  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 perform
interferometry of the thermoelectric transport in a quantum point contact
(QPC). We observe an interference pattern both in SGM and TSGM images, and
evidence large differences between the two signals in the low density regime of
the QPC. In particular, a large phase jump appears in the interference fringes
recorded by TSGM, which is not visible in SGM. We discuss this difference of
sensitivity using a microscopic model of the experiment, based on the
contribution from a resonant level inside or close to the QPC. This work
demonstrates that combining scanning gate microscopy with thermoelectric
measurements offers new information as compared to SGM, and provides a direct
access to the derivative of the device transmission with respect to energy,
both in amplitude and in phase.
