Magnesium diboride, MgB2, has the highest transition temperature (T(c) = 39 K) of the known metallic superconductors. Whether the anomalously high T(c) can be described within the conventional BCS (Bardeen-Cooper-Schrieffer) framework has been debated. The key to understanding superconductivity lies with the 'superconducting energy gap' associated with the formation of the superconducting pairs. Recently, the existence of two kinds of superconducting gaps in MgB2 has been suggested by several experiments; this is in contrast to both conventional and high-T(c) superconductors. A clear demonstration of two gaps has not yet been made because the previous experiments lacked the ability to resolve the momentum of the superconducting electrons. Here we report direct experimental evidence for the two-band superconductivity in MgB2, by separately observing the superconducting gaps of the sigma and pi bands (as well as a surface band). The gaps have distinctly different sizes, which unambiguously establishes MgB2 as a two-gap superconductor.

In conventional superconductors, the pairing energy gap (∆) and superconducting phase coherence go hand-in-hand. As the temperature is lowered, both the energy gap and phase coherence appear at the transition temperature T c . In contrast, in underdoped high-T c superconductors (HTSCs), a pseudogap appears at a much higher temperature T * , smoothly evolving into the superconducting gap at T c [1,2]. Phase coherence on the other hand is only established at T c , signaled by the appearance of a sharp quasiparticle (QP) peak [3] in the excitation spectrum. Another important difference between the two types of superconductors is in the ratio of 2∆/T c ≡ R. In BCS theory, R ∼ 3.5, is constant. In the HTSCs this ratio varies widely, continuing to increase in the underdoped region, where the gap increases while T c decreases. Here we report that in HTSCs it is the ratio z A ∆ m /T c which is approximately constant, where ∆ m is the maximum value of the d-wave gap, and z A is the weight of the coherent excitations in the spectral function. This is highly unusual, since in nearly all phase transitions, T c is determined by an energy scale alone. We further show that in the lowtemperature limit, z A increases monotonically with increasing doping x. The growth is linear, i.e. z A (x) ∝ x, in the underdoped to optimally doped regimes, 1

We report angle-resolved photoelectron spectroscopy results of the Fermi surface of Ca1.5Sr0.5RuO4, which is at the boundary of magnetic/orbital instability in the phase diagram of the Ca-substituted Sr ruthenates. Three t(2g) energy bands and the corresponding Fermi surface sheets are observed, which are also present in the Ca-free Sr2RuO4. We find that while the Fermi surface topology of the alpha,beta (d(yz,zx)) sheets remains almost the same in these two materials, the gamma (d(xy)) sheet exhibits a holelike Fermi surface in Ca1.5Sr0.5RuO4 in contrast to being electronlike in Sr2RuO4. Our observation of all three volume conserving Fermi surface sheets clearly demonstrates the absence of orbital-selective Mott transition, which was proposed theoretically to explain the unusual transport and magnetic properties in Ca1.5Sr0.5RuO4.

Ca(2-x)Sr(x)RuO4 single crystals with 0.1 < or = x < or = 2.0 have been studied systematically using scanning tunneling microscopy (STM) and spectroscopy, low-energy electron diffraction, and angle resolved photoelectron spectroscopy (ARPES). In contrast with the well-ordered lattice structure, the local density of states at the surface clearly shows a strong doping dependent nanoscale electronic inhomogeneity, regardless of the fact of isovalent substitution. Remarkably, the surface electronic roughness measured by STM and the inverse spectral weight of quasiparticle states determined by ARPES are found to vary with x in the same manner as the bulk in-plane residual resistivity, following the Nordheim rule. For the first time, the surface measurements--especially those with STM--are shown to be in good agreement with the bulk transport results, all clearly indicating a doping-induced electronic disorder in the system.

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