Zero-field current density, temperature

Insight into the temperature dependence of the zero-field current density can be obtained by considering a theoretical upper limit to current density of a superconductor, namely, the "depairing current density , where the kinetic energy of the superconducting electrons equals the condensation energy H2/8tt. At low temperatures and zero applied field, one finds (14)... 

Fig. 8 Temperature dependence of the zero field hole mobility in the low carrier density limit in a polyfluorene copolymer. The data are inferred from space-charge-limited current experiments and analyzed in terms of the extended Gaussian disorder model (see Sect. 4.1). From [90] with permission. Copyright (2008) by the American Institute of Physics...

Current-voltage (I-V) characteristics were also measured at different temperatures in magnetic fields applied perpendicularly to the surface of the substrate, i.e. parallel to the c-axis of the film. The critical current densities at T=2.1 K and in zero field are above 10 A/m. They have been defined by the electric field criterion E=Ec=10 V/cm. As an example, I-V characteristics for different values of the external magnetic field at T = 4.2 K are reported in Fig. 2. The values of the measured critical current density are slightly lower with respect to some others reported in the literature which, however, refer to epitaxial thin films in which Ce doping level was equal to its optimum value x = 0.15 [9]. We believe this is related to the reduced value of the critical temperature T in this system with respect to the optimally Ce-doped samples. 

A/cm2 at 77 K, more than an order of magnitude lower than at 4.2 K. Thus YBaCuO at 77 K has a fundamental disadvantage in zero-field critical current density compared to, say, Nb3Sn at 4.2 K. The same effect impacts the hope for practical room temperature superconductors To maintain reasonable critical current density at 300 K or 27 C, the superconducting transition would have to be closer to 400 K or 127 C ... 

Critical current density also depends on magnetic field, decreasing monotonically to zero at the upper critical field Hc2 (16-17). In YBaCuO the slope of Hc2 with temperature is unusually large, of order 2 T/K when field is applied parallel to the predominant conduction planes of the structure (18-19). This implies record values (up to 200 T has been estimated) for the upper critical field at low temperatures and opens up the possibility of very high field magnets. 

A portion of the film on SrTi03 shown in fig. 13(b) was patterned into a 16 urn wide line by reactive ion etdiing to measure the critical current density and for other magnetotransport measurements. Figure 14 shows the temperature dependence of the critical current density, J. It can been seen that at 77 K and in zero field, a current density of 0.69 x 10 A/cm is measured. The film critical current density is greater than 4 x 10 A/cstr at 50 K and in a field of 14 Tesla. More detailed magnetotransport results will be mentioned later. 

Figure 14. Critical current density as a function of temperature for an as depouted film on (100) SrTi03. at 77 K is 0.69 X 10 fi/atr in zero field.

Critical current densities on the order of 10 A cm at 77 K in zero field were measured on BSCCO thin films. In Fig. 4.2-46 the field dependence of 7c of a B12212 film is shown for two temperatures [2.90] and Fig.4.2-47 demonstrates the Jc(B, T) dependence of a B12223 film [2.87]. In magnetic fields aligned parallel to the plane of the film, that is perpendicular to the c axis of the crystal structure, 7c is practically independent on the field strength, even at higher temperatures such as 60 K. The reasons for this behavior are discussed below in connection with the Jc(B, T) correlation of wires and tapes. 

Combined with densities, molecular weights, and transference numbers (fractions of the current carried by the various ionic constituents), the conductivity yields the relative velocities of the ionic constituents under the influence of an electric field. The mobilities (velocity per unit electric field, cm2 s-1 V-1) depend on the size and charge of the ion, the ionic concentration, temperature, and solvent medium. In dilute aqueous solutions of dissociated electrolytes, ionic mobilities decrease slightly as the concentration increases. The equivalent conductance extrapolated to zero electrolyte concentration may be expressed as the sum of independent equivalent conductances of the constituent ions... 

At ordinary temperatures, this thermal particle density is extremely small. But quantum field theory has now revealed the thermod5mamic importance of the state p = 0. It is a state of thermal equilibrium that matter could reach indeed matter was in such a state during the early part of the universe. Had matter stayed in thermal equilibrium with radiation, at the current temperature of the universe the density of protons and electrons, given by (11.6.5) or its modifications, would be virtually zero. The existence of particles at their present temperatures has to be viewed as a nonequilibrium state. As a result of the particular way in which the universe has evolved, matter was not able to convert to radiation and stay in thermal equilibrium with it. 

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