Magnetic phase diagram of cuprates and universal scaling laws

TL;DR

This paper explores the magnetic phase diagram of hole-doped cuprates using the pairon model, revealing universal scaling laws for critical magnetic fields related to pair energies and predicting Fermi arc behavior under magnetic fields.

Contribution

It introduces a novel framework linking pair energies to magnetic fields and derives universal scaling laws, providing new insights into the magnetic properties of cuprates.

Findings

$B_{c2}$ scales with $T_c$, approximately 1.65 T/K.

$B_{pg}$ scales with the pseudogap temperature $T^*$.

Fermi arcs are predicted to appear under magnetic fields.

Abstract

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 {\it pairon model}, we show that the two characteristic energies, the pair binding energy (the gap $\Delta_p$) and the condensation energy ($\beta_c$) resulting from pair correlations, give rise to two major magnetic fields, the upper critical field $B_{c2}$ and a second field, $B_{pg}$, 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 $B_{c2}$ and $B_{pg}$ are derived: $B_{c2}$ scales with the critical temperature, $B_{c2}/T_c\simeq 1.65$ T/K, in agreement with many experiments, and $B_{pg}$ 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.