Unveiling Odd-Frequency Pairing around a Magnetic Impurity in a Superconductor

We study the unconventional superconducting correlations caused by a single isolated magnetic impurity in a conventional $s$-wave superconductor. Because of the local breaking of time-reversal symmetry, the impurity induces unconventional superconductivity, which is even in both space and spin variables but odd under time inversion. We derive an exact proportionality relation between the even-frequency component of the local electron density of states and the imaginary part of the odd-frequency local pairing function. By applying this relation to scanning tunneling microscopy spectra taken on top of magnetic impurities immersed in a Pb/Si(111) monolayer, we show experimental evidence of the occurrence of the odd-frequency pairing in these systems and explicitly extract its superconducting function from the data.

Figure 1

(a) Scanning tunneling microscopy image of the Pb monolayer where a magnetic defect is present as a triangular protrusion. (b) Corresponding conductance map measured at the Fermi level by scanning tunneling spectroscopy at 320 mK.

Figure 2

(a) Measured differential conductance at the impurity site (blue dots), far away from the impurity (black dots) and the one obtained from convolution of the extracted LDOS with the Fermi-Dirac derivative (red line). (b) LDOS obtained after deconvolution taking into account the finite temperature $T=320\mathrm{mK}$ (red dots). LDOS fitted with Eq. (17) by using the parameter set: $E_0=0.074\mathrm{meV}$, $\eta =0.012\mathrm{meV}$, $u^2=0.28{\nu }_0$, $v^2=0.38{\nu }_0$ (green curve).

Figure 3

$-\mathrm{Im}{F}_{\mathrm{odd}}^R(\omega )/\pi$ extracted at the position of the impurity (the values are relevant only inside the gap) from the measured LDOS shown in Fig. 2.