Evolution of Magnetic and Superconducting Fluctuations with Doping of High- T _c Superconductors

Abstract

Electronic Raman scattering from high-and low-energy excitations was studied as a function of temperature, extent of hole doping, and energy of the incident photons in Bi 2 Sr 2 CaCu 2 O 8Ϯ␦ superconductors. For underdoped superconductors, short-range antiferromagnetic (AF ) correlations were found to persist with hole doping, and doped single holes were found to be incoherent in the AF environment. Above the superconducting (SC) transition temperature T c , the system exhibited a sharp Raman resonance of B 1g symmetry and energy of 75 millielectron-volts and a pseudogap for electron-hole excitations below 75 millielectron-volts, a manifestation of a partially coherent state forming from doped incoherent quasi particles. The occupancy of the coherent state increases with cooling until phase ordering at T c produces a global SC state.The normal state properties of doped cuprate high-temperature superconductors are markedly different from those of conventional metals and are usually viewed as manifestations of strong electron-electron correlations. These correlations cause the AF state in undoped cuprates. In the SC state, inelastic neutron scattering reveals a novel resonant magnetic excitation (1, 2). Here, we report a Raman active resonance that is present in doped cuprate superconductors above T c and gains strength with cooling.The doping phase diagram of high-T c cuprate superconductors and parent materials can be divided into four doping regions: (i) a spin S ϭ ½ AF insulator with the spin localized on Cu atoms of the CuO 2 planes, a strong superexchange constant J Ϸ 125 meV, and a high Néel temperature T N Ϸ 300 K that rapidly drops with hole doping in the CuO 2 planes until a metal-insulator transition is reached; (ii) an underdoped superconductor, where T c increases with increasing hole doping; (iii) an optimally doped superconductor, where T c reaches its maximum; and (iv) an overdoped superconductor, where the cuprate becomes a better metal as hole doping progresses and T c decreases. Two phase transition lines separate the "normal" high-temperature state from the low-temperature AF and SC phases.In addition to these AF and SC phase transitions, the phase diagram contains two crossover lines that start at high temperatures for low doping, decrease in temperature for the underdoped region, and merge at the SC transition line for the slightly overdoped SC (3). At the upper crossover temperature, short-range AF correlations develop, which, for very low doping and lower temperatures, evolve into the long-range ordered AF state. The second, lower, crossover temperature is experimentally suggested for the underdoped materials. At this temperature, the system develops a suppression of the density of lowenergy excited states, characterized as the result of a "pseudogap" (4). The gap removes only a fraction of the states at the Fermi energy (E F ). The material remains metallic and, moreover, shows an increase in the component of the electrical conductivity parallel to the CuO 2 planes (5). Nuclear magnetic re...

Theory of electronic Raman scattering in nearly antiferromagnetic Fermi liquids

“…Raman measurements on several systems have shown a remarkable channel dependence in the normal state for the optimallyand under-doped cuprates in a variety of systems [4][5][6][7][8]. For scattering geometries of B 1g symmetry, an almost [8] temperature independent Raman spectrum has been observed up to frequencies of a few J, while for B 2g orientations the spectra show a temperature dependence that tracks that of the DC resistivity [5,7]. Moreover, the overall magnitude of the electronic continuum is observed to be relatively independent of doping for the B 2g channel, but decreases dramatically with underdoping for the B 1g channel, with spectral weight transferring out to two-magnon energies [7,8].…”

“…For scattering geometries of B 1g symmetry, an almost [8] temperature independent Raman spectrum has been observed up to frequencies of a few J, while for B 2g orientations the spectra show a temperature dependence that tracks that of the DC resistivity [5,7]. Moreover, the overall magnitude of the electronic continuum is observed to be relatively independent of doping for the B 2g channel, but decreases dramatically with underdoping for the B 1g channel, with spectral weight transferring out to two-magnon energies [7,8]. One is to conclude that the qps near (π, 0) which are probed by the B 1g channel are particularly incoherent and become more incoherent with underdoping, in agreement with the results from ARPES.…”

Superconductivity-induced resonant Raman scattering in multilayer high-Tcsuperconductors

“…where ωL≈ωS and e L = e S ≡ e. The electronic Raman scattering has been intensively studied over a wide range of excitation energies in HTSC [20][21][22][23][24][25]. The resonant phenomena occur at around 2.0 eV and above 2.5 eV.…”

Interplay between the pseudogap and superconductivity in underdopedHgBa2CuO4+δsingle crystals

“…Being a two-particle probe, ERS is able to access the charge dynamics in both the normal and the superconducting states. 8,9,10,11 Moreover, through the use of particular sets of incident and scattered polarizations, it is able to probe different regions of the Fermi surface, i.e. the nodal (along the (0,0)-(π, π) direction) and antinodal (along the (0,0)-(π, 0) direction) quasiparticles.…”