Pure odd-frequency superconductivity at the cores of proximity vortices

After more than a decade, direct observation of the odd frequency triplet pairing state in superconducting hybrid structures remains elusive. We propose an experimentally feasible setup that can unambiguously reveal the zero energy peak due to proximity-induced equal spin superconducting triplet correlations. We theoretically investigate a two-dimensional Josephson junction in the diffusive regime. The nanostructure consists of a normal metal sandwiched between two ferromagnetic layers with spiral magnetization patterns. By applying an external magnetic field perpendicular to the junction plane, vortices nucleate in the normal metal. The calculated energy and spatially resolved density of states, along with the pair potential, reveal that remarkably, only triplet Cooper pairs survive in the vortex cores. These isolated odd frequency triplet correlations result in well defined zero energy peaks in the local density of states that can be identified through tunneling spectroscopy experiments. Moreover, the diffusive regime considered here rules out the possibility of Andreev bound states in the vortex core as contributors to the zero energy peaks.

Figure 1

Schematic of the S-Ho/N/Ho-S junction subject to a perpendicular external magnetic field $\mathbf{H}$. The junction plane resides in the $z=0$ plane and the N/Ho interfaces are located at $x=\pm L/2$. The junction has a length and width of $L$ and $W$, respectively. The two helimagnets (holmium type) with internal fields $\mathbf{h}$ (see text) are adjacent to a diffusive normal metal (N) solely for producing spin-1 triplet pair correlations. The perpendicular external magnetic field induces proximity vortices in the N region, as depicted schematically.

Figure 2

($\mathrm{a}$) Color map of the normalized local density of states as a function of quasiparticles energy $\varepsilon$ and location along the junction width $y$ at $x=0$ inside the diffusive normal metal N when the outer Ho layers are nonmagnetic, i.e., $h_0=0$. ($\mathrm{b}$) Corresponding spatial map of the normalized singlet pair potential.

Figure 3

(a) Local density of states as a function of quasiparticles energy $\varepsilon$ at the vortex core $x=y=0$ (shown in Fig. 2) for four values of the internal field in the Ho layers, $h_0=0.0,2.0{\mathrm{\Delta }}_0,4.0{\mathrm{\Delta }}_0$, and $6.0{\mathrm{\Delta }}_0$. (b) Corresponding singlet pair potential $U_{\text{pair}}$ along the junction length $x$ in the same location as the vortex core, i.e., $y=0$. Panels (a) and (b) are obtained within the full proximity limit and the other parameters are identical to those of Fig. 2. (c)–(e) The modulus of the singlet $\left|\text{S}\right(\varepsilon \left)\right|$, spin-1 $|{\text{T}}_y\left(\varepsilon \right)|$, and spin-0 $|{\text{T}}_z\left(\varepsilon \right)|$ triplets against $\varepsilon$ within the low proximity limit. The solid lines show the correlations at the vortex core while the dashed lines correspond to a representative location outside of the vortex core: $x=0.35L,y=0$.