Mechanism for Unconventional Superconductivity in the Hole-Doped Rashba-Hubbard Model

Motivated by the recent resurgence of interest in topological superconductivity, we study superconducting pairing instabilities of the hole-doped Rashba-Hubbard model on the square lattice with first- and second-neighbor hopping. Within the random phase approximation, we compute the spin-fluctuation-mediated pairing interactions as a function of filling. Rashba spin-orbit coupling splits the spin degeneracies of the bands, which leads to two van Hove singularities at two different fillings. We find that, for a doping region in between these two van Hove fillings, the spin fluctuations exhibit a strong ferromagnetic contribution. Because of these ferromagnetic fluctuations, there is a strong tendency towards spin-triplet $f$-wave pairing within this filling region, resulting in a topologically nontrivial phase.

Figure 1

(a)–(c) Calculated Fermi surface topology and (d)–(i) static $\omega =0$ spin susceptibility for the fillings $n=0.50$, $n=0.83$, and $n=0.95$, with $t^{\prime }=0.3$, $V_{\mathrm{so}}=0.5$, $T=0.01$, and $U=0.4$. The second and third rows show the longitudinal and transversal susceptibilities ${\chi }_{\mathrm{long}}={\chi }_{\uparrow \uparrow \uparrow \uparrow }-{\chi }_{\uparrow \downarrow \downarrow \uparrow }$ and ${\chi }_{\text{trans}}={\chi }_{\uparrow \uparrow \downarrow \downarrow }$, respectively (see Supplemental Material [29]).

Figure 2

The critical interaction strength $U_c$ as a function of filling $n$ is indicated by the red line. The color scale represents the relative intensity of the ferromagnetic fluctuations in the longitudinal susceptibility. The inset shows the density of states versus filling for $V_{\mathrm{so}}=0$ (dashed line) and $V_{\mathrm{so}}=0.5$ (solid line).

Figure 3

(a) Filling dependence of the superconducting couplings ${\lambda }_i^{\mathrm{eff}}$, as determined from Eq. (6) for $U=0.4$, and for the lowest-harmonic pairing symmetries given by Eq. (S11). Here, we do not show the $s$-wave pairing channel, since it is highly suppressed (i.e., negative) for the entire hole-doping range. For the numerical evaluation of Eq. (6), we used 408 Fermi momenta. (b) ${\lambda }_i^{\mathrm{eff}}$ versus $U$ for the filling $n=0.78$. We present results up to $U=0.7$ to show the regime where $f$-wave is dominant. With increasing $U$, the curves increase monotonically, and $d$-wave becomes dominant while $f$-wave subdominant for $U\gtrsim 0.5$. Near the magnetic instability $U=U_c$, we find that ${\lambda }_d^{\mathrm{eff}}\sim 0.2$ and ${\lambda }_f^{\mathrm{eff}}\sim 0.15$. (c) Filling dependence of the intra- and inter-FS pairing strengths ${\lambda }_i^{\alpha \alpha }$ and ${\lambda }_i^{\alpha \beta }$ for the $f$-wave channel with same-spin projections.