Tunneling spectroscopy in engineered SrTiO$_{\mathrm{3}}$ heterostructures

Despite decades of intense research on the topic, superconductivity in the dilute high-$k$ semiconductor SrTiO$_{\mathrm{3}}$ (STO) has posed a long-standing problem. In light of the recent reports of unconventional 2D superconductivity in STO-based heterostructures, this problem deserves renewed attention in the bulk limit. Tunneling spectroscopy, which directly measures the electronic density of states, is a powerful tool to investigate the superconducting ground state as well as the relevant electron-phonon couplings. A limiting obstacle for employing this technique is the long depletion lengths formed when semiconducting SrTiO$_{\mathrm{3}}$ is contacted with a metal in Schottky junctions, which obstructs access to the intrinsic bulk electronic properties. Here, using band alignment engineered planar tunneling junctions to minimize these long depletion lengths, we experimentally re-examine canonical tunneling experiments in Nb-doped STO. We discuss our results on the extraction of the electron-phonon coupling in SrTiO$_{\mathrm{3}}$ and it's relevance to the superconducting condensate.