Quasi-Low-Dimensional Electron Gas with One Populated Band as a Testing Ground for Time-Dependent Density-Functional Theory of Mesoscopic Systems

We find an exact analytical solution to the exchange-only time-dependent density-functional theory (TDDFT) problem for a significant class of quasi-low-dimensional (QLD) materials: QLD electron gas with only one band filled in the direction perpendicular to the layer or wire. The theory yields the TD exchange potential as an explicit nonlocal operator of the TD spin density. The dressed interband (image states) excitation spectra of quasi-two-dimensional electron gas are obtained, while the comparison with the Kohn-Sham transitions provides insights into the qualitative and quantitative role of the many-body interactions. Important cancellations between the Hartree $f_H$ and the exchange $f_x$ kernels of TDDFT are found in the low-density regime, elucidating the interrelations between the Kohn-Sham and the many-body dynamics in mesoscopic systems.

Figure 1

Schematics of the quasi-two-dimensional electron gas (Q2DEG) under the action of a time-dependent external potential.

Figure 2

Excitation energies of a spin-neutral Q2DEG with one transverse band filled. Circles, squares, and triangles are TDEXX, RPA, and KS excitation energies, respectively. Plus and minus signs mark even and odd excitations, respectively. Dashed lines connect eigenvalues of the even and odd self-oscillations, separately.

Figure 3

The same as Fig. 2, but for the fully spin-polarized Q2DEG.

Figure 4

Self-oscillations of the density of the spin-neutral EG of $r_s=5$, corresponding to the transitions to the first four excited states.