Universality of optical absorptance quantization in two-dimensional group-IV, III-V, II-VI, and IV-VI semiconductors

Abstract

The optical absorptance of a single graphene layer over a wide range of wavelengths is known to be remarkably constant at the universal value πα where α is the fine structure constant. Using atomistic tight-binding calculations, we show that the absorptance spectra of nanometer-thin layers (quantum wells) of group-IV, III-V, II-VI or IV-VI semiconductors are characterized by marked plateaus at integer values of πα, in the absence of excitonic effects. In the case of InAs, the results obtained are in excellent agreement with the currently available experimental data. By revisiting experimental data on semiconductor superlattices, we show that πα is also a metric of their absorption when normalized to a single period. We conclude that the πα quantization is universal in semiconductor quantum wells provided that excitonic effects are weak, and is therefore not specific to the zero-gap graphene case. The physical origin of this universality and its limits are discussed using analytical models that capture the main underlying physics of the lowest optical transitions in III-V and II-VI semiconductor quantum wells. These models show that the absorptance is ruled by πα independent of the material characteristics because of the presence of a dominant term in the Hamiltonian, linear in the wave vector k (∼ V • k), which couples the conduction band to the valence bands. However, the prefactor in front of πα is not unity as in graphene due to the different nature of the electronic states. In particular, the spin-orbit coupling plays an important role in bringing the absorptance plateaus closer to integer values of πα. The case of IV-VI semiconductor (PbSe) quantum wells characterized by a rocksalt lattice and multi-valley physics is very similar to that of graphene, with the specification that a "massful gap" is formed around the Dirac points.

Dielectric and optical properties of superlattices of epitaxially connected nanocrystals

“…By definition, the two-level model (green solid line) describes only the S h − S e transitions forming the lowest energy absorption peak. wells of PbSe and CdSe, respectively [19]. A value close to 4πα is found for the bilayer of PbSe NCs [Fig.…”

“…We conclude that atomically coherent superlattices of NCs are promising materials for cost-effective photodetectors, [39] not only for their tunable energy spectrum and their improved transport properties compared to assemblies of disconnected NCs [16] but also for their high absorptance, relatively close to the upper limit corresponding to the perfectly crystalline thin film (nanowire) in 2D (1D) systems, thanks to a reduced screening of the electric component of the external electromagnetic field. The present study of the permeation of the electromagnetic field in low-dimensional semiconductors is inspired by the recent findings [15] that this upper limit for band-edge absorptance in 2D systems such as graphene [17], semiconductor quantum wells [18,19] and atomically coherent superlattices of NCs have a universal character directly related to the absorptance quantum πα, where α is the fine structure constant.…”

Quantum Dot Acceptors in Two-Dimensional Epitaxially Fused PbSe Quantum Dot Superlattices

“…Despite a temperature of 77 K, which is not low enough to resolve the small valence peaks lying deeper in energy, the shape of distinct experimental spectra obtained at negative bias (Figure e) compares well with the theoretical DOS calculated for the valence band (Figure f). The DOS amplitude grows with increasing coupling, and the background, which is better observed for the quantum well as the steps are not flat, is caused by the linear dispersion encountered in PbSe. , Therefore, the valence electron distribution is distorted in comparison with that of isolated QDs. For most of the QDs, we estimated the necking size being 0.5 time the size of the QDs based on the STEM images.…”

“…The DOS amplitude grows with increasing coupling, and the background, which is better observed for the quantum well as the steps are not flat, is caused by the linear dispersion encountered in PbSe. 32,36 Therefore, the valence electron distribution is distorted in comparison with that of isolated QDs. For most of the QDs, we estimated the necking size being 0.5 time the size of the QDs based on the STEM images.…”