The interplay between the spin-orbit
coupling at the surface of a topological insulator (TI), the conventional pair
potential from a superconductor, and an external magnetic field creates a very
exotic induced pair potential in a TI-based
normal-superconductor junction. In addition to a superposition of
spin-singlet and triplet components, a new, unconventional type of
superconducting condensate can be induced in this system: one with a
spin-triplet component that is both odd in frequency and even in its
spatial coordinates. An unambiguous experimental detection of such
odd-frequency condensate has not been achieved.

We propose a detection scheme based on nonlocal conductance measurements on the
one-dimensional edge of a two-dimensional TI: we show a one-to-one
correspondence between crossed Andreev reflection processes and the emergence
of odd-frequency triplet superconductivity [1].

We also consider the proximity effect on a three-dimensional TI-superconductor
junction under the effect of an external magnetic field [2]. We find that the
magnetic field induces even- and odd-frequency spin-triplet terms in the
pairing amplitude, which are always superposed with an even-frequency
spin-singlet term. The competition between all these components results in a
rich subgap structure with emerging zero-energy peaks. Using very basic
ingredients such as a conventional superconductor and an external magnetic
field, standard experimental techniques like conductance spectroscopy can be
used to detect signatures of odd-frequency superconductivity.

[1] F. Crépin, P. Burset, B. Trauzettel, arXiv:1503.07784.

[2] P. Burset, B. Lu, G. Tkachov, Y. Tanaka, E.M. Hankiewicz, B. Trauzettel, in
preparation.