A Mesoscopic Mach-Zehnder Interferometer

Abstract

Double-slit electron interferometers, fabricated in high mobility two-dimensional electron gas (2GES), proved to be very powerful tools in studying coherent wave-like phenomena in mesoscopic systems [Yacobi 1994; Yacobi 1995; Schuster 1997; van der Viel 1997; Buks 1998; Ji 2000]. However, such interferometers have their disadvantages. They support multiple channels in each slit and consequently suffer from a small fringe visibility [Schuster 1997]. Their open geometry, required to eliminate multiple paths interference, allows only a small fraction of the injected current to be collected [Buttiker 1986; Schuster 1997; Buks 1998; Ji 2000]. Moreover, they do not function in a high magnetic field, which imposes a strong Lorentz force on the electrons and destroys the symmetry between the left and right slits. Hence, they are limited in their applications and cannot be employed, for example, in the quantum Hall effect (QHE) regime. We have fabricated and measured a novel, single channel, two-path electron interferometer, that functions in a high magnetic field. It is the first electronic analog of the well-known optical Mach-Zehnder (MZ) interferometer [Born 1999]. Based on a single edge state transport in the QHE regime, the interferometer collects all the injected electrons, hence having extremely high visibility (up to 62%) and high sensitivity to a small number of injected electrons. We find, unexpectedly that the interference pattern is extemely sensitive to the electron temperature or energy. By performing shot noise measurements of the interfering electrons we show that the observed loss of interference results from phase averaging among electrons and not due to incoherent scattering processes.