Section 6.8 Superconductivity
Superconductivity, in principle, is quite similar to superfluidity. A superconductor is a material which, if cooled sufficiently, has zero electrical resistance. In other words, a superconductor can carry an electrical current without any dissipative losses. Again, though, the material must be cooled below a critical temperature \(T_c\text{.}\) Superconductivity has been observed in more than 20 metallic elements and in thousands of alloys. The element with the highest critical temperature is niobium, with a critical temperature of \(9.3\, \mbox{K}\text{.}\)
Recent breakthroughs have led to the discovery of layered copper oxide materials that have a critical temperatures as high at \(115\,\mbox{K}\text{.}\) While this is still quite cold (\(-158^\circ\, \mbox{C}\)), it is above the boiling temperature for liquid nitrogen, which is easy to make and is relatively inexpensive. Consequently, these high temperature superconductors, as they are called, have many practical applications. Here are some examples:
Zero electrical resistance means that electromagnets can be made that require zero power to maintain. Furthermore, since there is no dissipation, the magnets don't heat up. Once the current is initiated in the magnet, it can continue indefinitely. Magnetic resonance imaging (MRI) devices, in particular, require very strong magnetic fields. Using normal conductors, an MRI device burns up a lot of electrical power. Worse, massive refrigeration units are required to cool the electro-magnets (solenoids). Newer MRI devices use wires made of high-temperature superconducting materials, which dramatically lowers the operating cost of the devices.
Power transmission: without any electrical resistance, superconducting wires could be used to transmit electrical power without any dissipative loss. (Note: this will really only be practical if materials can be found that go superconducting at ambient temperatures.)
Magnetic levitation: as will be discussed below, superconductors have a property referred to as the Meissner effect which enables them to levitate magnets. This principle could potentially be used in the future to make virtually frictionless trains at an economical cost.
High-speed electronics: superconducting materials make it possible to make circuits with substantially higher switching speeds.
Magnetic energy storage: a superconducting solenoid with a very large magnetic field can be used like a battery, since the current in the solenoid won't die down.
Superconductors, like superfluids, are based on the principle of Bose condensation, but this time electrons are the particles. Of course electrons are fermions and not bosons. But the electrons pair into composite particles called “Cooper pairs,” and these Cooper pairs are then bosons, which can Bose condense. This was not easy to show. After the phenomenon of superconductivity was discovered experimentally, it took almost 50 years for physicists to work out the subtleties of the pairing process and the Bose condensation.
Subsection 6.8.1 The Meissner Effect
In addition to having zero resistance, superconductors are also noted by a second important property, called the Meissner effect. When a material goes into its superconducting state, any applied magnetic fields are expelled from the material. Put another way, inside a superconducting material the magnetic field is given by \(\vec B=0\text{.}\) This expulsion process is sketched in Figure 6.6.
The Meissner effect has some interesting implications. First, if \(\vec B= 0\) inside the superconductor, the superconductor itself must be acting like a magnet that opposes the externally applied magnetic field. The total magnetic field is the sum of the applied field \(\vec B_\text{ app }\) and the opposing magnetic field from the superconductor \(\vec B_\text{ sc }\text{:}\)
Inside the superconductor, \(\vec B_\text{ total } = 0\text{,}\) so
inside the superconductor. In words, the Meissner effect requires that a superconductor in a magnetic field becomes a magnet that always opposes the applied field. 1 As you will see in the homework assignment, this simple result is the basis behind levitation of magnets over a superconductor (or vice-versa).
The opposing field \(\vec B_\text{ sc }\) set up by the superconductor requires circulating currents within the superconductor. These currents — referred to as shielding currents — flow along the outside of the superconductors. In fact, all of the current passing through a superconductor flows in thin layers near the outside of the superconductor. Because of Ampere's law, if there were any currents within the superconductor, the magnetic field wouldn't be zero inside.
Subsection 6.8.2 Limits on Superconductivity
Even for temperatures below the critical value (\(T \lt T_c\)), the superconductivity can be destroyed by excessive magnetic fields and/or currents. As we increase the strength of an externally applied magnetic field, the magnitude of the shielding currents must also increase in order to provide a shielding field \(\vec B_\text{ sc }\) that cancels the externally applied field within the bulk of the superconductor. But there is only a finite amount of energy that is released by the condensation process, so the shielding currents can only be so large. Consequently, there is only so much applied magnetic field that can be shielded. The maximum applied magnetic field is referred to as the critical magnetic field strength \(B_c\text{.}\) If \(B_\text{ app }\) exceeds \(B_c\text{,}\) then the shielding currents aren't strong enough to cancel the magnetic field within the material. As a result, the material remains in its normal, non-superconducting state even though the temperature is below \(T_c\text{.}\) The critical magnetic field is typically independent of the geometry of the sample.
A phenomenon closely related to the critical magnetic field, and of great practical importance, is the existence of a critical current. As an externally applied current (not a circulating shielding current) carried by a superconducting sample is increased, there comes a point at which the superconductor becomes normal, because the current carried by a superconductor produces a field at the surface of the material. If the current is too large, then the magnetic field at the surface can exceed the critical magnetic field \(B_c\text{.}\)