Proximity-Induced Odd-Frequency Superconductivity in a Topological Insulator

At an interface between a topological insulator (TI) and a conventional superconductor (SC), superconductivity has been predicted to change dramatically and exhibit novel correlations. In particular, the induced superconductivity by an $s$-wave SC in a TI can develop an order parameter with a $p$-wave component. Here we present experimental evidence for an unexpected proximity-induced novel superconducting state in a thin layer of the prototypical TI, ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ proximity coupled to Nb. From depth-resolved magnetic field measurements below the superconducting transition temperature of Nb, we observe a local enhancement of the magnetic field in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ that exceeds the externally applied field, thus supporting the existence of an intrinsic paramagnetic Meissner effect arising from an odd-frequency superconducting state. Our experimental results are complemented by theoretical calculations supporting the appearance of such a component at the interface which extends into the TI. This state is topologically distinct from the conventional Bardeen-Cooper-Schrieffer state it originates from. To the best of our knowledge, these findings present a first observation of bulk odd-frequency superconductivity in a TI. We thus reaffirm the potential of the TI-SC interface as a versatile platform to produce novel superconducting states.

Figure 1

(a) (top) Schematic showing the $\mu \mathrm{SR}$ geometry where the applied field is parallel to the surface and perpendicular to the muon spin and momentum directions. The lines depict the expected magnetic field depth profile due to screening of the applied field inside the heterostructure with (solid gray) and without (dotted black) proximity induced superconductivity in the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ layer. (bottom) Calculated muon implantation profiles at different implantation energies using Trim.SP [25]. (b) Measured local mean field as a function of implantation energy above (black squares) and below (red circles) the superconducting transition temperature. The black horizontal line represents the applied field value, $B_{\mathrm{ext}}$, and the blue line is a fit to the theoretical model (see text).

Figure 2

(a) Local field distribution calculated from fast Fourier transform of the muon polarization measured in the heterostructure, above and below the superconducting transition temperature. Different energies are offset for clarity. The solid lines represent results from the fitting procedure (see the Supplemental Material [29]). (b) Temperature dependence of the field shift in the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and Nb layers.