As Bardeen-Cooper-Schrieffer (BCS) were able to show, is that the electron-phonon interaction mediates superconductivity. In a cartoon picture, a passing light and fast (Fermi velocity v_F) electron with its negative charge distorts the lattice of the heavy masses of the positive ions of the lattice. This allows a second electron to feel this distortion, as the lattice distortion disappears only at the speed of sound (v_s) and v_F>>v_s. This leads to an attractive interaction between the electrons which then will from Cooper pairs and undergo a phase transition to superconductivity.

Let’s use them as an example, and here we look at CeCoIn₅. Ce³⁺ ion in this compounds is magnetic. Thus if one measures the magnetic susceptibility at high temperatures, one observes this moment and from fitting a Curie-Weiss law, one gets a negative intercept which for a normal magnetic material one would interpret as antiferromagnetic interactions, which give rise to magnetic order. However, unexpectedly, one finds a superconducting phase transition. Now there exists a non-magnetic analogue, LaCoIn₅, which has the very same crystal structure and thus most probably the same electron-phonon interactions. Curiously, LaCoIn₅ is a normal metal and does not become superconducting. So the magnetic moment on the Ce is an important ingredient for superconductivity. Also, no the huge difference in Sommerfeld coefficient C_m/T between CeCoIn₅ and LaCoIn₅, which indicates strong electronic correlations, or so-called “heavy” electron masses.

Superconductivity can be destroyed by applying a magnetic field. Normally, for a type-II superconductor such as CeCoIn5 one should observe only two phases: the Meissner phase, where supercurrents completely shield the interior of the superconductor from the magnetic field, at very low fields (very hard to observe in CeCoIn₅) and the Abrikosov phase where the magnetic field pierces the superconductors in units of the flux quantum, not unlike when one sticks spaghetti into a slice of hot dog. However, for very high fields and very low temperature, there is an additional phase, the so-called “Q-phase” (the T_FFLO line in the graphic), in CeCoIn₅.

A careful neutron scattering study on CeCoIn₅ single crystals showed, that antiferromagnetic order is present inside the Q-phase. What makes this so unusual is, that the AFM exists just inside the superconducting part of the phase diagram, but is absent in the normal state.