Pascal conductance series in ballistic one-dimensional LaAlO${}_3$/SrTiO${}_3$ channels

Abstract

The ability to create and investigate composite fermionic phases opens new avenues for the investigation of strongly correlated quantum matter. We report the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the LaAlO${}_3$/SrTiO${}_3$ interface. The waveguide conductance follows a characteristic sequence within Pascal's triangle: $(1,3,6,10,15,...)\cdot e^2/h$, where $e$ is the electron charge and $h$ is the Planck constant. The robustness of these steps with respect to magnetic field and gate voltage indicate the formation of a new family of degenerate quantum liquids formed from bound states of $n=2,3,4,...$ electrons. These experiments could provide solid-state analogues for a wide range of composite fermionic phases ranging from neutron stars to solid-state materials to quark-gluon plasmas.