  Stars provide an enormous gain for interstellar communications at their
gravitational focus, perhaps as part of an interstellar network. If the Sun is
part of such a network, there should be probes at the gravitational foci of
nearby stars. If there are probes within the solar system connected to such a
network, we might detect them by intercepting transmissions from relays at
these foci. Here, we demonstrate a search across a wide bandwidth for
interstellar communication relays beyond the Sun's innermost gravitational
focus at 550 AU using the Green Bank Telescope (GBT) and Breakthrough Listen
(BL) backend. As a first target, we searched for a relay at the focus of the
Alpha Centauri AB system while correcting for the parallax due to Earth's orbit
around the Sun. We searched for radio signals directed at the inner solar
system from such a source in the L and S bands. Our analysis, utilizing the
turboSETI software developed by BL, did not detect any signal indicative of a
non-human-made artificial origin. Further analysis excluded false negatives and
signals from the nearby target HD 13908. Assuming a conservative gain of 10^3
in L-band and roughly 4 times that in S-band, a ~1 meter directed transmitter
would be detectable by our search above 7 W at 550 AU or 23 W at 1000 AU in
L-band, and above 2 W at 550 AU or 7 W at 1000 AU in S-band. Finally, we
discuss the application of this method to other frequencies and targets.
