Orbital-specific Tunability of Many-Body Effects in Bilayer Graphene by Gate Bias and Metal Contact

Graphene, a 2D crystal bonded by π and σ orbitals, possesses excellent electronic properties that are promising for next-generation optoelectronic device applications. For these a precise understanding of quasiparticle behaviour near the Dirac point (DP) is indispensable because the vanishing density of states (DOS) near the DP enhances many-body effects, such as excitonic effects and the Anderson orthogonality catastrophe (AOC) which occur through the interactions of many conduction electrons with holes. These effects renormalize band dispersion and DOS, and therefore affect device performance. For this reason, we have studied the impact of the excitonic effects and the AOC on graphene device performance by using X-ray absorption spectromicroscopy on an actual graphene transistor in operation. Our work shows that the excitonic effect and the AOC are tunable by gate bias or metal contacts, both of which alter the Fermi energy, and are orbital-specific.


S1. Characterization of graphene device
shows an optical micrograph of the graphene device, which consists of the graphene, a SiO 2 (90 nm thick) insulator, a Si(100) substrate used as the backgate and Ni thin films used as the metal electrodes. In the optical micrograph, the graphene is visible due to the interference effect 1 . The bilayer graphene in the device was characterized by Raman microspectroscopy, as shown in Figure S1b.
The incident laser energy used was 2.41 eV. In the spectra there are two fundamental modes of graphene 2,3 : the G (~1580 cm -1 ) and G (~2700 cm -1 ) bands. On the other hand, the D band (~1360  cm -1 ), which is related to the existence of defects, cannot be seen. This indicates that graphene contains hardly any defects [2][3][4] . The G band is fitted by four peaks, which are explained within the framework of double resonant Raman scattering 2,3 . Figure S1c shows a typical resistance-gate voltage curve of a bilayer graphene transistor. The charge neutrality point (CNP) where the Fermi level is situated at the Dirac point is around V g = 0 V, which indicates that our -XAS measurements are performed around CNP.

S2. Polarization dependence of -XAS spectra
In this work, an elliptically polarized X-ray beam was used as the incident light for microscopic p-polarized light could not be used. The degree of the polarization is ~ 0.6 5 . The light was incident on the graphene device with a grazing angle of 74° with respect to surface normal through the PEEM installed at SPring-8 6 . Figure S2 shows the polarization dependence of the -XAS spectrum of the graphene. The intensity of the * peak with surface parallel polarized light was weaker than that with the circularly polarized light. This was due to the dipole moment of the * orbital being normal to the molecular plane. Some of the * peak intensity remained for light polarized parallel to the surface because the polarization was incomplete. Figure S3 shows schematically the background correction used for the analysi -XAS spectra.

S3. Peak decomposition of -XAS spectra
It is assumed that the line shape of the continuum step is determined by the core hole 7 . This implies the convolution of a square step with a Lorentzian function, yielding an arctan function 7 : where P, H and  L are the position of the inflection, the step height of the function and the width of the step, respectively. E is the independent variable energy. Details are described well in the textbook by Stöhr 7 . This background correction has been applied in XAS studies of excitonic effects near the C-K edge 8 , and is therefore suitable for our work.
Using this background correction, the peak decomposition of the -XAS spectrum was performed to extract information on the * (~285 eV) and  G * (~307 eV) peaks. The decomposed  A * (~292 eV) and  B * (~297 eV) peaks, in which there are actually many peaks 9 , are somewhat ambiguous with respect to shape and line width. An example is shown in Supplementary Figure S3.
The fitted curve in the energy ranges of the * and * peaks reproduces the experimental data.