Overscreening

Abstract: The multichannel Kondo model exhibits non-Fermi-liquid behavior in the overscreened case, when the number of channels, k, is greater than twice the size of the impurity spin, s. We show that, for overscreening, exchange anisotropy is irrelevant at the low-temperature fixed point for s=1/2 or s=k/2-1/2, but relevant for all other values of s. However, an external field or channel asymmetry is relevant, producing crossover to Fermi-liquid fixed points with different phase shifts for each spin in the first case and for each channel in the second. These results are elucidated by explicit comparison of analytic finite-size spectra derived from conformal field theory with those obtained from numerical renormalization-group calculations. The relevance of the results (for k=2 and s=1/2) to the quadrupolar Kondo Hamiltonian (which has been proposed as a model for many uranium-based heavy-fermion materials) will be briefly discussed. Also, a larger, a/Isymplectic symmetry Sp(2k) is shown to be present in the k-channel Kondo model.

Abstract: The electric double layer structure and differential capacitance of single crystalline Au(100) electrodes in the ionic liquid 1-butyl-3-methyl-imidazolium hexafluorophosphate are investigated using molecular dynamics simulations. Results show strong adsorption on the electrode surface. The potential of zero charge (pzc) and maxima of differential capacitance are strongly dependent on the adsorption layer structure. At potentials near the pzc, cations and anions adjacent to the electrode surface are coadsorbed on the same screening layer. This strong adsorption layer results in overscreening effects on the compact layer and induces both a bell-shaped differential capacitance curve and a positive pzc. Moreover, the potential required for transition from overscreening to overcrowding is about 4.0 V. This transition potential may be attributed to the higher interaction energy between the Au(100) electrode and ions compared with the binding energy in our cation–anion system.

Abstract: We have found that our Letter [1] needs two corrections to the details of the example calculation which does not alter any of the conclusions of the Letter. (1) Although our model successfully represents short-range Coulomb correlations and ion exclusion effects in the ionic liquid, as a step towards a more subtle account for the atomic structure of the interface, we added in series an interfacial ‘‘compact layer’’ contribution to capacitance. This is a standard approximation in electrochemical modeling, and, in this case, it introduces no new parameters, since we take the width of the compact layer to be the distance of closest approach of the ions (i.e., the ionic radius) with the same long-wavelength dielectric constant as in the bulk ionic liquid. This procedure serves its purpose, providing additional reduction of capacitance at the potential of zero charge. However, to be consistent, this requires a recalculation of the potential drop in the diffuse double layer through the total potential drop across the whole double layer (composed of the voltage across the compact layer and the diffuse layer). In Fig. 4 of Ref. [1], we have actually shown the overall double-layer differential capacitance as a function of the diffuse layer voltage instead of the total voltage. Only the latter is a controllable variable, and the drop across the diffuse layer should be expressed through it. (2) A factor (the ratio of the bulk ion density to the maximum possible density) was missing in our modified Debye screening length, D. The proper definition of D should read D 1⁄4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi "kBTv=ðz2e2 Þ p