Conductivity due to superconducting fluctuations studied in optimally doped YBa 2 Cu 3 O 7−δ films displays a stronger decay law in temperature than explainable by theory. A formula is proposed, which fits the data very well with two superconductive parameters, Tc and the coherence length ξ c0 , and an energy scale ∆*. This is also valid in underdoped materials and enables to describe the conductivity up to 300 K with a single-particle excitations channel in parallel with a channel whose contribution is The variation of the resistivity as a function of temperature in High-Tc superconductors (HTSC) remains to elucidate and in particular why it is so different in the underdoped and in the overdoped regions. At optimal doping in YBa 2 Cu 3 O 7−δ , the resistivity is linear from Tc to 325 K and extrapolates to zero resistivity at zero temperature. This cannot be explained by phonon dependency as it is well below the Debye temperature and has been depicted in the framework of the Marginal Fermi Liquid theory [1]. As soon as the material is underdoped, the resistivity exhibits no linear dependency any more but marked downward curvature from Tc to 325 K. When the material is strongly underdoped however, there seems to be a competition between this downward curvature and an upward curvature usually attributed to localisation. On the opposite, in the overdoped region of the phase diagram, the resistivity follows a rather more Fermi-liquid behaviour.One other peculiarity of most of the underdoped cuprates lies in the density of states in the normal state, which exhibits a depression firstly discovered by NMR measurements [2,3] and confirmed among others by specific heat [4], STM [5,6], ARPES [7-11] measurements… The energy scale on which this depression takes place is about the superconducting gap energy, which enables to think that the pseudogap could be related to superconductivity itself. This is the hypothesis of the particle-particle channel correlations [12][13][14][15][16]. However
Leridon et al. Reply: Luo et al. [1] report on the applicability of the formula proposed in Ref.[2] to extremely underdoped YBa 2 Cu 3 O 7ÿ thin films. The fit remains accurate even for the more underdoped samples. The variations of the fitting parameters a, b, c0 , and " 0 are consistent with our results, with physically correct orders of magnitude. However, Luo et al. claim that the variations of two parameters ''raise disturbing obscurities.'' We answer them on the following points.(i) If ''conventional wisdom'' says that a residual resistivity cannot be negative, it also says that the extrapolation to zero temperature of the high-temperature behavior of the resistivity never gives the ''residual resistivity.'' To estimate the residual resistivity one has to know the variation at low temperature of the normal-state resistivity, which is, by definition, impossible in a superconductor at zero frequency. Numerous examples could be shown where the extrapolation to zero of hightemperature resistivity gives a negative value: most of high-quality optimally doped high-T c single crystals [3], underdoped samples [3,4], and even good metals as gold (between 40 and 295 K, the extrapolation to zero gives a negative resistance only 6 times smaller than the room temperature resistivity) [5]. However, the physical meaning of b remains an open question, as does the nature of the normal state in optimally doped and underdoped cuprates, and the apparent contradictory behavior between Hall effect and resistivity, etc. In absence of a clear consensual theory for the normal-state resistivity of high temperature superconductors, nobody is able to make predictions on the values of b and decide whether it is ''artificial'' or not. The value of b might nevertheless be related to the defect concentration, and, on this point, we have an observation. There is no reason to think that the oxygen concentration can be varied in the proportion given by the authors without increasing the level of defects in the sample. Underdoping implies then two different effects: the decrease of the number of carriers and the increase of disorder due to oxygen vacancies. Both can contribute differently to a, b, 1 , or T 0 , and this may be the origin of the change of slope in the variation of b. It is probably not very accurate to test the expression proposed in [2] on the more underdoped samples where, obviously, carrier localization occurs and where two additional parameters ( 1 and T 0 ) may lead to a multivalued set of solutions. The interest of the work presented in [2] lies more in the observation of modified Aslamazov-Larkin fluctuations above T c in the slightly underdoped compounds than in the existence or not of a variable range hopping term in the strongly underdoped. However, we found it of interest to offer a consistent scenario for the whole phase diagram.(ii) The variation of the parameter is somewhat more puzzling. The authors find that increases and
We propose the use of two-dimensional (2D) photonic crystals (PhCs) with engineered defects for the generation of an arbitrary-profile beam from a focused input beam. The cylindrical harmonics expansion of complex-source beams is derived and used to compute the scattered wave function of a 2D PhC via the multiple scattering method. The beam shaping problem is then solved using a genetic algorithm. We illustrate our procedure by generating different orders of Hermite-Gauss profiles, while maintaining reasonable losses and tolerance to variations in the input beam and the slab refractive index.
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