The superconducting state of underdoped cuprates is often described in terms of a single energyscale, associated with the maximum of the (d-wave) gap. Here, we report on electronic Raman scattering results, which show that the gap function in the underdoped regime is characterized by two energy scales, depending on doping in opposite manners. Their ratios to the maximum critical temperature are found to be universal in cuprates. Our experimental results also reveal two different quasiparticle dynamics in the underdoped superconducting state, associated with two regions of momentum space: nodal regions near the zeros of the gap and antinodal regions. While antinodal quasiparticles quickly loose coherence as doping is reduced, coherent nodal quasiparticles persist down to low doping levels. A theoretical analysis using a new sum-rule allows us to relate the low-frequency-dependence of the Raman response to the temperature-dependence of the superfluid density, both controlled by nodal excitations.

SrTiO 3 , a quantum paraelectric 1 , becomes a metal with a superconducting instability after removal of an extremely small number of oxygen atoms 2 . It turns into a ferroelectric upon substitution of a tiny fraction of strontium atoms with calcium 3 . The two orders may be accidental neighbours or intimately connected, as in the picture of quantum critical ferroelectricity 4 . Here, we show that in Sr 1−x Ca x TiO 3−δ (0.002 < x < 0.009, δ < 0.001) the ferroelectric order coexists with dilute metallicity and its superconducting instability in a finite window of doping. At a critical carrier density, which scales with the Ca content, a quantum phase transition destroys the ferroelectric order. We detect an upturn in the normal-state scattering and a significant modification of the superconducting dome in the vicinity of this quantum phase transition. The enhancement of the superconducting transition temperature with calcium substitution documents the role played by ferroelectric vicinity in the precocious emergence of superconductivity in this system, restricting possible theoretical scenarios for pairing.A perovskite of the ABO 3 family, SrTiO 3 is a quantum paraelectric whose dielectric constant rises to ∼20,000 at low temperature 1 , but avoids long-range ferroelectric order. It becomes a metal by substituting Sr with La, Ti with Nb, or by removing O. It has been known for half a century that this metal is a superconductor at low temperatures 2 . More recently, a sharp Fermi surface and a superconducting ground state have been found to persist down to a carrier concentration of 10 17 cm −3 in SrTiO 3−δ (refs 5,6 However, mobile electrons screen polarization and therefore only insulating solids are expected to host a ferroelectric order. Hitherto, as a paradigm, ferroelectric quantum criticality, in contrast to its magnetic counterpart, was deprived of an experimental phase diagram in which a superconducting phase and a ferroelectric order share a common boundary.Here, we produce such a phase diagram in the case of Sr 1−x Ca x TiO 3−δ . The main new observations are the following: metallic Sr 1−x Ca x TiO 3−δ hosts a phase transition structurally indistinguishable from the ferroelectric phase transition in insulating Sr 1−x Ca x TiO 3 ; the coexistence between this ferroelectric-like order and superconductivity ends beyond a threshold carrier concentration; and, in the vicinity of this quantum phase transition, calcium substitution enhances the superconducting critical temperature and induces an upturn in the normal-state resistivity.Figure 1 summarizes what we know about the emergence of ferroelectricity, metallicity and superconductivity in this system. When a small fraction of Sr atoms (x > 0.002) is replaced with isovalent Ca, Sr 1−x Ca x TiO 3 becomes ferroelectric 3 , with a Curie temperature steadily increasing with Ca content in the dilute limit 0.002 < x < 0.02 (refs 3,13,14). Macroscopic polarization below the Curie temperature has been observed in dielectric and linear birefringence measurements, a...

We unravel the magnon spectra of BiFeO3 by means of low-energy inelastic light scattering. We show the existence of two species of magnons corresponding to spin wave excitations in and out of the cycloidal plane. These excitations might be interpreted as electromagnon modes. The present observations present an unique opportunity to study the competition between ferroelectric and magnetic orders.