Unraveling the interlayer-related phonon self-energy renormalization in bilayer graphene

Abstract

In this letter, we present a step towards understanding the bilayer graphene (2LG) interlayer (IL)-related phonon combination modes and overtones as well as their phonon self-energy renormalizations by using both gate-modulated and laser-energy dependent inelastic scattering spectroscopy. We show that although the IL interactions are weak, their respective phonon renormalization response is significant. Particularly special, the IL interactions are mediated by Van der Waals forces and are fundamental for understanding low-energy phenomena such as transport and infrared optics. Our approach opens up a new route to understanding fundamental properties of IL interactions which can be extended to any graphene-like material, such as MoS2, WSe2, oxides and hydroxides. Furthermore, we report a previously elusive crossing between IL-related phonon combination modes in 2LG, which might have important technological applications.

Intra- and Interlayer Electron-Phonon Interactions in 12/12C and 12/13C BiLayer Graphene

“…However, when 2|E F | > ω q the production of real e-h pairs becomes forbidden due to the Pauli principle. This leads to a phonon mode hardening where the phonons are not damped any more (they are now long lived) [60][61][62][63][64][65][66]. If 2|E F | = ω q , the phonon mode softening shows its highest values, which represent two singularities, as shown by the black solid curve in the inset of Figure 10e.…”

“…From these insets, we observe that when 2|E F | < ω q , real e-h pairs can be created (annihilated), which leads to a stronger electron-ion interaction screening. As a consequence, the phonon mode softens [60][61][62][63][64][65][66]. However, when 2|E F | > ω q the production of real e-h pairs becomes forbidden due to the Pauli principle.…”

“…As a reminder, there are two types of e-ph interactions, namely intra-valley (AV) (Figure 10a,c) and inter-valley (EV) (Figure 10b,d) processes [60][61][62][63][64]. For an AV process, the initial and final states both occur within the region close to a K [K ] point, while for inter-valley processes, K is connected to K in a different valley by a q = 0 phonon.…”

“…Next, lithography followed by liftoff is required to place contacts on the flake so that gate voltages (V g ) can be applied to the device in a backgate configuration, as illustrated in Figure 11a. Then, for each V g value, Raman spectrum is taken and analyzed using Lorentzian line-shapes from which frequencies and decay widths are extracted [60][61][62][63][64]. Note that resonance Raman spectroscopy provides information about both the electronic and vibrational structures, while the V g variation allows for control of the Fermi level energy (E F ) of the 2LG.…”

“…Thus the AV (EV) process corresponds to Γ (K) point phonons. The phonon wavevector q for AV (EV) processes are measured from the Γ (K) points with both q = 0 and q = 0 possible [60][61][62][63][64].…”