A quantum point contact (QPC) is a very basic nano-electronic device: a short and narrow transport channel between two electron reservoirs. In clean channels electron transport is ballistic and the conductance $G$ is then quantised as a function of channel width with plateaus at integer multiples of $2e^2/h$ ($e$ is the electron charge and $h$ Planck's constant). This can be understood in a picture where the electron states are propagating waves, without need to account for electron-electron interactions. Quantised conductance could thus be the signature of ultimate control over nanoscale electron transport. However, even studies with the cleanest QPCs generically show significant anomalies on the quantised conductance traces and there is consensus that these result from electron many-body effects. Despite extensive experimental and theoretical studies understanding of these anomalies is an open problem. We report evidence that the many-body effects have their origin in one or more spontaneously localised states that emerge from Friedel oscillations in the QPC channel. Kondo physics will then also contribute to the formation of the many-body state with Kondo signatures that reflect the parity of the number of localised states. Evidence comes from experiments with length-tunable QPCs that show a periodic modulation of the many-body physics with Kondo signatures of alternating parity. Our results are of importance for assessing the role of QPCs in more complex hybrid devices and proposals for spintronic and quantum information applications. In addition, our results show that tunable QPCs offer a rich platform for investigating many-body effects in nanoscale systems, with the ability to probe such physics at the level of a single site.

NOTE: 59 page document. Pages 1-17 main text (with 4 figures); pages 18-45 supplementary information; pages 46-59 example of full data set