Temperature dependence of the superfluid density in a noncentrosymmetric superconductor

For a noncentrosymmetric superconductor such as $\mathrm{Ce}{\mathrm{Pt}}_3\mathrm{Si}$, we consider a Cooper pairing model with a two-component order parameter composed of spin-singlet and spin-triplet pairing components. We calculate the superfluid density tensor in the clean limit on the basis of the quasiclassical theory of superconductivity. We demonstrate that such a pairing model accounts for an experimentally observed feature of the temperature dependence of the London penetration depth in $\mathrm{Ce}{\mathrm{Pt}}_3\mathrm{Si}$, i.e., line-node-gap behavior at low temperatures.

Figure 1

Schematic figures of the gap structure on the Fermi surfaces. (a) On Fermi surface I, the gap is $\mid \Psi +\Delta \sin \theta \mid$. (b) On Fermi surface II, the gap is $\mid \Psi -\Delta \sin \theta \mid$. In these figures, it is assumed that both $\Psi$ and $\Delta$ are real and positive, and $\Psi <\Delta$.

Figure 2

Plots of the reciprocal square root of the superfluid densities vs temperature, $1∕\sqrt{{\rho }_{xx}}$ (a) and $1∕\sqrt{{\rho }_{zz}}$ (b), for several values of the difference in the density of states $\delta$. The singlet-to-triplet components ratio $\nu$ is set as $\nu =0.6$. For comparison, dotted lines indicate those for a point-node gap, i.e., pure $p$-wave gap $\mid \Delta \sin \theta \mid$ $(\Psi =0)$.

Figure 3

The temperature dependence of the superfluid densities, ${\rho }_{xx}$ (a) and ${\rho }_{zz}$ (b), for several values of the difference in the density of states $\delta$. The singlet-to-triplet components ratio $\nu$ is set as $\nu =0.6$.

Figure 4

The temperature dependence of the superfluid densities, ${\rho }_{xx}$ (a) and ${\rho }_{zz}$ (b), for several values of the singlet-to-triplet components ratio $\nu$. The difference in the density of states is set as $\delta =-0.2$.

Figure 5

Plots of the ratio ${\rho }_{zz}∕{\rho }_{xx}$ vs temperature for several values of the singlet-to-triplet components ratio $\nu$. The difference in the density of states is set as $\delta =-0.2$.

Figure 6

The temperature dependence of the superfluid densities ${\rho }_{xx}$ and ${\rho }_{zz}$ for the Fermi velocity model, $v_{\mathrm{I},\mathrm{II}}\propto 1∕N_{\mathrm{I},\mathrm{II}}$. $\nu =0.6$ and $\delta =0.9$.