Magnetic phase diagram of cuprates and universal scaling laws

In this article we consider the magnetic field phase diagram of hole-doped high- T c cuprates, which has been given much less attention than the temperature diagram. In the framework of the pairon model , we show that the two characteristic energies, the pair binding energy (the gap Δ p ) and the condensation energy ( β c ) resulting from pair correlations, give rise to two major magnetic fields, the upper critical field B c 2 and a second field, B p g , associated with the pseudogap (PG). The latter implies a second length scale in addition to the coherence length, characteristic of incoherent pairs. Universal scaling laws for both B c 2 and B p g are derived: B c 2 scales with the critical temperature, B c 2 / T c ≃ 1.65 T/K, in agreement with many experiments, and B p g has a similar scaling with respect to T ⁎ . Finally, Fermi arcs centered on the nodal directions are predicted to appear as a function of magnetic field, an effect testable experimentally. • The magnetic field phase diagram of cuprates is explored in the framework of the pairon model. • In addition to the coherence length, a second length scale is associated with incoherent pairs. • The upper critical field, linked to superconducting coherence, scales with Tc. • A second characteristic field exists, linked to the pairing energy and the pseudogap phase. • Fermi arcs are predicted to exist in the nodal directions with increasing magnetic field, which can be tested experimentally.