Weak localization effects in a quasi-one-dimensional electron system over liquid helium

Magnetoresistance $\rho_{xx}$ measurements are performed for a quasi-one-dimensional electron system over liquid helium in the gas-scattering region (the temperature range $1.3$–$2.0$ K). The measurements show that, as the magnetic field increases, the magnetoresistance $\rho_{xx}$ first decreases and then passes through a minimum and increases according to the law $\rho_{xx}\sim B^2$ . It is suggested that the negative magnetoresistance observed in the experiment is caused by the weak localization effects. The results of the experiment are in qualitative agreement with the theoretical model describing the weak localization effects in a one-dimensional nondegenerate electron system.