Title: Ohm’s law revisited: Mesoscopic microwave conductance
Abstract: The quantum nature of electronic conductance is manifest in magnetoresistance fluctuations due
to the interference of multiply scattered electronic waves at ultralow temperatures in micron-
sized mesoscopic conductors, in which the wave is temporally coherent. Quantum transport is
also seen in the stepwise increase in electronic conductance in ballistic heterojunctions with
increasing width as new wave channels are introduced. Equivalent steps in ballistic optical
transmittance are observed when an aperture is illuminated with diffuse light. Dips in the
conductance have been found in simulations in diffusive media, but measurements of the
conductance or the transmittance have not been performed despite the centrality of conductance
in mesoscopic physics. Here we measure the microwave transmittance through random
waveguides and find dips that arise due to the vanishing of transmission in an eigenchannel of
the transmission matrix arising from two distinct effects: Either the energy density on the output
surface vanishes as transmission zeros in the map of the phase of the determinant of the
transmission matrix reach the real axis of the complex frequency plane before the crossover to a
new channel, or the longitudinal velocity of a newly introduced transmission eigenchannel
vanishes. Even though the transmission in the lowest transmission eigenchannel is exponentially
small, correlation between the transmission eigenvalues pulls down the transmission of other
eigenchannels, thereby affecting the conductance. The changing statistics of transmission zeros
with sample dimensions determines both the departures from and the approach to Ohm’s law in
mesoscopic conductors. The zero in eigenchannel velocity at the crossover to a new channel is
reminiscent of the Wigner cusp anomaly in the nuclear scattering cross sections when a new
channel is opened.