Quantum of optical absorption in two-dimensional semiconductors

Abstract

The optical absorption properties of free-standing InAs nanomembranes of thicknesses ranging from 3 nm to 19 nm are investigated by Fourier transform infrared spectroscopy. Stepwise absorption at room temperature is observed, arising from the interband transitions between the subbands of 2D InAs nanomembranes. Interestingly, the absorptance associated with each step is measured to be ∼1.6%, independent of thickness of the membranes. The experimental results are consistent with the theoretically predicted absorptance quantum, A Q = πα/n c for each set of interband transitions in a 2D semiconductor, where α is the fine structure constant and n c is an optical local field correction factor. Absorptance quantization appears to be universal in 2D systems including III-V quantum wells and graphene.T he optical properties of heterostructure quantum wells (QWs) have been extensively studied since the 1970s, in GaAs/ AlGaAs (1), GaInAs/AlInAs (2, 3), InGaAs/InP (4), and HgCdTe/ CdTe (5). Here we do a careful quantitative examination of the intrinsic absorption properties of free-standing 2D semiconductor thin films, which has previously been done only for layered structures, such as MoS 2 (6). (The criterion of real two-dimensionality is that the material thickness be smaller than the electron Bohr radius.)Previous work has shown that graphene, a 2D semimetal, has a universal value of light absorption, namely πα, where α is the fine structure constant (7). Here, we use free-standing InAs membranes with exceptionally small thickness as a model material system to accurately probe the absorption properties of 2D semiconductors as a function of thickness. We demonstrate that the magnitude of the light absorption is an integer product of a quantum of absorptance. Specifically, each set of interband transitions between the 2D subbands results in a quantum unit of absorptance of A Q ∼ πα/n c , where n c is the optical local field correction factor. The total absorptance for the first several sets of interband transitions is simply given as A = MA Q , where M is the integer number of allowed transitions for a given photon energy. The result here appears to be universal, except for small correction factors associated with higher bands.Recently, there has been a high level of interest in exploring the fundamental science (6-10) and associated devices (11-20) of free-standing (i.e., attached to a substrate by van der Waals or other weak forces) 2D semiconductors. In one example system, InAs quantum membranes (QMs) with adjustable thicknesses down to a few atomic layers have been realized by a layer transfer process onto a user-defined substrate (12). The approach enables the direct optical absorption studies of fully relaxed (i.e., unstrained) (21) 2D III-V semiconductors by using transparent substrates, without the constraints of the original growth substrate (10). Here, we use InAs membranes of thickness L z ∼ 3-19nm on CaF 2 support substrates as a model material system for examining the absorption properties of 2D semiconduc...

Transparency of graphene and other direct-gap two-dimensional materials

“…The aforementioned finding [5] that a 2D nanomembrane of a direct-gap semiconductor also displays the same πα quantum of absorption attests that it is the dimensionality of these systems (specifically, the electronic density of states in 2D) that underlies their beautiful optical characteristics. In this paper we show that by applying the "minimal coupling"…”

“…The optical properties of graphene [1][2][3][4] as well as membranes of InAs [5] have been measured in recent studies. Remarkably, the transparency of both materials in the visible range is simply T ≈ 1 − πα, where α = e 2 / c is the fine structure constant.…”

Extraordinary Absorption of Decorated Undoped Graphene

“…The universality of the broadband constancy of the conductivity outside gap regions [31] then yields equivalently universal absorption results in decorated planar absorbing layers. Semiconductor heterostructures and multilayer graphene can thus be directly analyzed in this way.…”

Universal absorption of two-dimensional systems

“…With ν = 1, g s = 2, and g v = 2, we obtain the well-known absorption of A = πα for suspended graphene, whereas with ν = 2, g s = 2, and g v = 1 and (1 + r) = t = 2 1+n s with n s the refractive index of the substrate, we obtain the final result of Ref. [12], i.e., the absorption of a InAs monolayer on top of a dielectric. Equation (19) represents the basic result of this work.…”

“…Recent absorption experiments on InAs monolayers show an absorption of A = παF with the local field correction F = 4 (1+n s ) 2 due to the substrate with refractive index n s [12]. This translates into an effective optical conductivity of σ (ω ≈ ω ) = e 2 4 for transitions close to the frequency that corresponds to the band gap ω .…”