Mixed correlation phases in elongated quantum dots

It is theoretically shown, within the local spin-density-functional theory framework, that inhomogeneous confining potentials in elongated, diluted $N$-electron quantum dots may lead to the formation of mixed phases in which some regions of the $N$-electron system behave like a Fermi liquid while, simultaneously, other, more dilute regions display quasiclassical Wigner crystallization. The characterization of the mixed phases in the addition energy spectrum and the infrared response is reported. An infrared sensor of electron filling is suggested.

Figure 1

(a) Schematic geometry of the nanostructures under study. (b) Schematic profile of the spatial confining potential along the $z$ axis.

Figure 2

(a) Addition energy spectrum of the studied nanodumbbell (cylinder of $R=2\text{nm}$ radius and length $L=55\text{nm}$, ended with two $R=2.2\text{nm}$ radius spherical caps). [(b)–(r)] Ground state $z$-density profiles of this nanodumbbell populated with 4 up to 20 electrons, respectively. Solid line: total charge density. Dotted/dashed line: spin up/down density. Panels (d)–(r): density profiles have been cut to better display it in the ND trunk region.

Figure 3

Ground state $z$-density profiles of the studied nanorod (cylinder of $R=2\text{nm}$ radius and length $L=55\text{nm}$) populated with 2 up to 16 electrons, respectively. Solid line: total charge density. Dotted/dashed line: spin up/down density.

Figure 4

NR ground state $z$-density profiles (the NR is modeled by a cylinder of $R=2\text{nm}$ radius and $L=55\text{nm}$ length) populated with $N=6$ electrons, subject to a 20 kV/cm electric field along the $z$ direction. Solid line: total charge density. Dotted/dashed line: spin up/down density.

Figure 5

(Color online) Spin-density (dashed lines) and charge-density (solid lines) transverse responses (arb. units) of different NRs and NDs. Geometry and electron population are indicated at each of the panels. Panels (b) and (c), on the one hand, and (d) and (e), on the other hand, correspond to the same number of electrons in the central cylinder (4 and 12, respectively).

Figure 6

(Color online) Low-energy (left column) and high-energy (right column) spin-density (dashed lines) and charge-density (solid lines) axial responses (arb. units) of different NRs and NDs. Geometry and electron population are indicated at each of the panels and both are the same for every row of panels. Grouped panels correspond to the same number of electrons in the central cylinder. Responses are magnified two orders of magnitude in panels (g)–(j) with respect to their corresponding low-energy responses in panels (b)–(e).