Many-body effects, orbital mixing, and cyclotron resonance in bilayer graphene

Abstract

In a magnetic field bilayer graphene supports, at the lowest Landau level, eight characteristic zeroenergy levels with an extra twofold degeneracy in Landau orbitals n = {0, 1}. They, under general one-body and many-body interactions, evolve into pseudo-zero-mode (PZM) levels. A close look is made into the detailed structure and characteristics of such PZM levels and cyclotron resonance they host, with full account taken of spin splitting, interlayer bias, weak electron-hole asymmetry and Coulomb interactions. It is pointed out that the PZM levels generally undergo orbital level mixing (in one valley or both valleys) as they are gradually filled with electrons and that an observation of interband cyclotron resonance over a finite range of filling provides a direct and sensitive probe for exploring many-body effects and orbital mixing in bilayer graphene.

Orbital mixing in few-layer graphene and non-Abelian Berry phase

“….) is taken into account, u cr becomes smaller (∼ 30 meV at B = 20 T) in valley K and far larger (∼ −100 meV) in K ′ [17]. Accordingly, we focus, in what follows, on quantum phenomena related to a crossing of empty levels in valley K.] Such a level inversion signals a level crossing or instability with filling, which actually is avoided via mixing of n = {0, 1} levels, as noted earlier [13].…”

“…See Ref. [17] for details of the renormalization procedure. The empty PZM levels in valley K, e.g., acquire the following renormalized spectra…”

“…This orbital degeneracy has a topological origin in the index of (the leading part of) the one-body Dirac Hamiltonian. In the presence of spin and band anisotropies and many-body interactions, these zero-mode levels evolve into pseudo-zeromode (PZM) levels, or into a variety of broken-symmetry quantum Hall states, as discussed theoretically [6][7][8][9][10][11][12][13][14][15][16][17] and explored experimentally [18][19][20][21][22][23][24][25][26]. It was noted, in particular, that the orbital degeneracy is also lifted by Coulomb interactions alone [13], with the zero-energy modes orbitally Lamb shifted due to quantum fluctuations of the filled valence band.…”