Tunable Magneto-electric Subbands in Oxide Electron Waveguides

Strontium titanate-based complex-oxide interfaces hold great promise for exploring new correlated electron physics and applications in quantum technologies. Previous reports show electron mobility can be greatly enhanced in 1D \footnote {Nano. Lett. \textbf{13}, 364 (2013), Phys. Rev. Lett.\textbf{17}, 096801 (2016)}, while the 2D interface can contain 1D channels due to the presence of ferroelastic domains. In addition, carrier density measurements at the 2D interface by Shubnikov-de Haas (SdH) oscillations and Hall effect reveal a large discrepancy. Here we fabricate quasi-1D electron waveguides at the LaAlO$_3$/SrTiO$_3$ (LAO/STO) interface to locally probe the interface. The conductance of the waveguides is fully quantized, and the corresponding magneto-electric subbands can be depopulated by increasing the magnetic field. The 2D carrier densities (10$^{12}$ cm$^{-2}$) extracted from magnetic depopulation are consistent with measurements by SdH oscillations at the 2D interface. Our results show that magneto-electric subbands of quasi-1D electron waveguides can reproduce known SdH signatures without discrepancies in electron density, and suggest that 2D SdH measurements may also arise from quasi-1D channels.