8.9.3 Critical Current Density
Another important characteristic feature of the superconducting state is that when the
current density through the sample exceeds a critical value 7C, it is found that superconductivity
disappears. This is not surprising since the current through the superconductor
will itself generate a magnetic field and at sufficiently high current densities,
the magnetic field at the surface of the sample will exceed the critical field and extinguish
superconductivity. This plausible direct relation between Bc and Jc is only true
for Type I superconductors, whereas in Type II superconductors, Jc depends in a complicated
way on the interaction between the current and the flux vortices. New high-rc
superconductors have exceedingly high critical fields, as apparent in Table 8.7, that do
not seem to necessarily translate to high critical current densities. The critical current
density in Type II superconductors depends not only on the temperature and the
applied magnetic field but also on the preparation and hence the microstructure (e.g.,
polycrystallinity) of the superconductor material. Critical current densities in new
high-rc superconductors vary widely with preparation conditions. For example, in
Y-Ba-Cu-O, Jc may be greater than 107 A cm-2 in some carefully prepared thin films
and single crystals but around 103-106 A cm
-2 in some of the polycrystalline bulk
material (e.g., sintered bulk samples). In NbsSn, used in superconducting solenoid
magnets, on the other hand, Jc is close to 107 A cm
-2 at near 0 K.
The critical current density is important in engineering because it limits the total current
that can be passed through a superconducting wire or a device. The limits of
superconductivity are therefore defined by the critical temperature Tc, critical magnetic
field Bc (or B ), and critical current density Jc. These constitute a surface in a threedimensional
plot, as shown in Figure 8.52, which separates the superconducting state
from the normal state. Any operating point (Tu Bu J) inside this surface is in the
superconducting state. When the cuprate ceramic superconductors were first discovered,
their Jc values were too low to allow immediate significant applications in engineering