Spatiotemporal dynamics of Coulomb-correlated carriers in semiconductors

When the excitation of carriers in real space is focused down to the nanometer scale, the carrier system can no longer be viewed as homogeneous, and ultrafast transport of the excited carrier wave packets occurs. In state-of-the-art semiconductor structures such as low-dimensional heterostructures or monolayers of transition-metal dichalcogenides, the Coulomb interaction between excited carriers becomes stronger due to confinement or reduced screening. This demands a fundamental understanding of strongly interacting electrons and holes and the influence of Coulomb correlations. To study the corresponding particle dynamics in a controlled way, we consider a system of up to two electron-hole pairs exactly within a wave-function approach. We show that the excited wave packets contain a nontrivial mixture of free-particle and excitonic states. We further scrutinize the influence of the Coulomb interaction on the wave-packet dynamics, revealing its different role for below- and above-band-gap excitation.

Figure 1

Sketch of localized photoexcitation of a quantum wire resulting in traveling electron-hole pairs coupled via the Coulomb interaction $V_C$.

Figure 2

Linear absorption spectrum (dashed line) and spectrum (solid lines) of the exciting laser pulses with different excess energy $E_{\mathrm{ex}}$.

Figure 3

Dynamics of the electron (left) and hole (right) density $n_{e/h}$ in the low-density limit for an excitation (a) resonant to the $1s$ exciton and (b) within the continuum. All the distributions have been normalized to their respective maxima.

Figure 4

Energy contributions normalized to the final electron number for an excitation (a) resonant to the exciton and (b) within the continuum.

Figure 5

Spatiotemporal carrier dynamics in the high-density case after a $100\mathrm{fs}$ pulse with excess energy $E_{\mathrm{ex}}=-24\mathrm{meV}$. (a) Dynamics of electron and hole distributions and (b) energy contributions.

Figure 6

Variance of the electronic wave packet as a function of time for the low-intensity $(N_e\approx {10}^{-4}$, blue line) and high-intensity $(N_e\approx 1.7$, red line) case. The black dashed lines indicate quadratic fits $\propto t^2$ to the respective curves.

Figure 7

Spatiotemporal carrier dynamics after a $100\mathrm{fs}$ pulse with excess energy $E_{\mathrm{ex}}=10\mathrm{meV}$. (a) Dynamics of electron and hole distributions and (b) energy contributions.

Figure 8

Normalized two-particle density [cf. Eq. (8)] for continuum excitation in (a) the low-density limit and (b) the high-density limit.

Figure 9

Energy distribution of the carrier occupations $f^{e/h}$ as a function of time in the low- (left panels) and high-density limit (right panels).

Figure 10

Final excitonic (circles) and continuum (triangles) occupation probabilities for different carrier densities for $E_{\mathrm{ex}}=-24\mathrm{meV}$ (red symbols) and $E_{\mathrm{ex}}=10\mathrm{meV}$ (blue symbols).

Figure 11

Normalized $1s$ exciton distribution as a function of center-of-mass energy at the end of the simulation for (a) excitonic and (b) continuum excitation. The black solid line corresponds to the high-density limit and the blue solid line to the low-density limit.

Figure 12

Electronic (left column) and hole (right column) densities for continuum excitation in the high-density limit using (a) a Hartree-Fock (HF) simulation and (b) the wave-function-based CI simulation [cf. Fig 7].

Figure 13

Wave-packet variance $\mathrm{\Delta }{z}_e^2$ as a function of time (cf. Fig. 6) now also including the Hartree-Fock simulation (orange dashed line). A polynomial fit is shown as a black solid line.