Picosecond timescale scattering of an electron-hole pair in semiconductor heterostructures
Federico Grasselli
Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia
1. Federico Grasselli, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia, and S3, Consiglio Nazionale delle Ricerche, Istituto Nanoscienze, Via Campi 213/a, Modena, Italy
2. Andrea Bertoni, S3, Consiglio Nazionale delle Ricerche, Istituto Nanoscienze, Via Campi 213/a, Modena, Italy
3. Guido Goldoni Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia, and S3, Consiglio Nazionale delle Ricerche, Istituto Nanoscienze, Via Campi 213/a, Modena, Italy.
We study the exact time-dependent dynamics and scattering of a Wannier-Mott exciton in a semiconductor heterostructure, taking into account the full two-particle quantum evolution on the picosecond timescale. This is, on the one hand, a basic problem in quantum mechanics, extending the text-book example of single-particle wave-packet propagation, and it can be probed by optical spectroscopy in properly designed nanostructures on sub-nanosecond timescale; On the other hand, it may have implications both for optoelectronic devices, and the study of macroscopically ordered quantum phases.[1, 2] In this contribution, I discuss exciton scattering in 1D and 2D structures, with typical potential landscapes generated by properly designed gates, such as ramps, barriers, wells, quantum point contacts or dots/antidots. We used both a numerically exact, unitary Schroedinger evolution – based on the Fourier split-step algorithm – of the quantum system,[3, 4] and a new self-energy approach, whereby the centre-of-mass degrees of freedom are evolved in a properly designed energy-dependent potential. We show explicitly that energy transfer between centre-of-mass and internal degrees of freedom may induce strong renormalization of scattering resonances and tunneling probabilities. Furthermore, we investigate the time-dependent dynamics originated by the few-body internal dynamics during excitation to higher e–h relative energy levels and exciton dissociation, as well as new phenomena such as dwelling of the exciton nearby the external potential edge, wave packet fragmentation, or two-body-induced diffraction patterns. Mean-field approaches, neglecting dynamical two-body correlations, are intrinsically unable to reproduce the correct phenomenology. Indeed, for external potential below or even comparable to the first relative-motion excitation threshold, internal virtual transition are shown to be the fundamental missing ingredient, and can be restored through a properly designed local self-energy term, which can be computed from the knowledge of the internal eigenstates alone. Self-energy corrected mean-field calculations are in very good agreement with exact calculations at an extremely reduced computational cost.[5] Implications for nuclear and molecular scattering will also be discussed.
References:
- L. V. Butov. J. Phys. Condens. Matter, 16(50):R1577, 2004.
- M. Alloing, et al. Europhys. Lett. 107(1):10012, 2014.
- FG, Andrea Bertoni, and Guido Goldoni. Space- and time-dependent quantum dynamics of spatially indirect excitons in semiconductor heterostructures. J. Chem. Phys. 142(3):034701, 2015.
- FG, Andrea Bertoni, and Guido Goldoni. Exact two-body quantum dynamics of an electron-hole pair in semiconductor coupled quantum wells: A time-dependent approach. Phys. Rev. B, 93(19):195310, 2016.
- FG, Andrea Bertoni, and Guido Goldoni. Time-dependent scattering of a composite particle: The role of internal virtual transitions. In preparation.