital crossover. The crossover becomes universal in the limit that the local interaction is much larger than the level width. For completeness, we also compute the shot noise and discuss the resulting Fano factor.

Quantum critical systems derive their finite temperature properties from the influence of a zero temperature quantum phase transition.1 The paradigm is essential for understanding unconventional high-T c superconductors and the nonFermi liquid properties of heavy fermion compounds. However, the microscopic origins of quantum phase transitions in complex materials are often debated.Here we demonstrate experimentally, with support from numerical renormalization group calculations, a universal crossover from quantum critical non-Fermi liquid behavior to distinct Fermi liquid ground states in a highly controllable quantum dot device. Our device realizes the non-Fermi liquid two-channel Kondo state, 2, 3 based on a spin-1/2 impurity exchange-coupled equally to two independent electronic reservoirs. 4 Arbitrarily small detuning of the exchange couplings results in conventional screening of the spin by the more strongly coupled channel for energies below a Fermi liquid scale T * . We extract a quadratic dependence of T * on gate voltage close to criticality and validate an asymptotically exact description of the universal crossover between strongly correlated non-Fermi liquid and Fermi liquid states. 5, 6A conventional second-order quantum phase transition (QPT) features quantum mechan- (FL) scale that vanishes at the quantum critical point (QCP); away from the QCP, a crossover from non-FL to FL behavior is observed at low energies. A diverging effective mass m * at the QCP, seen in both materials, signifies the absence of quasiparticles at the Fermi surface. 8In many heavy fermion materials and in high-T c superconductors, the relevant degrees of freedom and the effective Hamiltonian can be controversial. We aim to understand quantitatively a second-order QPT outside the usual order-parameter-fluctuation description.Quantum dots provide an experimental framework for realizing known quantum impurityHamiltonians that can feature tunable second-order QPTs. 9, 10 However, QCPs are challenging to reach even in engineered systems, since perturbations that steer away from quantum criticality may be inherently uncontrolled, as in two-impurity Kondo experiments to date. 11-13At the QCP of a two-channel Kondo (2CK) system, a single overscreened spin yields a non-FL state with no quasiparticles (i.e. only collective excitations) at the Fermi surface.An order parameter is typically not invoked; rather, the critical behavior is owing to the single spin. A FL scale T * results from several relevant perturbations: Zeeman splitting, difference in exchange couplings, and charge transfer between the two channels. Requiring that all these perturbations be small would seem to diminish prospects for observing the QCP in bulk systems. Nonetheless, two-channel Kondo physics has been invoked to explain experiments on heavy fermion materials 14-16 and two-level tunneling centers. 17-19 A 2CK state has been predicted 2 and observed 3 in a quantum dot tunnel-coupled to a "metallic grain," an electron reservoir big enough to have a small lev...