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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Cuprate high-T c superconductors exhibit enigmatic behavior in the nonsuperconducting state. For carrier concentrations near "optimal doping" (with respect to the highest T c s) the transport and spectroscopic properties are unlike those of a Landau-Fermi liquid. On the Mott-insulating side of the optimal carrier concentration, which corresponds to underdoping, a pseudogap removes quasiparticle spectral weight from parts of the Fermi surface and causes a breakup of the Fermi surface into disconnected nodal and antinodal sectors. Here, we show that the near-nodal excitations of underdoped cuprates obey Fermi liquid behavior. The lifetime τ(ω, T) of a quasi-particle depends on its energy ω as well as on the temperature T. For a Fermi liquid, 1/τ(ω, T) is expected to collapse on a universal function proportional to (h ω) 2 + (pπk B T) 2 . Magnetotransport experiments, which probe the properties in the limit ω = 0, have provided indications for the presence of a T 2 dependence of the dc (ω = 0) resistivity of different cuprate materials. However, Fermi liquid behavior is very much about the energy dependence of the lifetime, and this can only be addressed by spectroscopic techniques. Our optical experiments confirm the aforementioned universal ω-and T dependence of 1/τ(ω, T), with p ∼ 1.5. Our data thus provide a piece of evidence in favor of a Fermi liquid-like scenario of the pseudogap phase of the cuprates.optical spectroscopy | superconductivity | mass renormalization | self energy T he compound HgBa 2 CuO 4+δ (Hg1201) is the single-layer cuprate that exhibits the highest T c (97 K). We therefore measured the optical conductivity of strongly underdoped single crystals of Hg1201 ðT c = 67 KÞ. Here we are interested in the optical conductivity of the CuO 2 layers. We therefore express the optical conductivity as a 2D sheet conductance GðωÞ = d c σðωÞ, where d c is the interlayer spacing. The real part of the sheet conductance normalized by the conduction quantum G 0 = 2e 2 =h is shown in Fig. 1. As seen in the figure, a gap-like suppression below 140 meV is clearly observable for temperatures below T c and remains visible in the normal state up to ∼250 K. This is a clear optical signature of the pseudogap. We also observe the zero-energy mode due to the free charge carrier response, which progressively narrows upon lowering the temperature. In materials where the charge carrier relaxation is dominated by impurity scattering, the width of this "Drude" peak corresponds to the relaxation rate of the charge carriers. Relaxation processes arising from interactions have the effect of replacing the constant (frequency-independent) relaxation rate with a frequencydependent one. The general expression for the optical conductivity of interacting electrons is then Gðω; TÞ = iπK Zω + Mðω; TÞ G 0 :[1]The spectral weight K corresponds to minus the kinetic energy if the frequency integration of the experimental data is restricted to intraband transitions. The effect of electron-electron interactions and coupling to collective mo...

We explore the interplay of electron-electron correlations and spin-orbit coupling in the model Fermi liquid Sr2RuO4 using laser-based angle-resolved photoemission spectroscopy. Our precise measurement of the Fermi surface confirms the importance of spin-orbit coupling in this material and reveals that its effective value is enhanced by a factor of about two, due to electronic correlations. The self-energies for the β and γ sheets are found to display significant angular dependence. By taking into account the multi-orbital composition of quasiparticle states, we determine self-energies associated with each orbital component directly from the experimental data. This analysis demonstrates that the perceived angular dependence does not imply momentum-dependent many-body effects, but arises from a substantial orbital mixing induced by spin-orbit coupling. A comparison to single-site dynamical mean-field theory further supports the notion of dominantly local orbital self-energies, and provides strong evidence for an electronic origin of the observed non-linear frequency dependence of the self-energies, leading to 'kinks' in the quasiparticle dispersion of Sr2RuO4. * present address: ISIS Facility, Rutherford

We report optical measurements demonstrating that the low-energy relaxation rate (1/τ) of the conduction electrons in Sr 2 RuO 4 obeys scaling relations for its frequency (ω) and temperature (T ) dependence in accordance with Fermi-liquid theory. In the thermal relaxation regime, 1/τ ∝ (ħ hω) 2 + (pπk B T ) 2 with p = 2, and ω/T scaling applies. Many-body electronic structure calculations using dynamical mean-field theory confirm the low-energy Fermi-liquid scaling, and provide quantitative understanding of the deviations from Fermi-liquid behavior at higher energy and temperature. The excess optical spectral weight in this regime provides evidence for strongly dispersing "resilient" quasiparticle excitations above the Fermi energy. PACS numbers: 78.47.db, 71.10.Ay, 72.15.Lh, 74.70.Pq Liquids of interacting fermions yield a number of different emergent states of quantum matter. The strong correlations between their constituent particles pose a formidable theoretical challenge. It is therefore remarkable that a simple description of low-energy excitations of fermionic quantum liquids could be established early on by Landau [1], in terms of a dilute gas of "quasiparticles" with a renormalized effective mass, of which 3 He is the best documented case [2, 3].Breakdown of the quasiparticle concept can be observed in the transport of metals tuned onto a quantum phase transition, but Fermi-liquid (FL) behavior is retrieved away from the quantum-critical region [4, 5]. The relevance of FL theory to electrons in solids is documented by a number of materials, such as transition metals [6], heavy-fermion compounds [7], and doped semiconductors [8]. Among transition-metal oxides, Sr 2 RuO 4 is a remarkable example which has been heralded as the solid-state analogue of 3 He [9] for at least three reasons: remarkably large and clean monocrystalline samples can be prepared, transport properties display low-temperature FL characteristics [10], and there is evidence for p-wave symmetry of its superconducting phase [11], as in superfluid 3 He.FL theory makes a specific prediction for the universal energy and temperature dependence of the inelastic lifetime of quasiparticles: Because of phase-space constraints imposed by the Pauli principle as well as momentum and energy conservation, it diverges as 1/ω 2 or 1/T 2 [1, 5]. More precisely, the inelastic optical relaxation rate is predicted to vanish according to the scaling law 1/τ ∝ (ħ hω) 2 + (pπk B T ) 2 , with p = 2 [12][13][14]. This leads to universal ω/T scaling of the optical conductivity σ(ω) in the thermal regime ħ hω ∼ k B T [14]. Surprisingly however, despite almost 60 years of research on Fermi liquids, this universal behavior of the optical response, and especially the specific statistical factor p = 2 relating the energy and temperature dependence have not yet been established experimentally [13][14][15][16][17].Here, we report optical measurements of Sr 2 RuO 4 with 0.1 meV resolution [18,19] which reveal this universal FL scaling law [20]. We establish experiment...