Proximity effect with noncentrosymmetric superconductors

We describe the superconducting proximity effect taking place in a contact between a noncentrosymmetric superconductor and a diffusive normal/ferromagnetic metal within the quasiclassical theory of superconductivity. By solving numerically the Usadel equation with boundary conditions valid for arbitrary interface transparency, we show that the analysis of the proximity-modified local density of states in the normal side can be used to obtain information about the exotic superconductivity of noncentrosymmetric materials. We point out the signatures of triplet pairing, the coexistence of triplet and singlet pairing, and particular orbital symmetries of the pair potential. Exploiting the directional dependence of the spin polarization pair breaking effect on the triplet correlations, we show how the order relation between triplet and singlet gaps can be discriminated and that an estimation of the specific gap ratio is possible in some cases.

Figure 1

In (a) the system under consideration is sketched. It is a contact between a NCS and a diffusive ferromagnet (DF) separated by an infinitely thin insulator. In such a setup the proximity effect features can be probed by looking at how the normal LDOS in DF is modified by the presence of the superconductor with, e.g., a position and energy resolved STM measurement. In the particular case of NCS both even-frequency spin-singlet and odd-frequency spin-triplet superconducting correlations are expected to propagate in the normal part of the contact; the latter can be long ranged depending on the relative orientation of exchange field in DF and d-vector in NCS. In (b) the amplitude and phase of the pair potentials matrices in two different types of NCSs are considered. Numerical simulations suggest that in cerium family NCSs $df$ potentials could be stabilized rather than the more commonly assumed $sp$ ones (Ref. 66).

Figure 2

LDOS calculated in the nonsuperconducting side of a NCS/DN contact (see Fig. 1) for different NCSs. Several $r={\Delta }^t/{\Delta }^s$ values are plotted in both panels ($r=0,0.5,1,2,\infty$ from bottom to top at $\varepsilon =0$). $L=\xi$, $\Gamma =0.1$, $Z=2$ are fixed. The LDOS is calculated at $x=L$.

Figure 3

LDOS calculated in the nonsuperconducting side of a NCS/DF contact (see Fig. 1) for different NCSs, gaps ratio values, exchange field amplitudes, and directions in DF. The NCS/DN case (dotted lines) is plotted for comparison. Short-dashed, long-dashed, and solid lines are for $h/{\Delta }_0=0.5,1,5,$ respectively. $L=\xi$, $\Gamma =0.1$, $Z=2$ are fixed. The LDOS is calculated at $x=L$.

Figure 4

Zero-energy LDOS calculated in the nonsuperconducting side of a NCS/DN contact (a) and of a NCS/DF contact [(b)–(e)] as a function of the normalized distance from the interface $L/\xi$. Here only the $sp$ symmetry is plotted since at zero energy the $df$ symmetry results differ only quantitatively. Everywhere $\Gamma =10$, $Z=10$ are fixed and a dashed line representing the absence of proximity effect is plotted. In (a) $r={\Delta }^t/{\Delta }^s=0,0.5,2,\infty$ are considered from bottom to top (the first two are superposed and practically indistinguishable). In (b) and (c) the case ${\Delta }^t<{\Delta }^s$ is considered for two orientations of the exchange field in the nonsuperconducting side and $h/{\Delta }_0=5$. The cases $r=0,0.4,0.6,0.8,0.9$ are plotted from bottom to top close to the interface. In (d) and (e) the case ${\Delta }^t>{\Delta }^s$ is considered for two orientations of the exchange field in the nonsuperconducting side and $h/{\Delta }_0=5$. The cases $r=1.5,2,\infty$ are plotted from bottom to top close to the interface and everywhere the LDOS is calculated at $x=L$.