Cross-over between collective and independent-particle excitations in quasi-2D electron gas with one filled miniband

TL;DR

This paper analytically demonstrates that in a quasi-2D electron gas with one filled miniband, exchange and Hartree kernels cancel at all densities at short distances, influencing the nature of excitations depending on confinement.

Contribution

It provides an analytical proof of kernel cancellation at arbitrary densities and explores how confinement affects excitation energies in the system.

Findings

Exchange and Hartree kernels cancel at all densities at short distances.

Strong confinement causes excitation energies to approach single-particle Kohn-Sham energies.

Spin polarization influences the degree of this convergence.

Abstract

While it has been recently demonstrated that, for quasi-2D electron gas (Q2DEG) with one filled miniband, the dynamic exchange $f_x$ and Hartree $f_H$ kernels cancel each other in the low-density regime $r_s\rightarrow \infty$ (by half and completely, for the spin-neutral and fully spin-polarized cases, respectively), here we analytically show that the same happens at arbitrary densities at short distances. This motivates us to study the confinement dependence of the excitations in Q2DEG. Our calculations unambiguously confirm that, at strong confinements, the time-dependent exact exchange excitation energies approach the single-particle Kohn-Sham ones for the spin-polarized case, while the same, but less pronounced, tendency is observed for spin-neutral Q2DEG.