Experimental evidence of plasmarons and effective fine structure constant in electron-doped graphene/h-BN heterostructure

Electron-electron interaction is fundamental in condensed matter physics and can lead to composite quasiparticles called plasmarons, which strongly renormalize the dispersion and carry information of electron-electron coupling strength as defined by the effective fine structure constant $\alpha_{ee}^*$. Although h-BN with unique dielectric properties has been widely used as an important substrate for graphene, so far there is no experimental report of plasmarons in graphene/h-BN yet. Here, we report direct experimental observation of plasmaron dispersion in graphene/h-BN heterostructures through angle-resolved photoemission spectroscopy (ARPES) measurements upon {\it in situ} electron doping. Characteristic diamond-shaped dispersion is observed near the Dirac cone in both 0$^\circ$ (aligned) and 13.5$^\circ$ (twisted) graphene/h-BN, and the electron-electron interaction strength $\alpha_{ee}^*$ is extracted to be $\alpha_{ee}^*\approx0.9\pm 0.1$, highlighting the important role of electron-electron interaction. Our results suggest graphene/h-BN as an ideal platform for investigating strong electron-electron interaction with weak dielectric screening, and lays fundamental physics for gate-tunable nano-electronics and nano-plasmonics.


Introduction
Electron-electron interaction is ubiquitous in solids and plays an important role in condensed matter physics. In graphene, the strength of the electron-electron interaction is quantified by the ratio of the Coulomb potential U = e 2 k F / to the kinetic energy K =hv F k F , [1][2][3] where v F and k F are the Fermi velocity and Fermi momentum respectively, and is the dielectric constant. This ratio defines a fundamental constant α * ee = U/K = e 2 / hv F , 4,5 which is in analogy to the fine structure constant α = e 2 /hc = 1/137 in quantum electrodynamics, with the speed of light c replaced by the Fermi velocity v F and the effective dielectric screening of the environment taken into account by .
Because of this analogy, α * ee is called the effective fine structure constant. The effective fine structure constant α * ee reflects the relative strength of electron-electron interaction and determines many fundamental physical properties of graphene, e.g., optical absorption 5 and transport properties. 6 Moreover, by tuning the carrier concentration and electron-electron correlation, superconductivity has been reported in twisted bilayer graphene placed on h-BN substrate. 7 Revealing the electronelectron interaction strength and extracting the effective fine structure constant are fundamentally important.
Electron-electron interaction can significantly affect the electronic dispersion by reshaping the graphene Dirac cone dispersion with a modified Fermi velocity. [8][9][10][11] Moreover, collective excitations of electron gas can form plasmons, 12 and the interaction between plasmons and charges leads to composite quasiparticles called plasmarons, 13 which strongly modify the electronic dispersion with newly generated plasmaron bands. As an atomically thin material with unique conical dis-persion as shown in Fig. 1a, graphene shows a stronger plasmon-charge interaction [14][15][16] than other two-dimensional (2D) materials with parabolic dispersions in general. In particular, the coupling between charges and plasmons with the same group velocity leads to low-energy plasmaron dispersions displaced from the original Dirac cone, forming a characteristic diamond-shaped dispersion near the Dirac point [14][15][16][17][18] as schematically illustrated in Fig. 1b. Since the energy and momentum separation between the Dirac cone and plasmaron bands is determined by the effective fine structure constant α * ee , [14][15][16][17][18] observing plasmaron dispersion allows to extract α * ee experimentally, which is critical for revealing the fundamental physics of electron-electron interaction in graphene-based electronics and plasmonics.
Plasmarons have been reported for graphene grown on SiC substrates by angle-resolved photoemission spectroscopy (ARPES) measurements, 17  ture with the weakest effective dielectric screening. In addition, despite the strong plasmaron, the dispersions remain sharp at high electron doping. This suggests the plasmarons and dopants do not significantly affect the electron scattering at such high electron doping, which is useful for gate-tunable nano-electronics and nano-plasmonics applications.

