  Electronic analogues of optical interferences have been used to investigate
quantum phenomena in condensed matter. However, the most sensitive, Sagnac
optical interference, has not been realized in the electronic domain. We report
electronic Sagnac interference using ultraclean carbon nanotubes. We show that
Sagnac interference manifests as conductance oscillations versus gate voltage.
Compared to Fabry-Perot conductance oscillations, Sagnac oscillations have a
larger period and are more robust to temperature. Using nanotubes of known
structure, we show that Sagnac oscillations are a probe of nanotube chirality
in a transport measurement. Furthermore, upon tuning the system through a
topological phase transition in a magnetic field, we find that the Sagnac
interference undergoes a {\pi} phase-shift. Our interferometry may be used for
electronic structure characterization and study of many-body & photogalvanic
effects in these model chiral one-dimensional systems.
