Self-consistent one-dimensional electron system on liquid helium suspended over a nanoscale dielectric substrate

TL;DR

This paper develops a self-consistent analytical model for one-dimensional electron systems on liquid helium suspended over nanoscale dielectric substrates, revealing strong coupling effects and quantization gaps in the electron energy levels.

Contribution

It introduces a novel analytical approach to describe coupled transverse and lateral quantizations in electrons on liquid helium over nanoscale substrates, highlighting strong mutual interactions.

Findings

Quantization gaps of over 10 meV and 1 meV for transverse and lateral directions.

Strong mutual coupling enhances quantization effects.

Analytical model based on an adiabatic approximation for electron quantization.

Abstract

For electrons above a superfluid helium film suspended on a specially designed dielectric substrate, $z=h(y)$, we obtain that both the transverse, along $z$, and the lateral, along $y$, quantizations are strongly enhanced due to a strong mutual coupling. The self-consistent quantum wires (QWs) with non-degenerated one-dimensional electron systems (1DESs) are obtained over a superfluid liquid helium (LH) suspended self-consistently on different dielectric substrates with a nanoscale modulation. A gap $\gtrsim 10$meV ($\gtrsim 1$meV) is obtained between the lowest two electron levels due to mainly the transverse (lateral) quantization. Our analytical model takes into account a strong interplay between the transverse and the lateral quantizations of an electron. It uses that the characteristic length (energy) along the former direction is essentially smaller (larger) than the one along the latter, in a close analogy with the adiabatic approximation.