Transport of a wave packet through nanostructures: Quantum kinetics of carrier capture processes

Capture processes of an electronic wave packet traveling in a quantum wire into localized states of an embedded quantum dot by means of phonon emission are studied in a quantum kinetic approach. It turns out that due to the ultrashort length and time scales involved the capture processes exhibit a variety of quantum kinetic features which cannot be described by a simple semiclassical capture rate. We find in general a nonmonotonic rise of the occupation of bound states even at low temperatures where no phonon absorption is possible. This is related to the finite collision duration and the presence of coherent superpositions between initial and final states in the scattering process giving rise to phonon Rabi oscillations between free and trapped states. In the case of more than one bound state in the dot typically a linear combination of these bound states is populated, which leads to a nontrivial dynamics of the trapped carrier density. For potential profiles with large reflection probability it turns out that also the transmission and reflection behavior is modified by the capture process. Finally the theory is applied to a two-band model including optical excitation and excitonic effects. For the scenarios studied in the paper these phenomena lead to some quantitative modifications but they do not change the characteristic quantum features of the capture dynamics.

Figure 1

Electron density in the one-band model as a function of space and time (a) without and (b) with carrier-phonon interaction. Inset: initial electron distribution and quantum dot potential in real space with one bound level at $-14.4\mathrm{meV}$.

Figure 2

(a) Occupation of the bound level at $-14.4\mathrm{meV}$ as a function of time and (b) occupation of the continuum states at $t=0$ and 550 fs for the same scenario as in Fig. 1.

Figure 3

Spatially resolved electron density at different times for the case of an electron wave packet approaching two identical quantum dot potentials. The lower part shows the double quantum dot potential with effectively uncoupled bound states of the dots at $-14.4\mathrm{meV}$.

Figure 4

Occupation of the bound levels in the two quantum dots of Fig. 3 as a function of time.

Figure 5

Electron density as a function of space and time for the case of an electron wave packet approaching a quantum dot potential with three bound states.

Figure 6

Spatial profile of the electron density at different times for the case of a quantum dot potential with three bound states; dotted lines are without and solid lines with electron-phonon interaction. The lower part shows the potential profile together with the energies of the bound states.

Figure 7

(a) Occupations of the bound levels as functions of time (level 1, $-30.6\mathrm{meV}$; level 2, $-15.2\mathrm{meV}$; level 3, $-5.8\mathrm{meV}$) and (b) imaginary part of the coherences between the bound levels.

Figure 8

Spatial profiles of the electron density at different times for the case of an electron wave packet approaching a square well potential. (a) refers to an initial excess energy of 12 meV (reflection maximum) and (b) to an excess energy of 34 meV (transmission maximum). The dotted lines are without and the solid lines with carrier-phonon interaction.

Figure 9

(a), (b) Occupations of the bound states and (c), (d) coherences between these states as a function of time for the case of a square well potential. The left part (a), (c) refers to an initial energy of 12 meV (reflection maximum), the right part (b), (d) to an initial energy of 34 meV (transmission maximum).

Figure 10

Spatial profiles of the (a), (b) electron and (c), (d) hole density at different times for the case of a quantum dot potential with three bound states obtained from simulations within a two band model. The left part refers to a calculation without Coulomb interaction; in the right part Coulomb interaction has been included on the mean-field level (time-dependent Hartree-Fock approximation).

Figure 11

(a), (b) Occupations of the bound electron states and (c), (d) coherences between the bound electron states obtained from simulations within a two-band model. The left part refers to a calculation without Coulomb interaction; in the right part the Coulomb interaction has been included on the mean-field level.