Linear scaling approach for atomistic calculation of excitonic properties of 10-million-atom nanostructures

2020

Sci Rep

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We report studies of $${\varvec{k}}$$ k -dependent Landé g-factor, performed by both continuous media approximation $${\varvec{k}}{\varvec{\cdot }}{\varvec{p}}$$ k · p method, and atomistic tight-binding $$\hbox {sp}^3\hbox {d}^5\hbox {s}^*$$ sp 3 d 5 s ∗ approach. We propose an effective, mesoscopic model for InAs that we are able to successfully compare with atomistic calculations, for both very small and very large nanostructures, with a number of atoms reaching over 60 million. Finally, for nanostructure dimensions corresponding to near-zero g-factor we report electron spin states anti-crossing as a function of system size, despite no shape-anisotropy nor strain effects included, and merely due to breaking of atomistic symmetry of cation/anion planes constituting the system.

Section: Nanostructuresmentioning

confidence: 94%

Electron g-factor in nanostructures: continuum media and atomistic approach

Gawarecki

2020

Sci Rep

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“…Finally, the excitonic spectra are calculated with the configuration interaction method 2,[104][105][106][107][108] . Configuration interaction calculations are performed in a computationally challenging basis 63 involving 20 (with spin) lowestenergy electron and hole states (up to the f shell of a single cylindrical quantum dot) and leading to the total 400 excitonic configuration, wheres the largest computational cost is related to calculation of 160,000 electron-hole Coulomb integrals 105,106 over a computational box containing over 1.3 × 10 6 atoms. Results obtained in a smaller basis of lowest 4 excitonic configurations are shown in the "Appendix" for comparison.…”

Section: Methodsmentioning

confidence: 99%

Vanishing fine structure splitting in highly asymmetric InAs/InP quantum dots without wetting layer

2020

Sci Rep

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Contrary to simplified theoretical models, atomistic calculations presented here reveal that sufficiently large in-plane shape elongation of quantum dots can not only decrease, but even reverse the splitting of the two lowest optically active excitonic states. Such a surprising cancellation of bright-exciton splitting occurs for shape-anisotropic nanostructures with realistic elongation ratios, yet without a wetting layer, which plays here a vital role. However, this non-trivial effect due to shapeelongation is strongly diminished by alloy randomness resulting from intermixing of InAs quantumdot material with the surrounding InP matrix. Alloying randomizes, and to some degree flattens the shape dependence of fine-structure splitting giving a practical justification for the application of simplified theories. Finally, we find that the dark-exciton spectra are rather weakly affected by alloying and are dominated by the effects of lateral elongation. Quantum dots 1,2 are man-made semiconductor nanostructures that come in a wide variety of types 3-5 , and are extensively studied with interest driven by both basic scientific curiosity as well as promising applications in quantum information 6 , computing 7,8 , and cryptography 9. Apart from the elementary excitations, electrons and holes, quantum dots can confine interacting electron-hole pairs, namely excitons. 10 An emission cascade from a two exciton (biexciton) state, through two indistinguishable exciton states should lead to the emission of polarization entangled photon pairs. 9,11-13 However, in realistic quantum dots the intermediate exciton state is often split by the electron-hole exchange interaction 14-16 hindering the efficiency of the entanglement generation. This energetic difference between the two bright exciton states, known as the fine-structure splitting or the bright exciton splitting (BES) is typically (10-100 µeV) much larger than the emission linewidth (∼ 1 µeV). Tailoring the BES in nanostructures is thus essential due to its relevance for photon entanglement generation. 7,11,17,18 This is particularly important for InAs/InP nanostructures, which are promising candidates for quantum emitters at 1.3 or 1.55 µm telecommunication relevant wavelengths 19-22. Notably, InAs/InP nanostructures can be fabricated in various ways, including self-assembled and nanowire quantum dots 23-27 of quasi-cylindrical shapes, as well as strongly elongated dots 28-42 , sometimes referred to as quantum dashes. Similarly to cylindrically-shaped dot systems, quantum dashes have the potential for applications 30,31,43-45 combined with considerable tuning capabilities 46,47. The manipulation of the BES aimed towards generation of entangled photon pairs is a vital and broad research area with significant efforts have been made utilizing post-growth annealing 48,49 , spectral filtering 9 , sample selection 50,51 , growth of highly symmetric structures 24,26,52-54 , and the application of external electric 55,56 , magnetic 18,57,58 , and strain fields 59-61. With respect t...

“…71,82 In this work I go beyond this approximation and account for the f -shell as well, resulting in total 20 (with spin) electron and 20 hole single particle states entering many-body calculations and total of over 0.6 million Coulomb direct and exchange integrals calculated over 1.3 million atoms in the computational box. 71,83 Calculation of the multiexcitonic spectra produces thus a significant computational challenge and on a 192-core computer cluster it takes about 72-hours for all computational stages combined (i.e. strain, piezoelectricity, tight-binding and configuration interaction) for every single t value, with the configuration interaction being by far the most timedemanding part.…”

Section: A System and Methodsmentioning

confidence: 99%

From quantum dots to quantum dashes: Excitonic spectra of highly elongated InAs/InP nanostructures

2019

Phys. Rev. B

A transition from a cylindrical quantum dot to a highly elongated quantum dash is theoretically studied here with an atomistic approach combining empirical tight binding for single particle states and configuration interaction method for excitonic properties. Large nanostructure shape anisotropy leads to a peculiar trend of the bright exciton splitting, which at certain point is quenched with further shape elongation, contradicting predictions of simplified models. Moreover strong shape elongation promotes pronounced optical activity of the dark exciton, that can reach substantial 1% fraction of the bright exciton intensity without application of any external fields. An atomistic calculation is augmented with a elementary phenomenological model expressed in terms of lighthole exciton add-mixture increasing with the shape deformation. Finally, exctionic complexes X − , X + , and XX are studied as well and the correlations due to presence of higher excited states are identified as a key-factor affecting excitonic binding energies and the fine structure.