Results
Electron doping of graphene/h-BN and gap filling by Rb deposition Figure 2 shows an overview of the band structure evolution through the K point (indicated by dotted line in Fig. 2i) upon electron doping. In the undoped sample, the graphene Dirac point energy  With increasing electron doping, the energy separation between E 0 and E pm becomes larger. We note that the moiré superlattice period is determined by the lattice mismatch between graphene and h-BN 34 and is doping independent, and as a result, the separation between the moiré superlattice replica and the original Dirac cone is expected to be doping independent. Therefore, the increasing energy and momentum separation between the plasmaron bands and Dirac cone upon electron doping (see Supplementary Figure 3 for more details) confirms that it is not caused by overlapping 8 of graphene Dirac cone and moiré superlattice bands, but instead band renormalization induced by plasmon-charge interaction. In addition, the ARPES dispersions remain quite sharp, and indeed they are sharper than those at lower carrier concentration. This is in agreement with previous report on graphene/h-BN at a lower doping (with the Dirac point at ≈ -0.3 eV), 8 where the decrease of scattering rate is attributed to the increase of long-range impurity screening from the higher electron density. Here we show that at an even higher doping (with the Dirac point at -0.64 eV) and in the presence of plasmarons, the electron scattering rate still remains low, which is useful for gate-tunable nano-electronics and plasmonics.
Plasmaron bands observed in a 13.5 • twisted graphene/h-BN upon electron doping Since the moiré superlattice period of graphene/h-BN strongly depends on the twist angle 19 , to check whether the plasmaron features depend on the twist angle, we show in Fig. 3 ARPES results on a 13.5 • twisted graphene/h-BN heterostructure. The moiré superlattice period decreases from λ ≈ 14 nm at 0 • to 1.05 nm at 13.5 • , and therefore the superlattice replica Dirac cone is much farther away from the graphene Dirac cone. Figure 3a shows the exfoliated monolayer graphene, which was then transferred onto a h-BN flake (shown in Fig. 3b) with a designed twist angle of 13.5 • .
This twist angle is confirmed by the K points of graphene and h-BN from energy contours at the Fermi energy (Fig. 3c) and -2.9 eV (Fig. 3d). By performing ARPES measurements with in situ Rb deposition, the evolution of the band dispersion upon electron doping is revealed.  Fig. 4c and is the characteristic feature of plasmarons. Figure 4d shows a schematic sum- To quantify the size of the diamond-shaped dispersion along the momentum direction, we plot in Fig. 5f the MDCs at E pm (labeled in Fig. 4d) with the fitting peaks appended. The momentum separation ∆k of the two main peaks defines the momentum range of the diamond-shaped dispersion. Figure 5g shows that the extracted momentum separation ∆k scales linearly with the Fermi momentum k F , and the slope gives a renormalized dimensionless momentum separation δk = ∆k/k F = 0.42 ± 0.02. We note that the doping independent δE and δk are consistent with results calculated from the spectral function A(k, w), and they are uniquely determined by the α * ee value. 18 Figure 5h shows a replot of calculated δE and δk at different values of α * ee (open symbols). 18 Our extracted δE and δk (filled symbols) fall on the extrapolated curves and correspond to α * ee ≈ 0.9 ± 0.1. as well as the carbon face of SiC. 17,18 Our graphene/h-BN heterostructure shows the largest re-  ported α * ee value among all graphene samples. At the lowest order approximation, the effective fine structure constant is related to the dielectric environment by α * ee = e 2 / hv F , which is directly determined by the dielectric environment. We note that similar spectral features have also been discussed theoretically as satellite bands induced by weakly interacting electron-plasmon interaction 39 rather than strongly interacting plasmarons, which corresponds to a much larger electron-electron interaction strength. Therefore, our extracted value of α * ee ≈ 0.9 ± 0.1 gives the lower limit of the effective fine structure constant in graphene/h-BN heterostructure. Without considering the dielectric screening from the valence electrons and the Rb atoms, which is quite reasonable considering that δE and δk are both independent of carrier concentration or amount of Rb deposited, the effective dielectric constant is taken as the average value between dielectric constants of materials on both sides of graphene. In the extreme case for free-standing graphene without dielectric screening from the environment, = 1 and the effective fine structure constant is α * ee = 2.2 (orange symbol in Fig. 5i), which is an upper limit for α * ee . When graphene is placed on a substrate with dielectric constant s , the effective fine structure constant depends on the substrate dielectric constant s by α * ee ≈ 4.4/( s + 1) 18 , where the effective dielectric constant is taken as the average between the vacuum vac = 1 and s . The fitting function of α * ee ≈ 4.4/( s + 1) is also plotted in Fig. 5i.

Discussions
In summary, we report the experimental evidence of plasmaron and extract the fine structure constant of graphene/h-BN. We note that experimental values for the effective fine structure constant have been reported through optical transparency 5 and inelastic x-ray scattering measurement 4,30 on both graphene and graphite, and the fitting of the Dirac point velocity, 8 which involves both effects of the carrier screening and dielectric screening. Here by observing not only the Dirac cone but also the dispersion of the previously inaccessible plasmarons in graphene/h-BN at high electron density, we extract the dressed effective fine structure constant α * ee ≈ 0.9. Such large effective fine structure constant reveals the important role of the small dielectric constant of h-BN in reducing the dielectric screening. In addition, the dispersions remain quite sharp (Fig. 2c-h) under the presence of such a large number of carriers and strong plasmon-charge interaction, suggesting the insignificant contribution of both scattering channels in the electron scattering. Since many device applications require tunable electronic density, our finding on the small scattering of a highly electron-doped graphene/h-BN provides useful information for applications in gate-tunable nano-electronic and nano-plasmonic applications. 28,40 In the past decade, h-BN has been widely used as a substrate and a capping layer, for example, in magic-angle twisted bilayer graphene or ABC stacking trilayer graphene on h-BN, both exhibiting Mott insulator 7, 41 and superconductivity upon doping, 36,42 Revealing the effect of dielectric property of h-BN on the effective fine structure constant of graphene can also be helpful for understanding the electron-electron interaction in graphene/h-BN. Finally, it has been sug-gested that the effective fine structure constant is relevant to other Dirac systems 30 including topological insulator surface states, 43,44 and Dirac or Weyl materials. 45,46 Therefore, our results on graphene/h-BN heterostructure in principle can be extended to other Dirac materials for evaluating the electron-electron interaction and the effective fine structure constant.

Methods
Sample preparation. Sample preparation of the 0 • aligned graphene/h-BN sample. Single crystal h-BN flakes were first exfoliated onto a 300 nm SiO 2 /Si substrate by mechanical cleaving method.
Graphene samples were directly grown on h-BN substrates by the epitaxial method, as specified in previous work. 34 As-grown samples were characterized by tapping mode atomic force microscopy at room temperature in ambient atmosphere. We used freshly cleaved mica as shadow masks for