Distinguishing dxz+idyz and dx2

Physical review(2022)

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Abstract
Employing a realistic tight-binding model describing the Fermi surface in the normal state of ${\text{Sr}}_{2}{\text{RuO}}_{4}$, we map out magnetic field versus temperature phase diagrams for ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}({B}_{1g})$ and ${d}_{xz}+i{d}_{yz}({E}_{g})$ pairing types. Both produce (i) a similar Knight shift suppression of $\ensuremath{\sim}80%$ and (ii) a bicritical point at $T=0.88\phantom{\rule{4pt}{0ex}}\mathrm{K}$ separating low field second-order phase transitions from high-field Pauli limiting first-order transitions. We find, however, strikingly different phase behavior within the high-field Pauli limiting region. For ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing symmetry, an additional lower critical line of first-order transitions is found (terminating in a critical point at $T=0.09\text{\ensuremath{-}}0.22\phantom{\rule{4pt}{0ex}}\mathrm{K}$ depending on the choice of Hubbard $U$ parameters), while for ${d}_{xz}+i{d}_{yz}$ no such additional high-field phase transitions are found for any choice of Hubbard $U$. In conjunction with our earlier finding [Phys. Rev. B 102, 235203 (2020)] 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.
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