# Interaction of gated and ungated plasmons in two-dimensional electron systems

## TL;DR

This paper develops an analytical theory for the interaction of gated and ungated plasmons in partly gated two-dimensional electron systems, revealing a novel gapless mode with hybrid properties not previously studied.

## Contribution

It introduces the first analytical model describing the interaction of gated and ungated plasmons in a finite-width gated 2DES, discovering a new fundamental gapless plasmon mode.

## Key findings

- Discovery of a new gapless plasmon mode with square root dispersion.
- Identification of a 'near-gate plasmon' localized near the gate.
- Analytical description of propagating plasmon modes with multiple charge density nodes.

## Abstract

Unique properties of plasmons in two-dimensional electron systems (2DESs) have been studied for many years. Existing theoretical approaches allow for analytical study of the properties of ungated and gated plasmons in two fundamental, ideal cases - the 2DES in dielectric environment and under an infinite metallic gate, respectively. However, it is for the first time that we introduce an analytical theory of the interaction of gated and ungated plasmons in partly gated 2DES. Generally, a finitewidth gate is formed by a metallic strip placed over an infinite plane hosting 2D electrons. Our solution, in particular, describes the propagating plasmon modes with their charge density having N nodes under the gate. In this regard, a new mode with N = 0 has been found in addition to the gapped modes with N = 1, 2,..., previously derived from numerical calculations. Unexpectedly, this fundamental plasmon mode has been found to differ substantially from the rest. In fact, it is characterised by gapless square root dispersion and represents a hybrid of gated and ungated plasmons. In contrast to the higher modes, the currents and lateral fields of the fundamental mode are localized mainly to the outside area in the vicinity of the gate. Heretofore, such a 'near-gate plasmon' has never been considered.