Thermoelectric interferometry on a Quantum Point Contact

We introduce a new scanning probe technique derived from scanning gate microscopy (SGM) in order to investigate thermoelectric transport in two-dimensional semiconductor devices. The thermoelectric scanning gate microscopy (TSGM) consists in measuring the thermoelectric voltage induced by a temperature difference across a device, while scanning a polarized tip that locally changes the potential landscape. We apply this technique to investigate thermo-electric transport in a quantum point contact (QPC). We evidence large differences between SGM and TSGM signals in the low density regime of the QPC, where electron interactions are expected to be strong. We reveal from this set of measurements that Mott's law relating the thermopower to the conductance fails in this regime. In particular, a large phase jump appears in the interference fringes recorded by TSGM, which is not visible in SGM. We explain this difference of sensitivity using a microscopic model of the QPC, which includes the presence of a resonant level resulting from a spontaneous localization of electrons in the QPC channel at low transmission. This work demonstrates that combining scanning gate microscopy with thermoelectric measurements offers new information not available only with SGM, and thus provides deep understanding of the way the system transmission varies with energy, both in amplitude and in phase.