Normal-state gap

Figure 1 3 1. Energetic characteristics of a model cuprate on the doping scale. 1 - the underdoped state small pseudogap As 2 - the large pseudogap A, 3 - the defect system superconducting gap Aa 4 - the itinerant system superconducting gap Ay 5 - Tc. The insert shows normal state gaps. p = 0.18 Pp- 0.12 0 0.23 p(Tcm) = 0.23]...

The ratio Ap/kTc is nearly constant in the optimal doping region and it increases rapidly with c diminishing from c0. It is possible to speculate on various further properties of cuprates on the basis of the present model. If one asks about the temperature dependence of the normal state gaps, one must incorporate the complicated calculation of Qq T) [8] and account for the fluctuations of the superconductivity order partameter. 

Keywords Electron doped cuprates, optical conductivity, normal state gap... 

Recently, angle-resolved photoemission spectroscopy (ARPES) for Bi2212 showed that the electronic density of states of underdoped cuprates reveals a normal-state gap-... 

As previously discussed, in anion gap metabolic acidosis, the isoelectric state is maintained because unmeasured anions are present. With a normal anion gap metabolic acidosis, the isoelectric state is maintained by an increase in the measured... 

The Greek indices a,j3= II, B,G) count colors, the Latin indices i = u,d,s count flavors. The expansion is presented up to the fourth order in the diquark field operators (related to the gap) assuming the second order phase transition, although at zero temperature the transition might be of the first order, cf. [17], iln is the density of the thermodynamic potential of the normal state. The order parameter squared is D = d s 2 = dn 2 + dG 2 + de 2, dR dc dB for the isoscalar phase (IS), and D = 3 g cfl 2,... 

The Meissner effect is a very important characteristic of superconductors. Among the consequences of its linkage to the free energy are the following (a) The superconducting state is more ordered than the normal state (b) only a small fraction of the electrons in a solid need participate in superconductivity (c) the phase transition must be of second order that is, there is no latent heat of transition in the absence of any applied magnetic field and (d) superconductivity involves excitations across an energy gap. 

The above picture is in a good agreement with the theory of itinerant electron systems with interplay between superconductivity and magnetism [8], In that theory, an itinerant SDW gap may appear at the Fermi surface only before an SC gap, i.e. in the normal state. This SDW gap is highly anisotropic since it is only formed at symmetric parts of the Fermi surface [8] ( see, fig.2). Its width ASDW being unusually large for an SC gap, well conforms to that for an SDW gap because of inequality ASc < ASDW... 

This quantity has been computed and is shown in Figure 10 and seems to provide a good description of the experimental data up to Tc. In order to describe the susceptibility above Tc other singlet excitations not at heart related to the superconductivity can be invoked. Therefore we are in accord with Loram etal [26] whose view is that the normal state spin gap is not essentially related to the superconducting pairing. However such excitations in the normal state are yet to be included in our theory but our conjecture is that this will not alter... 

We consider the normal state spin-gap as of indirect significance for high temperature superconductivity but further work is needed to substantiate this standpoint. 

Figure 5. The energy gap in the normal state determined by fitting to the specific heat data with a model density of states by Loram et al. is shown in green. The tunneling experiments well below l c give the gap shown in red in agreement with ARPES shown in blue.

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