Determination of time-reversal symmetry breaking lengths in an InGaAs interferometer array.

Quantum interference oscillations due to the Aharonov-Bohm phase were measured in a ring interferometer array fabricated on a two-dimensional electron system in an InGaAs/InAlAs heterostructure. Coexisting oscillations with magnetic flux periodicity h/e and h/2e were observed and their amplitudes compared as function of applied magnetic field. The h/2e oscillations originate in time-reversed trajectories with the ring interferometers operating in Sagnac-type mode, while the h/e oscillations result from Mach-Zehnder operation. The h/2e oscillations require time-reversal symmetry and hence can be used to quantify time-reversal symmetry breaking, more particularly the fundamental mesoscopic dephasing length associated with time-reversal symmetry breaking under applied magnetic field, an effective magnetic length. The oscillation amplitudes were investigated over magnetic fields spanning 2.2 T, using Fourier transforms over short segments of 40 mT. As the magnetic field increased, the h/2e oscillation amplitude decreased due to time-reversal symmetry breaking by the local magnetic flux in the interferometer arms. A dephasing model for quantum-coherent arrays was used to experimentally quantify effective magnetic lengths. The data was then compared with analytical expressions for diffusive, ballistic and confined systems.