Weak localization leads to the same correction to both the conductivity and the McMillan's electron-phonon coupling constant λ (and λtr, transport electron-phonon coupling constant). Consequently the temperature dependence of the thermal electrical resistivity is decreasing as the conductivity is decreasing due to weak localization, which results in the decrease of the temperature coefficient of resistivity (TCR) with increasing the residual resistivity. When λ and λtr are approaching zero, only the residual resistivity part remains and it gives rise to the negative TCR. Accordingly, the Mooij rule is a manifestation of weak localization correction to the conductivity and the electron-phonon interaction. This understanding provides a new means of probing the phonon-mechanism in exotic superconductors and an opportunity of fabricating new novel devices

Weak localization has a strong influence on both the normal and superconducting properties of metals. In particular, since weak localization leads to the decoupling of electrons and phonons, the temperature dependence of resistance (i.e., λ tr ) is decreasing with increasing disorder, as manifested by Mooij's empirical rule. In addition, Testardi's universal correlation of T c (i.e., λ) and the resistance ratio (i.e., λ tr ) follows. This understanding provides a new means to probe the phonon mechanism in superconductors including MgB 2 . The merits of this method are its applicability to any superconductors and its reliability because the McMillan's electron-phonon coupling constant λ and λ tr change in a broad range, from finite values to zero, due to weak localization. Karkin et al's preliminary data of irradiated MgB 2 show the Testardi correlation, indicating that the dominant pairing mechanism in MgB 2 is the phonon-mediated interaction.

We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a nonideal two level subspace, identified as the qubit, and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model that we use is an rf-SQUID under macroscopic quantum coherence and coupled inductively to a flux noise characterized by an environmental spectrum. The model interaction can generate dipole couplings which can be appreciable between the qubit and the high levels. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We calculate the relaxation and dephasing times as the spectral parameters of the environment are varied. We observe that, these calculated time scales receive contribution from all available frequencies in the noise spectrum (even well above the system's resonant frequency scales) stressing the dominant role played by the nonresonant transitions. The relaxation and dephasing and the leakage times thus calculated, strongly depend on the appreciably interacting levels determined by the strength of the dipole coupling. Under the influence of these nonresonant and multilevel effects, the validity of the two level approximation is dictated not by the low temperature as conveniently believed, but by these multilevel dipole couplings as well as the availability of the environmental modes. ©2005 The American Physical Society

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180 / lQEC'98 / THURSDAY AFTERNOON 2-m-diameter beams from an He-Ne and/or argon-ion laser and two types of samples: (a) microscope cover-glass plates of 150 pm thickness and (b) Fabry-Perot plates of 0.5 mm thickness. The only difference between samples (a) and (b) was that, whereas the Fabry-Perot plates had only SSR with rms height h, the ordinary glass plates contained the same size SSR with the addition of LSR with rms height U. The LSR is a consequence of the deviation from perfect planarity of the glass surface, which was measured to be an average of 0.01-0.1 pm, on a horizontal scale of order 1 mm. The pres-enceofLSRofthissizeadded -10-50% tothetotal rms height of roughness, h, F= ( hz + 2) "', which means that in both cases, h, remains the same order of magnitude (much smaller than the wavelength A). The measured scattered intensity from the two samples, however, showed completely different farfield interference pattems. In the pattems obtained from the Fabry-Perot plate, the positions of interference rings are independent of the angle of incidence, ern. Their brightness, however, oscillates periodically as e,, is varied (Figs. la and lb). In stark