Many‐Body Effects in Suspended Graphene Probed through Magneto‐Phonon Resonances

Abstract

Pristine suspended monolayer graphene is a well-defined, unscreened 2D electronic system, in which a wealth of intriguing electronic, [1-5] optical, [6] and mechanical [7] properties have been uncovered. In particular, spectacular deviations from a simple one-electron picture of graphene's band structure (i.e., the Dirac cones) emerge at low carrier densities (below a few 10 11 cm À2). Due to electron-electron interactions, the velocity parameter diverges logarithmically as the Fermi energy approaches the Dirac point, [4] reaching values, well above the Fermi velocities of bulk graphite and supported graphene (%1 Â 10 6 m s À1). [8] In the presence of a transverse magnetic field B, the electronic states of graphene merge into discrete, highly degenerate Landau levels (LL). [9] The energy and lifetime of LL can be probed using magneto-transport measurements, [1,4] scanning tunnelling spectroscopy, [10] and magneto-optical spectroscopies. [9,11] Recently, micro-magneto-Raman spectroscopy (MMRS) [12-17] has been used to probe the electronic dispersion of suspended graphene layers [14] and also to demonstrate that electronic excitations between LL may be strongly affected by many-body effects. First, as B decreases, the energy of a given LL also decreases and electron-electron interactions lead to a logarithmic divergence of the corresponding velocity parameter (hereafter denoted v F for simplicity). [5,16,18] Second, inter-LL excitations lead to the formation of magneto-excitons, whose binding energies depend on the index n of the electron and hole LL they arise from, leading to n-dependent v F. [5] Thus far, Raman signatures of many-body effects have predominantly appeared on the electronic Raman scattering response of graphene [19] under a transverse magnetic field. [5,14] Recently, many-body effects have also been unveiled by monitoring magneto-phonon resonances (MPR) [12] between optically active inter-LL transitions [20] and zone-center optical phonons (i.e., Raman G-mode phonons [21]) in graphene encapsulated in hexagonal boron nitride (BN) films. [16] As recently suggested by Sonntag et al., [18] more prominent effects are expected in suspended graphene, where electron-electron interactions are minimally screened. In this letter, we report the results of MMRS measurements performed on suspended mono-to pentalayer graphene. For each number of layers N, we resolve a set of well-defined MPR. Using a single-particle effective bilayer model, we readily extract v F associated with each MPR. While a single parameter slightly above the bulk graphite value (≥ 1.05 Â 10 6 m s À1) suffices to fit all MPR for N ≥ 2 layer systems, We find that v F increases significantly up to (% 1.45 Â 10 6 m s À1 in monolayer graphene. This result is understood as a signature of enhanced many-body effects in unscreened graphene. The low-energy electronic electronic bands and magnetooptical response of mono-and N-layer graphene have been extensively discussed using an effective bilayer model. [14,22-26] To lowest order, this model uses o...