Tunneling spectroscopy has played a central role in the experimental verification of the microscopic theory of superconductivity in classical superconductors. Initial attempts to apply the same approach to high-temperature superconductors were hampered by various problems related to the complexity of these materials. The use of scanning tunneling microscopy and spectroscopy ͑STM and STS͒ on these compounds allowed the main difficulties to be overcome. This success motivated a rapidly growing scientific community to apply this technique to high-temperature superconductors. This paper reviews the experimental highlights obtained over the last decade. The crucial efforts to gain control over the technique and to obtain reproducible results are first recalled. Then a discussion on how the STM and STS techniques have contributed to the study of some of the most unusual and remarkable properties of high-temperature superconductors is presented: the unusually large gap values and the absence of scaling with the critical temperature, the pseudogap and its relation to superconductivity, the unprecedented small size of the vortex cores and its influence on vortex matter, the unexpected electronic properties of the vortex cores, and the combination of atomic resolution and spectroscopy leading to the observation of periodic local density of states modulations in the superconducting and pseudogap states and in the vortex cores.

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We report scanning tunneling spectroscopy imaging of the vortex lattice in single crystalline MgB2. By tunneling parallel to the c axis, a single superconducting gap (Delta=2.2 meV) associated with the pi band is observed. The vortices in the pi band have a large core size compared to estimates based on H(c2) and show an absence of localized states in the core. Furthermore, superconductivity between the vortices is rapidly suppressed by an applied field. These results suggest that superconductivity in the pi band is, at least partially, induced by the intrinsically superconducting sigma band.

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Using scanning tunneling spectroscopy, we investigated the temperature dependence of the quasiparticle density of states of overdoped Bi(2)Sr(2)CuO(6+delta) between 275 mK and 82 K. Below T(c) = 10 K, the spectra show a gap with well-defined coherence peaks at +/-Delta(p) approximately 12 meV, which disappear at T(c). Above T(c), the spectra display a clear pseudogap of the same magnitude, gradually filling up and vanishing at T(*) approximately 68 K. The comparison with Bi(2)Sr(2)CaCu(2)O(8+delta) demonstrates that the pseudogap and the superconducting gap scale with each other, providing strong evidence that they have a common origin.

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We present electronic-structure calculations, electrical resistivity data, and the first specific-heat measurements in the normal and superconducting states of quasi-one-dimensional M 2 Mo 6 Se 6 ͑M =Tl,In,Rb͒. Rb 2 Mo 6 Se 6 undergoes a metal-insulator transition at ϳ170 K: electronic-structure calculations indicate that this is likely to be driven by the formation of a dynamical charge-density wave. However, Tl 2 Mo 6 Se 6 and In 2 Mo 6 Se 6 remain metallic down to low temperature, with superconducting transitions at T c = 4.2 K and 2.85 K, respectively. The absence of any metal-insulator transition in these materials is due to a larger in-plane bandwidth, leading to increased interchain hopping which suppresses the density wave instability. Electronic heat-capacity data for the superconducting compounds reveal an exceptionally low density of states D E F = 0.055 states eV −1 atom −1 , with BCS fits showing 2⌬ / k B T c Ն 5 for Tl 2 Mo 6 Se 6 and 3.5 for In 2 Mo 6 Se 6 . Modeling the lattice specific heat with a set of Einstein modes, we obtain the approximate phonon density of states F͑͒. Deconvolving the resistivity for the two superconductors then yields their electron-phonon transport coupling function ␣ tr 2 F͑͒. In Tl 2 Mo 6 Se 6 and In 2 Mo 6 Se 6 , F͑͒ is dominated by an optical "guest ion" mode at ϳ5 meV and a set of acoustic modes from ϳ10 to 30 meV. Rb 2 Mo 6 Se 6 exhibits a similar spectrum; however, the optical phonon has a lower intensity and is shifted to ϳ8 meV. Electrons in Tl 2 Mo 6 Se 6 couple strongly to both sets of modes, whereas In 2 Mo 6 Se 6 only displays significant coupling in the 10-18 meV range. Although pairing is clearly not mediated by the guest ion phonon, we believe it has a beneficial effect on superconductivity in Tl 2 Mo 6 Se 6 , given its extraordinarily large coupling strength and higher T c compared to In 2 Mo 6 Se 6 .

Tunneling spectroscopy has played a central role in the experimental verification of the microscopic theory of superconductivity in classical superconductors. Initial attempts to apply the same approach to high-temperature superconductors were hampered by various problems related to the complexity of these materials. The use of scanning tunneling microscopy and spectroscopy ͑STM and STS͒ on these compounds allowed the main difficulties to be overcome. This success motivated a rapidly growing scientific community to apply this technique to high-temperature superconductors. This paper reviews the experimental highlights obtained over the last decade. The crucial efforts to gain control over the technique and to obtain reproducible results are first recalled. Then a discussion on how the STM and STS techniques have contributed to the study of some of the most unusual and remarkable properties of high-temperature superconductors is presented: the unusually large gap values and the absence of scaling with the critical temperature, the pseudogap and its relation to superconductivity, the unprecedented small size of the vortex cores and its influence on vortex matter, the unexpected electronic properties of the vortex cores, and the combination of atomic resolution and spectroscopy leading to the observation of periodic local density of states modulations in the superconducting and pseudogap states and in the vortex cores.