Superfluid density reduction and spin-imbalanced pairing in a fermionic superfluid due to dynamical boson exchange

We investigate superfluidity in nonrelativistic fermionic systems in which the pairing interaction includes a contribution from the exchange of a dynamical bosonic mode. We show that the dynamical boson exchange (DBE), which causes a retarded pairing interaction and thus violates the Galilean invariance of the fermion sector, generically leads to a quantum reduction of the superfluid density and hence a nonzero normal fraction even at zero temperature. For spin-singlet pairing, the DBE also leads to a nonvanishing spin susceptibility at zero temperature, providing a mechanism for the coexistence of pairing and magnetization. While these effects are negligible for weak pairing, they become sizable at strong pairing. For the double superfluidity in ultracold Fermi-Bose mixtures, the superfluid density reduction for the fermion sector induced by the DBE just gives rise to the Andreev-Bashkin drag effect, indicating a strong entrainment between the two superfluid components. The DBE may also provide a new source for the superfluid fraction reduction of neutron matter, which is crucial for models of neutron star glitches based on neutron superfluidity.

Figure 1

Results for the toy Yukawa model. (a) The dependence of ${\rho }_n$ (scaled by $n_{\mathrm{f}}$) and $\chi$ (scaled by ${\chi }_0$) on $v_{\varphi }/v_{\mathrm{F}}$ at $m_{\varphi }=0.1{\varepsilon }_{\mathrm{F}}$. (b) The dependence of ${\rho }_n$ and $\chi$ on $m_{\varphi }/{\varepsilon }_{\mathrm{F}}$ at $v_{\varphi }/v_{\mathrm{F}}=0$. (c) The frequency dependence of the gap function at $v_{\varphi }/v_{\mathrm{F}}=0$, for $m_{\varphi }/{\varepsilon }_{\mathrm{F}}=0.1,0.15,0.2,0.25$ (from top to bottom). The Yukawa coupling is fixed at $g^2/v_{\mathrm{F}}^3=0.1$.

Figure 2

The spin imbalance $(n_{\uparrow }-n_{\downarrow })/n_{\mathrm{f}}$ as a function of the Zeeman field $h$ (scaled by ${\varepsilon }_{\mathrm{F}}$) for $v_{\varphi }/v_{\mathrm{F}}=0$ and $m_{\varphi }/{\varepsilon }_{\mathrm{F}}=0.1$ in the toy Yukawa model. The Pauli limit is located at $h\simeq 0.145{\varepsilon }_{\mathrm{F}}$. The thin red line denotes the linear approximation $n_{\uparrow }-n_{\downarrow }\simeq \chi h$.

Figure 3

Results for the Fermi-Bose mixture. (a),(b) The dependence of ${\rho }_{\mathrm{d}}$ and $\chi$ on the mass ratio $m_{\mathrm{f}}/m_{\mathrm{b}}$ at ${\left(n_{\mathrm{b}}{a}_{\mathrm{bb}}^3\right)}^{1/3}=0.001$. (c),(d) The dependence of ${\rho }_{\mathrm{d}}$ and $\chi$ on the boson-boson interaction parameter ${\left(n_{\mathrm{b}}{a}_{\mathrm{bb}}^3\right)}^{1/3}$ at $m_{\mathrm{f}}/m_{\mathrm{b}}=6/133$ (${}^6\mathrm{Li}-{}^{133}\mathrm{Cs}$ mixture). The boson-fermion coupling is chosen as ${\left(n_{\mathrm{b}}{a}_{\mathrm{bf}}^3\right)}^{1/3}=0.1$ (solid lines) and 0.15 (dotted lines). The fermion density is $n_{\mathrm{f}}=0.1n_{\mathrm{b}}$.