Intra-Landau-Level Cyclotron Resonance in Bilayer Graphene

Interaction driven integer quantum-Hall effects are anticipated in graphene bilayers because of the near degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate $k^{3/2}$ dispersion. We speculate on the possibility of unusual localization physics associated with these modes.

Figure 1

Filling factor dependence of the integer filling factor HF theory occupied state (spectrum of the bilayer graphene octet at ${\Delta }_V=0$). Energies of occupied (solid red lines) and unoccupied (dashed blue lines) are in units of $(\pi /2{)}^{1/2}{e}^2/\epsilon l_B$. The Zeeman field ${\Delta }_Z$ value in these units is 0.023 at a magnetic field of 20 T. Octet space fractional pseudospin polarizations offset for clarity: spin (red squares), valley (green circles), and LL pseudospin (blue triangles).

Figure 2

Collective mode ${\omega }_q$ of the Landau-level pseudospin polarized state in units of interaction strength $e^2/ϵl_B=11.2(B[\mathrm{T}]{)}^{1/2}\mathrm{meV}$ as a function of $q{l}_B$ at different values of the external potential difference ${\Delta }_V$ at a magnetic field of 20 T. The solid black line indicates the $q{l}_B\to \infty$ asymptote for ${\Delta }_B=0$.