Direct Local Measurement of the Superconducting Energy Gap of Nb doped SrTiO$_{\mathrm{3}}$

Strontium titanate (STO) is a perovskite metal oxide insulator that can be electron doped by substitution of Ti or Sr sites with Nb or La, respectively, or by oxygen vacancies. When doped to high electron densities with concentration in the range of 5x10$^{\mathrm{19\thinspace }}$cm$^{\mathrm{-3\thinspace }}$to 2x10$^{\mathrm{20}}$ cm$^{\mathrm{-3}}$, STO becomes superconducting with a transition temperature below 400 mK, at a value highly dependent on the doping concentration. Previous observations were made on bulk crystals or films of doped STO by measuring the transitions in resistivity, magnetic susceptibility or thermal conductivity as a function of temperature or magnetic field. In this work, we use an ultra-low temperature scanning tunneling microscope(STM) to investigate the local electronic structure of the surface of Nb doped STO. The tunneling spectra taken at a sample temperature of $\approx $10 mK reveal a BCS energy gap of $\Delta =$ 40 ueV. Temperature and magnetic field dependent tunneling measurements show a critical temperature of $\approx $250 mK and upper critical field of $\approx $0.07 T. This is the first report of direct measurement of superconducting STO using an STM.