Introduction on superconductivity
The resistivity of metals is a decreasing function of temperature. For most of them, a limit value for T → 0 is reached, where T is the absolute temperature of the sample under investigation. However, there are some metals for which the resistivity vanishes for a critical temperature Tc above the absolute zero.
In 1911, Kamerlingh Onnes found that, for Mercury, Tc is equal to 4.15 K. In the same historical period, Tc was found equal to 3.72 K for Tin, and to 1.2 K for Aluminum. However, the real turning point came in 1986 with the discovery of a critical temperature of 35 K for a complex oxide of Lanthanum, Barium and Copper.
BCS model
BCS is the acronym for Bardeen, Cooper, and Schrieffer, the physicists who elaborated a phenomenological superconductivity model, which we’ll briefly explain.
In a metal, electrons constitute a particular “quantum gas” called Fermi gas. Electrons are fermions, or particles of half-integer spin (specifically, 1/2). In Statistical Quantum Mechanics, the behavior of an ideal Fermi gas at low temperatures is well known. Here, by ideality, we mean the absence of interactions between the gas particles. This is not the case for the conduction electrons of a metal due to Coulomb repulsion. However, in the zero order approximation it is legitimate to neglect this interaction and statistical quantum mechanics returns the behavior of metals as regards electrical conductivity (correcting the old Drude model).
In a further approximation, the interaction between the electrons is taken into account by adding a shield potential in the sense that the single electron does not “see” the bare charge of the neighboring electron but a charge shielded by the remaining electrons as well as by the lattice ions. This leads to the notion of Fermi liquid which differs from the Fermi gas due to a weak interaction.
We must also consider the effect due to the spin of the electrons. The latter tend to bind in a spin singlet state i.e., of zero spin. This occurs despite the repulsive electron-electron Coulomb force. The resulting pair (Cooper pair ) is called a quasi-particle in quantum statistical mechanics. A particle does not physically correspond to this entity. However its behavior is statistically (and quantumly) describable with quantum statistical mechanics.
The resulting physical system is an “ideal quantum gas” since the interaction between the individual pairs is zero. It is not a Fermi gas, but a Bose gas since the spin of its constituents is zero (the total spin of the electrons constituting a Cooper pair is zero). The term “Bose gas” refers to the fact that its constituents obey the Bose-Einstein statistic for which, as is well known, the Pauli exclusion principle is not valid, as occurs for fermions (and therefore, for single electrons).
It follows that this system exhibits the Bose-Einstein condensation phenomenon: there is a critical temperature Tc at which a phase transition occurs which sees a macroscopic number of Cooper pairs in the ground state of minimum energy. Such couples give rise to a supercurrent and it is not easy to explain the mechanism. Metaphorically, each pair of Coopers could be compared to a pair of football players who continuously pass the ball, and manage to dodge the tackles of the opposing players, reaching the goal. In this example, the tackles represent the collisions against the lattice, while the ball is the single electron bare charge.
Loading a metal with deuterium
Let’s try to ask ourselves: what happens if we load a metal with deuterium? We recall that deuterium (D) is an isotope of hydrogen (H): while the latter is made up of a proton p and an electron e−, the nucleus of deuterium is made up of a proton and a neutron n (Figure 1).
Thus, we have an electron gas and a proton gas. In a first and rough approximation we can consider these two systems decoupled with np (proton concentration) of the same order of magnitude as ne (electron concentration). If the metal used is a superconductor, by reducing the temperature the transition to the super-conducting state is achieved at Tc, thanks to the formation of Cooper pairs which we can represent symbolically by the following:
Protons also have spin 1/2 so they follow the same statistic as electrons. They are then subject to the Coulomb repulsion force and like the electrons they tend to complete the spin state, creating a spin singlet, thanks to which they “approach” giving rise to something analogous to the Cooper pairs:
However, unlike electrons, protons can “fuse” by releasing energy. Therefore, a process of energy release at a very low critical temperature cannot be excluded, which could be increased by increasing the concentration of protons. Presumably, such a process is challenging to observe and reproduce precisely because of the very low temperature to be reached.