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Register a new userEnergy gaps in high-$T_c$ superconductors: BCS after all?
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A major impediment to solving the problem of high-$T_c$ superconductivity is the ongoing confusion about the magnitude, structure and doping dependence of the superconducting gap, $Delta_0$, and of the mysterious pseudogap found in underdoped samplescite{TallonLoram}. The pseudogap opens around the ($pi$,0) antinodes below a temperature $T^*$ leaving Fermi arcs across the remnant Fermi surfacecite{Kanigel} on which the superconducting gap forms at $T_c$. One thing that seems agreed is that the ratio $2Delta_0/k_BT_c$ well exceeds the BCS value and grows with underdopingcite{Miyakawa1,Miyakawa2}, suggesting unconventional, non-BCS superconductivity. Here we re-examine data from many spectroscopies, especially Raman $B_{1g}$ and $B_{2g}$ scatteringcite{Sacuto,Guyard}, and reconcile them all within a two-gap scenario showing that the points of disagreement are an artefact of spectral-weight loss arising from the pseudogap. Crucially, we find that $Delta_0(p)$, or more generally the order parameter, now scales with the mean-field $T_c$ value, adopting the weak-coupling BCS ratio across the entire phase diagram.
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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.
The notion of a finite pairing interaction energy range suggested by Nam, results in some states at the Fermi level not participating in pairings when there are scattering centers such as impurities. The fact that not all states at the Fermi level participate in pairing is shown to suppress $T_c$ in an isotropic superconductor and destroy superconductivity. We have presented quantitative calculations of $T_c$ reduced via spinless impurities, in good agreements with data of Zn-doped YBCO and LSCO, respectively. It is not necessary to have the anisotropic order parameter, to account for the destruction of superconductivity via non-magnetic impurities.
We theoretically investigate the vortex state of the cuprate high-temperature superconductors in the presence of magnetic fields. Assuming the recently derived nonlinear $sigma$-model for fluctuations in the pseudogap phase, we find that the vortex cores consist of two crossed regions of elliptic shape, in which a static charge order emerges. Charge density wave order manifests itself as satellites to the ordinary Bragg peaks directed along the axes of the reciprocal copper lattice. Quadrupole density wave (bond order) satellites, if seen, are predicted to be along the diagonals. The intensity of the satellites should grow linearly with the magnetic field, in agreement with the result of recent experiments.
We address the origin of the Cooper pairs in high-$T_c$ cuprates and the unique nature of the superconducting (SC) condensate. Itinerant holes in an antiferromagnetic background form pairs spontaneously, without any `glue, defining a new quantum object the `pairon. In the incoherent pseudogap phase, above $T_c$ or within the vortex core, the pairon binding energies are distributed statistically, forming a `Cooper-pair glass. Contrary to conventional SC, it is the mutual pair-pair interaction that is responsable for the condensation. We give a natural explanation for the {it ergodic rigidity} of the excitation gap, being uniquely determined by the carrier concentration $p$ and $J$. The phase diagram can be understood, without spin fluctuations, in terms of a single energy scale $sim J$, the exchange energy at the metal-insulator transition.
The observation of an unusual spin resonant excitation in the superconducting state of various High-Tc ~copper oxides by inelastic neutron scattering measurements is reviewed. This magnetic mode % (that does not exist in conventional superconductors) is discussed in light of a few theoretical models and likely corresponds to a spin-1 collective mode.
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