Electron Lateral Trapping Induced by Non-Uniform Thickness in Solid Neon Layers

TL;DR

This work reveals that finite solid Ne thickness significantly strengthens electron binding above the Ne surface, and that thickness non-uniformity—naturally arising from substrate morphology—can create lateral trapping potentials for single electrons. Using a model that couples the perpendicular image-potential with a local-thickness description, the authors show $W^{\mathrm{G}}$ falls deeply for thinner layers (e.g., $L=10~\mathrm{nm}$ yielding $W^{\mathrm{G}} \approx -44.6$ to $-40.0~\mathrm{meV}$ depending on the substrate, compared to a bulk value of $-15.7~\mathrm{meV}$), while thickness fluctuations of $\Delta L \sim 3~\mathrm{nm}$ induce ground-state shifts of ~$10~\mathrm{meV}$. They propose a nanopatterned-substrate mechanism where engineered thickness variations generate controllable lateral traps, tunable by a perpendicular electric field with a nonlinear, polarity-dependent response, enabling scalable single-electron charge qubits. The framework suggests a path to multi-qubit architectures via patterned nanopillars that locally thin the Neon layer and couple to microwave resonators, potentially compatible with superconducting substrates. Overall, finite-thickness effects provide a robust, field-tunable route to lateral confinement in solid-Neon qubits with implications for quantum information processing.

Abstract

Recent experimental advances highlight electron charge qubits floating above solid neon as an emerging promising platform for quantum computing, but the physical origin of single-electron lateral trapping is still not fully understood. While prior theoretical work has mainly examined electrons above bulk solid neon, experimental systems usually feature neon layers of only $\lesssim 10$ nm thickness and non-uniformity, highlighting unresolved questions about how thickness influences electron trapping. Here we theoretically investigate the effect of finite thickness and non-uniformity of solid neon layers on electron trapping. For a 10 nm layer, the electron binding energy is enhanced threefold compared to bulk. Exploiting this thickness dependence, we propose a nanopatterned-substrate mechanism in which engineered thickness variations generate lateral trapping potentials for electrons. The lateral trapping potential can be finely tuned by a perpendicular electric field. Such non-uniform-thickness induced electron charge qubits open a viable pathway toward building multi-qubit systems for quantum computation.

Figures (4)

• Figure 1: (a) Schematic illustration of electrons hovering above a solid Ne layer. The blue and orange curves represent the perpendicular potential $V_{\perp}$ for a finite thickness ($L = 10~\mathrm{nm}$) and for the bulk case ($L = \infty$), respectively. (b) Schematic illustration of the formation process of a non-uniform solid Ne layer. Initially, a uniform liquid Ne film forms above the substrate. Due to the Gibbs–Thomson effect, solidification begins preferentially at the bottom of surface depressions. The remaining liquid then thermally diffuses to re-establish a uniform layer above the newly solidified regions. The interplay of these processes ultimately leads to a non-uniform solid Ne layer.
• Figure 2: Perpendicular potential profile $V_L^z(z)$ for various Ne layer thicknesses $L$. (b) Ground-state energy $W_L^{\mathrm{G}}$ and (c) mean electron height $h_e$ as functions of $L$ under different external electric fields $E_{\mathrm{ex}}$. The dashed lines indicate the corresponding values in the bulk limit ($L \to \infty$).
• Figure 3: (a) Schematic illustration of the model showing the variation in solid Ne layer thickness at $\rho = R$, corresponding to the edge of the substrate nanopillar. (b) Profile of the resulting effective lateral potential, which varies from $-V_0$ at the center to zero at large distances.
• Figure 4: (a) Potential depth $-V_0$ for different $L$ and $\Delta L$. (b) Lateral excitation energy $\Delta U$ versus $R$ and $\Delta L$ for $b = 2.0~\mathrm{nm}$ and $E_{\mathrm{ex}} = 0$. (c) $\Delta U$ and mean radius $\rho_e$ as functions of $E_{\mathrm{ex}}$ with $b= 2.0~\mathrm{nm}$ , $R = 110~\mathrm{nm}$, and $\Delta L = 0.5~\mathrm{nm}$. Black dashed lines indicate linear trends, highlighting the nonlinear field dependence of $\Delta U$.