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 $\ensuremath{\pi}\ensuremath{\alpha}$ where $\ensuremath{\alpha}$ 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 $\ensuremath{\pi}\ensuremath{\alpha}$, 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 $\ensuremath{\pi}\ensuremath{\alpha}$ is also a metric of their absorption when normalized to a single period. We conclude that the $\ensuremath{\pi}\ensuremath{\alpha}$ 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 $\ensuremath{\pi}\ensuremath{\alpha}$ independent of the material characteristics because of the presence of a dominant term in the Hamiltonian, linear in the wave vector $\mathbf{k}\phantom{\rule{4pt}{0ex}}(\ensuremath{\sim}\mathbf{V}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{k})$, which couples the conduction band to the valence bands. However, the prefactor in front of $\ensuremath{\pi}\ensuremath{\alpha}$ 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 $\ensuremath{\pi}\ensuremath{\alpha}$. The case of IV-VI semiconductor (PbSe) quantum wells characterized by a rocksalt lattice and multivalley physics is very similar to that of graphene, with the specification that a ``massful gap'' is formed around the Dirac points.