Abstract
We study the unitary propagation of a two-particle one-dimensional Schrödinger equation by means of the Split-Step Fourier method, to study the coherent evolution of a spatially indirect exciton (IX) in semiconductor heterostructures. The mutual Coulomb interaction of the electron-hole pair and the electrostatic potentials generated by external gates and acting on the two particles separately are taken into account exactly in the two-particle dynamics. As relevant examples, step/downhill and barrier/well potential profiles are considered. The space- and time-dependent evolutions during the scattering event as well as the asymptotic time behavior are analyzed. For typical parameters of GaAs-based devices, the transmission or reflection of the pair turns out to be a complex two-particle process, due to comparable and competing Coulomb, electrostatic, and kinetic energy scales. Depending on the intensity and anisotropy of the scattering potentials, the quantum evolution may result in excitation of the IX internal degrees of freedom, dissociation of the pair, or transmission in small periodic IX wavepackets due to dwelling of one particle in the barrier region. We discuss the occurrence of each process in the full parameter space of the scattering potentials and the relevance of our results for current excitronic technologies.
Highlights
Excitonic states are the fundamental below-gap resonances in semiconductors heterostructures, where stability and strength are strongly enhanced by quantum confinement.[1]
We study the unitary propagation of a two-particle one-dimensional Schrödinger equation by means of the Split-Step Fourier method, to study the coherent evolution of a spatially indirect exciton (IX) in semiconductor heterostructures
We have discussed the unitary space- and time-dependent quantum dynamics of a single IX in a coupled quantum wells (CQWs) system scattering against simple potential profiles
Summary
Excitonic states are the fundamental below-gap resonances in semiconductors heterostructures, where stability and strength are strongly enhanced by quantum confinement.[1]. In this paper we use a unitary propagation scheme to investigate theoretically the exact coherent dynamics of a single IX wavepacket describing scattering against different types of electrostatic potential landscapes, namely, steps/downhills and barriers/wells, using a minimal 1D model of an IX (Figure 1). In this sense, this is a two-particle generalization of the textbook description of one particle bouncing against potential steps and barriers. Details of the numerical method are given in Appendix A
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