Superconductivity through Quantum Critical Fluctuations in the ...

erg function is angle independent below the cutoff c putsan important constraint on the microscopic understanding ofthe cuprates. For example, it can put a limit on the correlationlength for the commonly assumed form of the antiferromagneticAF fluctuations. A phenomenological form ofthe overdamped AF fluctuations by the form: may be written as 2,30AFM fluct. spectra or any other spectra specified by acorrelation lengthis ruled out. AF k,k, = 2 / AFk − k − Q 2 2 +1 2 + / AF 2 . 18 AF , can be obtained after the integral over with bothMOMENTUM DEPENDENCE OF THE SINGLE-PARTICLE…k and k on the Fermi surface, that is,1.00.8 AF , = AF k,k,⇥ = a, , =0, 5, .., 2519where k and0.6k have the angle and with respect to thenodal cut, respectively. A straightforward = a/⇥ calculation revealsΧAFΘ,Ω0.4that a weak dependence of AF , means that /a10.2for AF , where AF is the characteristic AF energy scale.0.0This is shown 0in Fig. 1 10 for 2 /a=1/ 3 4 with5the blue and for/a=1 with the red lines. ΩΩFor AF each , the angles are =0° ,5° ,10° ,15° ,20° ,25° from above. As expected,FIG. 10. Color online The model Eliashberg function calculated, from becomes the overdamped angle independent as is decreased. The AFcollapse of 2 AF fluctuations of Eq. 18. The red andblue lines are forF, the AF correlation implieslength that/a=1 if it and is due 1/, to respec- the AF fluc-As discuss0.2 eV, thatonly to the8 is only atherefore fotex correcticonclusionstuation spefrequencywhich PHYS in dthe upper cbandwidthcorrectionsclusions haOne finaduced specfor the supparticle selthen followof the fluctof the supestudy of thAn angle-independentquantum-critical spectra hyliquid description ofmicroscopically 31,32 to beregion of the phase diagratum melting of the loopunderdopedregion of the cdeduced 2 F, whichthe low-energy bump atpresence of this bump maIm , which is notT. The linearity maytheory and earlier ARPESnot have the high resolutTc < 10 K for correlation length of a lattice constant.