Electronic phase diagram of high-temperature copper oxide superconductors

Abstract

In order to understand the origin of high-temperature superconductivity in copper oxides, we must understand the normal state from which it emerges. Here, we examine the evolution of the normal state electronic excitations with temperature and carrier concentration in Bi 2 Sr 2 CaCu 2 O 8þδ using angle-resolved photoemission. In contrast to conventional superconductors, where there is a single temperature scale T c separating the normal from the superconducting state, the high-temperature superconductors exhibit two additional temperature scales. One is the pseudogap scale T Ã , below which electronic excitations exhibit an energy gap. The second is the coherence scale T coh , below which sharp spectral features appear due to increased lifetime of the excitations. We find that T Ã and T coh are strongly doping dependent and cross each other near optimal doping. Thus the highest superconducting T c emerges from an unusual normal state that is characterized by coherent excitations with an energy gap.cuprates | photoelectron spectroscopy G eneral features of the phase diagram of the copper oxide superconductors have been known for some time. The superconducting transition temperature T c has a dome-like shape in the doping-temperature plane with a maximum near a doping δ ∼ 0.167 electrons per Cu atom. Although in conventional metals the electronic excitations for T > T c are (i) gapless and (ii) sharply defined at the Fermi surface (1), the cuprates violate at least one of these conditions over much of their phase diagram. These deviations from conventional metallic behavior are most easily described in terms of two energy scales T Ã (2, 3) and T coh (4), which correspond to criteria (i) and (ii), respectively.To address the role of these energy scales in defining the phase diagram, we concentrate on spectra where the superconducting energy gap is largest, the antinode [ðπ;0Þ → ðππÞ Fermi crossing], where the spectral changes with doping and temperature are most pronounced (the SI Appendix has further details). Spectral changes at the node have been previously studied by Valla et al.(5) and such spectra remain gapless for all doping values (6). In Fig. 1, we show spectra at fixed temperature as a function of doping. Data points are indicated in Fig. 1A (See SI Appendix for experimental conditions and sample details). Initially, we show spectra at fixed momenta as a function of energy (energy distribution curves, or EDCs) that have been symmetrized (7) about the Fermi energy to remove the effects of the Fermi function. Later, we show that equivalent results are obtained from division of the EDCs by a resolution-broadened Fermi function. In the following figures, because two values of the doping can result in the same T c , samples are labeled as OP for optimally doped, OD for overdoped, and UD for underdoped.The spectra at the antinode at the highest temperature (approximately 300 K) in Fig. 1D show two remarkable features: They are extremely broad in energy, exceeding any expected thermal broadening, and their line...

Signatures of superconductivity and pseudogap formation in nonequilibrium nodal quasiparticles revealed by ultrafast angle-resolved photoemission

“…3 matches the superconducting critical temperature T c measured by SQUID; (2) T p -node coincides with the onset temperature of superconducting phase fluctuations measured by Nernst effect; 31 and (3) T * -node coincides with the pseudogap temperature extracted from various momentum integrated probes 24,[33][34][35][36] and from ARPES along the antinodal direction (T * -antinode). 7,13,25 Revealing the presence of these energy scales in the spectral function of ungapped quasiparticles disrupts the conventional view that T c , T p , and T * are only associated with gapped antinodal states. The signature at T * is perhaps the most surprising of these, as the most popular explanation for the pseudogap phase at present is that it is associated with onset of charge ordering with a nesting vector along the (π,0) direction, resulting therefore in strongly suppressed antinodal electronic states.…”

“…3(d)), suggesting that the pseudogap temperature T * can be defined even for this overdoped sample, consistent with recent reports by equilibrium ARPES on antinodal quasiparticles. 13,25 The step indicates that nonequilibrium electronic states below T * result in a larger contribution to ∆I e at the node, even though there is no gap at the node itself as generally believed.…”

Doping Dependencies of Onset Temperatures for the Pseudogap and Superconductive Fluctuation in Bi2Sr2CaCu2O8+δ, Studied from Both In-Plane and Out-of-Plane Magnetoresistance Measurements

“…It is not yet conclusive whether it is a necessary ingredient (precursor) for high-T c superconductivity [1][2][3][4][5] or if it is a different ordered state. [6][7][8] In the former case, the pseudogap opening temperature T * coincides with the onset temperature of superconductive fluctuation, T sc f , and may merge with T c in the overdoped state.…”

Influence of optically quenched superconductivity on quasiparticle relaxation rates inBi2Sr2CaCu2O8+δ

“…Figure 4 shows nodal quasiparticle relaxation dynamics at comparable excitation densities (≈ 24 µJ/cm 2 ) for multiple dopings of Bi2212, corresponding to critical temperatures T c = 78 K (underdoped, UD78K), T c = 91 K (nearly optimally doped, OP91K), T c = 78 K (overdoped, OD78K), and T c = 59 K (very overdoped, OD59K). For the first three dopings, both equilibrium ARPES 47,48 and time-resolved ARPES 32 measurements have previously identified distinct transition temperatures T c and T * for the onset of superconductivity and the pseudogap, with T * occurring at 200 K for the UD78K sample, 150 K for the OP91K sample, and 97 K for the OD78K sample. The OD59K sample has no equilibrium pseudogap 47,48 .…”

“…For the first three dopings, both equilibrium ARPES 47,48 and time-resolved ARPES 32 measurements have previously identified distinct transition temperatures T c and T * for the onset of superconductivity and the pseudogap, with T * occurring at 200 K for the UD78K sample, 150 K for the OP91K sample, and 97 K for the OD78K sample. The OD59K sample has no equilibrium pseudogap 47,48 . In spite of these differences, two- • , φ = 37…”