Spectral features due to inter-Landau-level transitions in the Raman spectrum of bilayer graphene

TL;DR

This paper analyzes how inter-Landau-level electronic transitions influence the Raman spectrum of bilayer graphene, highlighting the effects of high-energy bands and magnetic fields on spectral features and transition efficiencies.

Contribution

It derives an effective scattering amplitude from a four-band model, improving the understanding of Raman features in bilayer graphene beyond the two-band approximation.

Findings

Effective scattering amplitude differs from contact interaction due to high-energy bands.

Spectral density is constant without magnetic field and has a threshold in doped structures.

Inter-Landau-level transitions dominate Raman activity in magnetic fields, with estimated quantum efficiency.

Abstract

We investigate the contribution of the low-energy electronic excitations towards the Raman spectrum of bilayer graphene for the incoming photon energy Omega >> 1eV. Starting with the four-band tight-binding model, we derive an effective scattering amplitude that can be incorporated into the commonly used two-band approximation. Due to the influence of the high-energy bands, this effective scattering amplitude is different from the contact interaction amplitude obtained within the two-band model alone. We then calculate the spectral density of the inelastic light scattering accompanied by the excitation of electron-hole pairs in bilayer graphene. In the absence of a magnetic field, due to the parabolic dispersion of the low-energy bands in a bilayer crystal, this contribution is constant and in doped structures has a threshold at twice the Fermi energy. In an external magnetic field, the dominant Raman-active modes are the n_{-} to n_{+} inter-Landau-level transitions with crossed polarisation of in/out photons. We estimate the quantum efficiency of a single n_{-} to n_{+} transition in the magnetic field of 10T as I_{n_{-} to n_{+}}~10^{-12}.