Distinguishing $d_{xz}+i d_{yz}$ and $d_{x^2-y^2}$ pairing in $Sr_2RuO_4$ by high magnetic field H-T phase diagrams

TL;DR

This study maps out magnetic field-temperature phase diagrams for different pairing symmetries in Sr2RuO4, revealing distinct high-field behaviors that can help identify the true pairing symmetry in this superconductor.

Contribution

It provides a detailed theoretical analysis of phase diagrams for d_{x^2-y^2} and d_{xz}+id_{yz} pairings, highlighting differences in high-field phase transitions.

Findings

d_{x^2-y^2} shows an additional high-field first order transition line.

d_{xz}+id_{yz} lacks this high-field transition line.

Both pairings exhibit similar Knight shift suppression and a bicritical point.

Abstract

Employing a realistic tight-binding model describing the Fermi surface in the normal state of $Sr_2RuO_4$ we map out magnetic field versus temperature phase diagrams for $d_{x^2-y^2} (B_{1g})$ and $d_{xz}+id_{yz} (E_g)$ pairing types. Both produce (i) a similar Knight shift suppression of $\sim\!80\%$ and (ii) a bicritical point at $T=0.88$K separating low field second order phase transitions from high field Pauli limiting first order transitions. We find, however, strikingly different phase behaviour within the high field Pauli limiting region. For $d_{x^2-y^2}$ pairing symmetry an additional lower critical line of first order transitions is found (terminating in a critical point at $T=0.09-0.22$K depending on the choice of Hubbard U parameters) while for $d_{xz}+id_{yz}$ no such additional high field phase transitions are found for any choice of Hubbard U. In conjunction with our earlier finding [{\it Physical Review B} {\bf 102} (23), 235203] for $p$-wave helical pairing of a still different high field phase structure (a lower critical field line meeting the upper critical field line exactly at the bicritical point), we suggest high field Pauli limiting phase structure as a possible route to distinguish pairing symmetries in this material.