Previous:  Resistance of Conductors

In the previous section we saw that the electrical resistivity of a conductor is controlled by two mechanisms, namely electron scattering from impurities and defects in the crystal lattice, and interactions between electrons and lattice vibrations.  The former process dominates at low temperatures, and the latter dominates at higher temperatures.  The result is that for a normal conductor, the resistivity varies with temperature as shown in the figure at the end of the previous article.  In particular, as the temperature approaches absolute zero, the resistivity approaches a limit determined by the scattering from lattice impurities and imperfections. 

In 1911, a Dutch physicist named Heike Kamerlingh Onnes was undertaking a series of experiments to measure the resistivity of mercury at very low temperatures.  Such experiments were possible because only a few years prior to this, the process of liquefaction of helium had been discovered, and hence very low temperatures could be attained for experimental purposes.  (Helium boils at around 4 K).  To his surprise, Onnes obtained a plot of resistance against temperature that was similar to that in the following figure.  The black dots on the graph represent approximately the measurements obtained by Onnes. 

He found that as the temperature decreased to around 4.2 K, the resistance of almost pure mercury suddenly dropped to an apparently zero value.  He also found that the addition of impurities to his mercury samples failed to change this state of affairs – the resistivity still dropped to an apparently zero value, rather than tending to a finite value that would be expected by conventional theory. 

Onnes referred to this new state of mercury, in which the electrical resistivity vanishes, as the “superconducting state”.  The temperature at which the transition to the superconducting state occurs is often referred to as the “transition temperature” or the “critical temperature”.  This temperature is marked on the figure above with a vertical line. 

In the above paragraphs we have consistently referred to an “apparently zero” resistivity in the superconducting state.  Years later, after Onnes made his discovery, experiments were undertaken to show that the resistivity probably is identically zero.  In the superconducting state, if the mercury has truly zero resistivity, then the mercury samples would not be able to dissipate an electric current set up in the samples – the current would persist forever.  Experiments have shown that when such currents are set up in superconducting materials, the currents persist for time periods of at least a year.  These experiments indicate that the resistivity in the superconducting phase is very small, and to all intents and purposes is zero. 

(It should be noted that the zero resistivity of the superconducting phase strictly applies only for a constant potential difference applied across the conductor.  For alternating currents some resistivity is observed in the superconducting phase, but provided the frequency is low, the finite resistivity for AC is small). 

Superconductors also have a second interesting property.  Consider a material (for example mercury) in its superconducting state.  It is found that if a sufficiently strong external magnetic field is applied to the material, then the normal resistivity of the sample is restored.  It is found that there is a critical value of the magnetic field such that, if the applied field is below the critical value, the superconducting state is maintained.  If the applied value is above the critical value, the normal state of the material is restored.  The critical magnetic field is a function of the temperature T of the sample, and is given approximately by 

where B₀ is a constant that depends on the material, and T_C is the critical temperature of the material.  For mercury, the critical field varies roughly as shown below with temperature. 

Note that the critical field becomes zero at the critical temperature (4.2 K for mercury).  This is because above this temperature the normal resistivity of mercury is restored anyway.

Next:  Meissner Effect