Phase-Resolved Surface Plasmon Interferometry of Graphene

Abstract

The surface plasmon polaritons (SPP) of graphene reflect the microscopic spatial variations of underlying electronic structure and dynamics. Access to this information requires probing the full SPP response function. We image the graphene SPP phase and amplitude by combining scanning probe tip coupled surface plasmon interferometry with phase resolved near-field signal detection. We show that a simple analytical cavity model can self-consistently describe the phase and amplitude response both for edge, grain boundary, and defect SPP reflection and scattering. The derived complex SPP wavevector, damping, and carrier mobility agree with the results from more complex models. This phase information opens a new degree of freedom for spatial and spectral graphene SPP tuning and modulation for opto-electronics applications. PACS numbers:The light-matter interaction of graphene is distinct from that of other forms of matter due to its unique electronic band structure. The high quantum yield has already enabled a range of opto-electronics and photonic applications based on single particle excitations. However, even more unusual are the collective particle excitations in the form of Dirac plasmons, typically in the infrared spectral range, with their properties controllable by electric field gating, doping, or multilayer stacking [1-5]. In the long wavelength limit the unique properties of massless Dirac fermions lead to a very large reduction of surface plasmon polariton (SPP) wavelength compared to the free space excitation wavelength:, with the fine structure constant α. The short SPP wavelength gives rise to a strong spatial confinement, but the momentum mismatch due to the associated large in plane wave vector concomitantly requires high k-vector field components for the SPP excitation. That coupling can be achieved through the near-field of the nanometer scale apex of a scanning probe tip [7][8][9]. Using the tip to excite and subsequently scatter the Dirac plasmons polarization into detectable far-field radiation, the expected deep-sub-wavelength SPP standing wave from boundary reflections at mid-IR frequencies could be imaged using scattering-type scanning near-field optical microscopy (s-SNOM) and described theoretically [10][11][12][13].The plasmon wavelength, its damping, and other spatial details directly relate to the local electronic structure, which is determined by doping or strain [1,2,14], the number of layers and their stacking order [5,15,16], and is further modified by atomic scale discontinuities at edges, grain boundaries, and defects. With the exquisite sensitivity of the spatial plasmon response to these parameters, near-field plasmon interferometry can serve as a sensitive probe for the electronic structure and its spatial inhomogeneities, which are difficult to access by other techniques.However, near-field imaging experiments have so far only analyzed the amplitude of the optical response [10][11][12][13]. The full characterization of s-SNOM amplitude and phase response is not only desirable in...

Edge and Surface Plasmons in Graphene Nanoribbons

“…The representative near-field images of the GNRs with widths of W = 480, 380, 270 and 155 nm are shown in Figure 1c-f, where we plot the near-field amplitude s() normalized to that of the bare Al2O3 substrate (Supporting Information). As documented in previous studies [4][5][6][7][8][9][10][11][12] , s() is a direct measure of the z-component electric field amplitude |Ez| underneath the AFM tip. In our experiments, we kept p-polarized light beam incident along the ribbons (Figure 1a) to avoid direct excitation of resonance modes of ribbons.…”

“…1 In particular, surface plasmons in graphene are collective oscillations of Dirac quasiparticles that reveal high confinement, electrostatic tunability and long lifetimes. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] Plasmons in graphene are promising for optoelectronic and nanophotonic applications in a wide frequency range from the terahertz to the infrared (IR) regime. 16,17 One common approach to investigate plasmons is based on nano-structuring of plasmonic media.…”

“…These fields have a wide range of in-plane momenta q thus facilitating energy transfer and momentum bridging from photons to plasmons. [3][4][5][6][7][8][9][10][11][12] Our GNR samples were fabricated by lithography patterning of high quality CVD-grown graphene single crystals 26 on aluminum oxide (Al2O3) substrates (Supporting Information). As discussed in detail below, the optical phonon of Al2O3 is below  = 1000 cm -1 ( Figure S2), allowing for a wide mid-IR frequency region free from phonons.…”

“…In nano-IR experiments, fringes originate from constructive interference between tip-launched and boundary-reflected plasmons (Figure 1a). [3][4][5][6][7][8][9][10][11][12] Apart from these familiar patterns, we also observed plasmonic characteristics due to ribbon confinement as the ribbon width (W) shrinks. First, the two principal fringes move closer to each other with decreasing W and consequently the total number of distinct fringes observable within GNRs decreases.…”

“…The general aspects of the ribbon confinement effects described above are consistent with previous studies of tapered GNRs. 4,5,9 Nevertheless, the data of straight GNRs are extremely valuable for quantitative analysis of the entire tip-ribbon system (Supporting Information).In order to explore the evolution of the fringe patterns with the frequency of IR radiation, we performed nano-imaging of the GNRs with both broadband and CW sources following an approach introduced in our recent study 27 . The broadband mapping is given in Figure 2a, where we plot a real-space line scan across the GNR in Figure 1c (along the red dashed line).…”