Quadratic electronic response of a two-dimensional electron gas

TL;DR

This paper evaluates the quadratic electronic response of a 2D electron gas and applies it to improve the accuracy of stopping power calculations for charged particles, revealing limitations of linear response in 2D systems.

Contribution

It provides the first self-consistent field calculation of the dynamical quadratic density-response function of a 2DEG and applies it to refine stopping power estimates.

Findings

Reproduces previous nonlinear stopping power results for slow antiprotons in high-density limit.

Calculates the $Z_1^3$ correction to stopping power across various projectile velocities.

Shows linear response is less reliable in 2D than in 3D for all projectile velocities.

Abstract

The electronic response of a two-dimensional (2D) electron system represents a key quantity in discussing one-electron properties of electrons in semiconductor heterojunctions, on the surface of liquid helium and in copper-oxide planes of high-temperature superconductors. We here report an evaluation of the wave-vector and frequency dependent dynamical quadratic density-response function of a 2D electron gas (2DEG), within a self-consistent field approximation. We use this result to find the $Z_1^3$ correction to the stopping power of a 2DEG for charged particles moving at a fixed distance from the plane of the 2D sheet, $Z_1$ being the projectile charge. We reproduce, in the high-density limit, previous full nonlinear calculations of the stopping power of a 2DEG for slow antiprotons, and we go further to calculate the $Z_1^3$ correction to the stopping power of a 2DEG for a wide range of projectile velocities. Our results indicate that linear response calculations are, for all projectile velocities, less reliable in two dimensions than in three dimensions.