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If high temperature cuprate superconductivity is due to electronic correlations, then the energy difference between the normal and superconducting states can be expressed in terms of the occupied part of the single particle spectral function. The latter can, in principle, be determined from angle resolved photoemission (ARPES) data. As a consequence, the energy gain driving the development of the superconducting state is intimately related to the dramatic changes in the photoemission lineshape when going below Tc. These points are illustrated in the context of the mode model used to fit ARPES data in the normal and superconducting states, where the question of kinetic energy versus potential energy driven superconductivity is explored in detail. We use our findings to comment on the relation of ARPES data to the condensation energy, and to various other experimental data. In particular, our results suggest that the nature of the superconducting transition is strongly related to how anomalous (non Fermi liquid like) the normal state spectral function is, and as such, is dependent upon the doping level.
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In conventional BCS superconductors, the electronic kinetic energy increases upon superfluid condensation (the change DEkin is positive). Here we show that in the high critical temperature superconductor Bi-2212, DEkin crosses over from a fully compatible conventional BCS behavior (DEkin>0) to an unconventional behavior (DEkin<0) as the free carrier density decreases. If a single mechanism is responsible for superconductivity across the whole phase diagram of high critical temperature superconductors, this mechanism should allow for a smooth transition between such two regimes around optimal doping.
In conventional metals, electron-phonon coupling, or the phonon-mediated interaction between electrons, has long been known to be the pairing interaction responsible for the superconductivity. The strength of this interaction essentially determines the superconducting transition temperature TC. One manifestation of electron-phonon coupling is a mass renormalization of the electronic dispersion at the energy scale associated with the phonons. This renormalization is directly observable in photoemission experiments. In contrast, there remains little consensus on the pairing mechanism in cuprate high temperature superconductors. The recent observation of similar renormalization effects in cuprates has raised the hope that the mechanism of high temperature superconductivity may finally be resolved. The focus has been on the low energy renormalization and associated kink in the dispersion at around 50 meV. However at that energy scale, there are multiple candidates including phonon branches, structure in the spin-fluctuation spectrum, and the superconducting gap itself, making the unique identification of the excitation responsible for the kink difficult. Here we show that the low-energy renormalization at ~50 meV is only a small component of the total renormalization, the majority of which occurs at an order of magnitude higher energy (~350 meV). This high energy kink poses a new challenge for the physics of the cuprates. Its role in superconductivity and relation to the low-energy kink remains to be determined.
Recent photoemission data in the high temperature cuprate superconductor Bi2212 have been interpreted in terms of a sharp spectral peak with a temperature independent lifetime, whose weight strongly decreases upon heating. By a detailed analysis of the data, we are able to extract the temperature dependence of the electron self-energy, and demonstrate that this intepretation is misleading. Rather, the spectral peak loses its integrity above Tc due to a large reduction in the electron lifetime.
The spectral energy gap is an important signature that defines states of quantum matter: insulators, density waves, and superconductors have very different gap structures. The momentum resolved nature of angle-resolved photoemission spectroscopy (ARPES) makes it a powerful tool to characterize spectral gaps. ARPES has been instrumental in establishing the anisotropic d-wave structure of the superconducting gap in high-transition temperature (Tc) cuprates, which is different from the conventional isotropic s-wave superconducting gap. Shortly afterwards, ARPES demonstrated that an anomalous gap above Tc, often termed the pseudogap, follows a similar anisotropy. The nature of this poorly understood pseudogap and its relationship with superconductivity has since become the focal point of research in the field. To address this issue, the momentum, temperature, doping, and materials dependence of spectral gaps have been extensively examined with significantly improved instrumentation and carefully matched experiments in recent years. This article overviews the current understanding and unresolved issues of the basic phenomenology of gap hierarchy. We show how ARPES has been sensitive to phase transitions, has distinguished between orders having distinct broken electronic symmetries, and has uncovered rich momentum and temperature dependent fingerprints reflecting an intertwined & competing relationship between the ordered states and superconductivity that results in multiple phenomenologically-distinct ground states inside the superconducting dome. These results provide us with microscopic insights into the cuprate phase diagram.
We review some previous studies concerning the intra-bilayer Josephson plasmons and present new ellipsometric data of the c-axis infrared response of almost optimally doped Bi_{2}Sr_{2}CaCu_{2}O_{8}. The c-axis conductivity of this compound exhibits the same kind of anomalies as that of underdoped YBa_{2}Cu_{3}O_{7-delta}. We analyze these anomalies in detail and show that they can be explained within a model involving the intra-bilayer Josephson effect and variations of the electric field inside the unit cell. The Josephson coupling energies of different bilayer compounds obtained from the optical data are compared with the condensation energies and it is shown that there is a reasonable agreement between the values of the two quantities. We argue that the Josephson coupling energy, as determined by the frequency of the intra-bilayer Josephson plasmon, represents a reasonable estimate of the change of the effective c-axis kinetic energy upon entering the superconducting state. It is further explained that this is not the case for the estimate based on the use of the simplest ``tight-binding sum rule. We discuss possible interpretations of the remarkable agreement between the Josephson coupling energies and the condensation energies. The most plausible interpretation is that the interlayer tunneling of the Cooper pairs provides the dominant contribution to the condensation energy of the bilayer compounds; in other words that the condensation energy of these compounds can be accounted for by the interlayer tunneling theory. We suggest an extension of this theory, which may also explain the high values of T_{c} in the single layer compounds Tl_{2}Ba_{2}CuO_{6} and HgBa_{2}CuO_{4}, and we make several experimentally verifiable predictions.
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