Pascal Liquid Phase in Electronic Waveguides*

Clean one-dimensional electron transport has been observed in very few material systems. The development of exceptionally clean electron waveguides formed at the interface between complex oxides LaAlO$_3$ and SrTiO$_3$ enables low-dimensional transport to be explored with newfound flexibility. This material system not only supports ballistic 1D transport\footnote{M. Tomczyk \textit{et al.}, PRL \textbf{117}, 096801 (2016)}, but possesses a rich phase diagram and strong attractive electron-electron interactions\footnote{G. Cheng \textit{et al.}, Nature \textbf{521}, 196 (2015)} which are not present in other solid-state systems. Here we report an unusual phenomenon in which quantized conductance increases by steps that themselves increase sequentially in multiples of $e^2/h$. The overall conductance exhibits a Pascal-like sequence: 1, 3, 6, 10... $e^2/h$, which we ascribe to ballistic transport of 1, 2, 3, 4 ... “bunches” of electrons. We will discuss how subband degeneracies can occur in non-interacting models that have carefully tuned parameters. Strong attractive interactions are required, however, for these subbands to “lock” together. This “Pascal liquid” phase provides a striking example of the consequences of strong attractive interactions in low-dimensional environments.