Exciton absorption in narrow armchair graphene nanoribbons

Abstract

We develop an analytical approach to the exciton optical absorption for narrow gap armchair graphene nanoribbons (AGNR). We focus on the regime of dominant size quantization in combination with the attractive electron-hole interaction. An adiabatic separation of slow and fast motions leads via the two-body Dirac equation to the isolated and coupled subband approximations. Discrete and continuous exciton states are in general coupled and form quasi Rydberg series of purely discrete and resonance type character. Corresponding oscillator strengths and widths are derived. We show that the exciton peaks are blue-shifted, become broader and increase in magnitude upon narrowing the ribbon. At the edge of a subband the singularity related to the 1D density of states is transformed into finite absorption via the presence of the exciton. Our analytical results are in good agreement with those obtained by other methods including numerical approaches. Estimates of the expected experimental values are provided for realistic AGNRs

Exciton absorption spectra in narrow armchair graphene nanoribbons in an electric field

“…(28) and (29) in which we ignore both the Stark ∆W N n (Ω 2 N /β N n ). It turns out to be not only much smaller than the energy W N n but also width Γ N n on the ribbon width d is the same as that in the unbiased AGNR [12].…”

“…Since the mathematical details of this approach have been presented in Ref. [12] only an outline of our calculations will be provided below. The equation for the exciton absorption coefficient has the form…”

“…The reasons for the latter approximation are as follows: (i) the shifts are much smaller than the corresponding widths and (ii) they do not change the form of the exciton spectrum. The widths Γ (el) N n transform the δ-function peaks in an unbiased AGNR [12] into the maxima of finite width Γ 26) and (28), respectively, are as follows…”

“…As expected, in the absence of the electric fields F = 0, Ω N = 0 eqs. (28) and (29) transform into those describing the δ-function type exciton peaks in an electrically unbiased AGNR [12]. In principle, the resonant widths Γ (el) N n and shifts ∆W N n ∼…”

Pair states in one-dimensional Dirac systems

“…However, there is still much debate concerning the existence of coupled pairs in intrinsic graphene [34,44,45]. The two-body problem has also been the subject of study in narrow-gap carbon nanotubes and graphene nanoribbons and some analytic solutions have been found [29,30,46,47]. Numerical methods have also been used to determine exciton bound states in metallic carbon nanotubes subjected to a magnetic field [25].…”