  Electric-field effect control of two-dimensional electron gases (2-DEG) has
enabled the exploration of nanoscale electron quantum transport in
semiconductors. Beyond these classical materials, transition metal-oxide-based
structures have d-electronic states favoring the emergence of novel quantum
orders absent in conventional semiconductors. In this context, the
LaAlO3/SrTiO3 interface that combines gate-tunable superconductivity and
sizeable spin-orbit coupling is emerging as a promising platform to realize
topological superconductivity. However, the fabrication of nanodevices in which
the electronic properties of this oxide interface can be controlled at the
nanoscale by field-effect remains a scientific and technological challenge.
Here, we demonstrate the quantization of conductance in a ballistic quantum
point contact (QPC), formed by electrostatic confinement of the LaAlO3/SrTiO3
2-DEG with a split-gate. Through finite source-drain voltage, we perform a
comprehensive spectroscopic investigation of the 3d energy levels inside the
QPC, which can be regarded as a spectrometer able to probe Majorana states in
an oxide 2-DEG.
