Quantum geometric magnetic monopole and two-phase superconductivity in CeRh$_2$As$_2$

Abstract

Recent angle-resolved photoemission spectroscopy (ARPES) and density functional theory plus Hubbard $U$ (DFT+$U$) studies revealed that a heavy-fermion superconductor CeRh$_2$As$_2$ exhibits van Hove singularities and the Dirac point near the Fermi level $E_{\mathrm F}$, which are key signatures of strong-correlation effects and quantum geometry. We have constructed a two-dimensional 12-orbital \textit{Dirac-Anderson} model as an effective model for CeRh$_2$As$_2$. The band structure and Fermi-surface topology of the Dirac-Anderson model agree well with the ARPES data and the DFT+$U$ calculations. We show that the quantum geometry strongly favors magnetic-monopole fluctuations because of the Dirac point at the $M$ point. By solving the linearized Éliashberg equation, we demonstrate that the $B_{1u}$ and $B_{2g}$ representations, spin-triplet states originating from the Dirac point, exhibit the leading superconducting instabilities. By comparing the random-phase approximation and the fluctuation-exchange approximation, we further demonstrate that strong-correlation effects mitigate the influence of quantum geometry. The phase diagram of CeRh$_2$As$_2$ under pressure is discussed in connection with the theoretical results.

Figures (5)

• Figure 1: (a) Crystalline structure of CeRh$_2$As$_2$. The Rh1 and Rh2 sites are indicated. The figure is adapted from Ref. Nogaki2021prr. (b) The DFT+$U$ band structure calculations for $U=5\,\mathrm{eV}$. The band structure along the $\Gamma$-$X$-$M$-$\Gamma$ line is shown. The orbital weight of Ce-4$f$, Rh1-5$d$, and Rh2-5$d$ orbitals are indicated by red, green, and blue, respectively. (c) The band structure of the Dirac-Anderson model. (d) The enlarged view of the Dirac-Anderson model around the Fermi level, $E_{\mathrm{F}}$. (e) The Fermi surface obtained from the DFT+$U$ calculation for $U=5\,\mathrm{eV}$. (f) The top view of the Fermi surface from the DFT+$U$ calculation. (g) The Fermi surface of the Dirac-Anderson model. The color indicates the weight of $f$-orbitals. Figures (b), (e) and (f) are adapted from Ref. Ishizuka2024prb.
• Figure 2: The momentum dependence of the static multipole susceptibilities $\chi^{\mathcal{Q}}(\bm{q},i\nu_n=0)$ for the Stoner factor $\alpha = 0.985$. The definition of the Stoner factor is given in Sec. \ref{['sec:sc']}. (a) Even-parity longitudinal magnetic multipole $s^z \otimes \sigma^0$. (b) Odd-parity longitudinal magnetic multipole $s^z \otimes \sigma^z$. (c) Even-parity transverse magnetic multipole $s^{\pm} \otimes \sigma^0$. (d) Odd-parity transverse magnetic multipole $s^{\pm} \otimes \sigma^z$. The color scale of panel (a) [panel (c)] is the same as panel (b) [panel (d)].
• Figure 3: (a) Eigenvalues $\lambda$ of the Éliashberg equation as a function of the Stoner factor $\alpha$. The eigenvalue for the $B_{2g}$ representation is nearly degenerate with the eigenvalue of the inversion partner, $B_{1u}$. (b-d) Spin-singlet component $\psi(\bm k)$ and spin-triplet components $\bm d(\bm k)$ of the gap function in the $A_{2u}$ state. (e-g) Corresponding components in the $B_{1u}$ state. Note that $z$-component of the spin-triplet component $d_z(\bm{k})$ is prohibited by the mirror symmetry $\sigma_h$ in the two-dimensional system.
• Figure 4: Comparison between the RPA and FLEX. Normalized momentum dependence of the bare susceptibility $\chi^{0}(\bm q)/\max_{\bm{q}}\chi^{0}(\bm q)$ for the magnetic monopole operator $s^{z}\!\otimes\!\sigma^{z}$ is shown. Each dataset is normalized to the maximum value $\max_{\bm{q}}\chi^{0}(\bm q)$. (a) Susceptibility calculated within the RPA. (b) The enlarged view of (a) around $[\pi/2, \pi]\times[\pi/2, \pi]$. (c) Susceptibility calculated by the FLEX approximation for $U=0.22$. (d) The enlarged view of (c) around $[\pi/2, \pi]\times[\pi/2, \pi]$. The color scale of panel (a) [panel (c)] is the same as panel (b) [panel (d)].
• Figure 5: (a) The ARPES data (intensity) with DFT+$U$ calculation (red line). The figure is adapted from Ref. Chen2024prx. (b) The band structure of the Dirac-Anderson model without renormalization factor $z$ and $\tilde{z}$. (c) The enlarged view of (b).