RAPID COMMUNICATIONS PHYSICAL REVIEW B 94, 121406(R) (2016) Robustness of the universal optical transmittance in monolayer and multilayer graphene flakes under Coulomb interactions Premlata Yadav, Pawan Kumar Srivastava, Nirat Ray, and Subhasis Ghosh * School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India (Received 31 March 2016; revised manuscript received 18 August 2016; published 22 September 2016) We present an experimental investigation on the universality of the optical transmittance of mono- and multilayer chemically exfoliated graphene flakes. By varying the exfoliating solvent, and thereby modulating the strength of electron-electron interactions, we find that the universality is not impacted over the visible region. The impact of modulating the interaction strength is clearly seen as shifts in the M-point exciton spectra. These shifts can then lead to a reduction in the wavelength regime over which universal wavelength independent optical transmittance is observed. At the level of first-order perturbation theory, our results are consistent with existing theoretical predictions for interaction corrections in optical properties of monolayer graphene. DOI: 10.1103/PhysRevB.94.121406 Graphene, a two-dimensional (2D) material, shows re- markable optical and electronic properties, such as a linear energy dispersion, chirality, and half-integer quantum hall effect [1–7]. Multilayer graphene flakes, held together by weak van der Waals forces have also attracted attention due to their stacking dependent electronic and optical properties [8–13]. Interestingly, a vast majority of these properties can be understood in terms of a noninteracting picture [5,14,15]. In particular, the optical conductivity σ 0 of monolayer graphene in the near infrared (IR) and visible range has been found to be independent of frequency, and equal to e 2 /4 [16]. For an N-layer graphene stack, the optical conductivity can be generalized to Nσ 0 [13], for frequencies exceeding the interlayer coupling scale but smaller than the π -bandwidth scale. The optical transmittance of an N-layer graphene stack is then given by [13,16,17]: T (ω) = 1  1 + 2Nπσ 0 c  2 = 1  1 + Nπα QED 2  2 , (1) where α QED = e 2 /c = 1/137, is the fine structure constant [18]. The universality for monolayer graphene can be under- stood starting with a linear energy dispersion [5,19] and a simple application of the Kubo formula. The two-dimensional density of states associated with the linear energy dispersion of monolayer graphene leads to an exact cancellation of the frequency dependence of the optical conductivity, and the resulting transmittance is approximately given as T ≈ 1 − πα QED . However, this simple calculation is expected to break down for thicker graphene flakes, which do not show a linear energy dispersion. More recently it has been theoretically shown that the origin of the universality can be attributed to the emergent chiral symmetry of the honeycomb lattice [13,16,17], however, to our knowledge there have been no experimental investigations into the same. Also, a single particle description is presently the basis for our understanding, and it is important to consider many-body and interlayer coupling effects on the optical properties of monolayer and multilayer graphene. The strength of Coulomb interactions U(r) = e 2 /ǫr in graphene is controlled by the ratio α = e 2 /ǫ v 0 , where ǫ * subhasis.ghosh.jnu@gmail.com is the effective dielectric constant of the environment [20]. The effect of many-body interactions on different properties of graphene has been experimentally tuned by modulating the dielectric screening [21,22], as well as by modulating the density of charge carriers with an external gate [14,23]. The effect of tuning these interactions was manifested in the form of shift, broadening and modification in the shape of exciton peaks [14,22,24], as well as changes in quasiparticle lifetimes [14]. However, the effect of tuning the interaction strength on the frequency independent universal optical conductance or transmittance of graphene has not been investigated, to our knowledge. In this Rapid Communication, we report the experimentally observed optical absorption and transmittance spectra for mono- and multilayer chemically exfoliated graphene flakes as a function of varying the electron-electron (e-e) interaction strength. The e-e or Coulomb interaction strength is varied both by modulating the dielectric constant of the exfoliating solvent, as well as changes in the carrier density n. We find that in the UV/visible frequency range, the universality remains robust to changes in the local dielectric environment and charge density, and therefore, varying the strength of electron-electron interactions has no observable effects on the optical properties. Interlayer interactions in multilayered graphene flakes, coupled with the varying Coulomb interaction strengths, also do not result in experimentally observable deviations from the universal transmittance behavior. The universality gives way when chiral symmetry is broken, as shown by the strong effect of Coulomb interactions on excitonic features observed in the ultraviolet range of the transmittance spectra of graphene, and our observations are therefore consistent with chiral symmetry as the origin of the universal behavior. Graphene layers are synthesized using a two step chemical exfoliation process [25]. Previously mechanical and chemical exfoliation techniques have been used to synthesize graphene flakes, and the resultant flakes are then transferred onto desired substrates. However, the dielectric environment of the graphene flakes on a substrate is difficult to tune. Chemical exfoliation offers the unique advantage of synthesis of direct graphene flakes in different dielectric environments, thereby facilitating the study of many-body effects in the solvent. We have used toluene (ǫ = 2.4), chlorobenzene (ǫ = 5.62), 2469-9950/2016/94(12)/121406(5) 121406-1 ©2016 American Physical Society