Electron pairing without superconductivity

Strontium titanate (SrTiO$_{\mathrm{3}})$ is the first and best known superconducting semiconductor. It exhibits an extremely low carrier density threshold for superconductivity, and possesses a phase diagram similar to that of high-temperature superconductors---two factors that suggest an unconventional pairing mechanism. Despite sustained interest for 50 years, direct experimental insight into the nature of electron pairing in SrTiO$_{\mathrm{3}}$~has remained elusive. Here we perform transport experiments with nanowire-based single-electron transistors at the interface between SrTiO$_{\mathrm{3}}$~and a thin layer of lanthanum aluminate, LaAlO$_{\mathrm{3}}$. Electrostatic gating reveals a series of two-electron conductance resonances---paired electron states---that bifurcate above a critical pairing field~$B_{\mathrm{p}}$~of about 1--4 tesla, an order of magnitude larger than the superconducting critical magnetic field. For magnetic fields below~$B_{\mathrm{p}}$, these resonances are insensitive to the applied magnetic field; for fields in excess of~$B_{\mathrm{p}}$, the resonances exhibit a linear Zeeman-like energy splitting. Electron pairing is stable at temperatures as high as 900 millikelvin, well above the superconducting transition temperature (about 300 millikelvin). These experiments demonstrate the existence of a robust electronic phase in which electrons pair without forming a superconducting state. Key experimental signatures are captured by a model involving an attractive Hubbard interaction that describes real-space electron pairing as a precursor to superconductivity.