Extrinsic thermoelectric response of coherent conductors

We investigate the thermoelectric response of a coherent conductor in contact with a scanning probe. Coupling to the probe has the dual effect of allowing for the controlled local injection of heat currents into the system and of inducing interference patterns in the transport coefficients. This is sufficient to generate a multiterminal thermoelectric effect even if the conductor does not effectively break electron-hole symmetry and the tip injects no charge. Considering a simple model for noninteracting electrons, we find a nonlocal thermoelectric response which is modulated by the position of the hot probe tip, and a nonreciprocal longitudinal response which leads to a thermoelectric diode effect. A separate investigation of the effects of dephasing and of quasielastic scattering gives further insights into the different mechanisms involved.