Controlling the transport of electrons on superfluid $^{4}$He in symmetric and asymmetric FET-like structures
When floating on a two-dimensional (2D) surface of superfluid $^{4}$He, electrons arrange themselves in 2D crystalline structure known as Wigner crystal. In channels, the boundaries interfere the crystalline order and in case of very narrow channels one observes a quasi-1D Wigner crystal formed by just a few rows of electrons and, ultimately, one row, i.e., in the ``quantum wire'' regime. Recently, the ``quantum wire'' regime was accessed experimentally [D. Rees {\it et al.}, Phys. Rev. Lett. {\bf 108}, 176801 (2012)] resulting in unusual transport phenomena such as, e.g., oscillations in the electron conductance. Using molecular dynamics simulations, we study the nonlinear transport of electrons in channels with constrictions: single and multiple symmetric and asymmetric geometrical constrictions with varying width and length, and saddle-point-type potentials with varying gate voltage. We analyze the average particle velocity versus driving force or the gate voltage. We have revealed a significant difference in the dynamics for long and short constrictions: the oscillations of the average particle velocity for the systems with short constrictions exhibit a clear correlation with the transitions between the states with different numbers of rows of particles while for longer constrictions these oscillations are suppressed. The obtained results are in agreement with the experimental observations. We proposed a FET-like structure that consists of a channel with asymmetric constrictions. We show that applying a transverse bias results either in increase of the average particle velocity or in its suppression thus allowing a flexible control tool over the electron transport. Our results bring important insights into the dynamics of electrons floating on the surface of superfluid $^{4}$He in channels with constrictions and allow an effective control over the electron transport.