Intra-Landau-Level Cyclotron Resonance in Bilayer Graphene

Abstract

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.PACS numbers: 76.40.+b,75.30.Ds Introduction-Because the Zeeman spin-splitting in most two-dimensional electron systems (2DES's) is much smaller than the Landau level separation, the magnetic band spectrum usually consists of narrowly-spaced doublets. When one of these doublets is half-filled and disorder is weak, Coulomb interaction physics leads to ferromagnetism i.e. to spontaneous spin polarization in the absence of a Zeeman field [1,2,3]. In some circumstances [4] other approximate Landau level degeneracies occur, often associated with layer degrees of freedom. These can also lead to broken symmetries which induce quasiparticle gaps and hence interaction driven integer quantum Hall effects. The case of bilayer 2DES's is particularly interesting because the which layer degree of freedom doubles Landau level degeneracies and leads to exciton condensation [5,6] at odd filling factors and to canted anti-ferromagnetic states [7] at even filling factors. In this Letter, we address the still richer case of graphene bilayer 2DES's in which chiral bands lead to an additional degeneracy doubling [8] at the Fermi energy of a neutral system. Bilayer graphene's Landau level octet is already apparent in present experiments [9] through the 8×(e 2 /h) Hall conductivity jump between well formed plateaus at Landau level filling factors ν = −4 and ν = +4. We anticipate that when external magnetic fields are strong enough or disorder is weak enough [10], interactions will drive quantum Hall effects at the octet's seven intermediate integer filling factors. We predict that these quantum Hall ferromagnets (QHFs) will exhibit unusual intraLandau-level cyclotron modes at odd filling factors, and that the collective mode excitations at these filling factors are nearly gapless even when there is no continuous symmetry breaking. Because the conductivity has Drude weight centered near zero-energy, we speculate that localization physics and quantum-Hall related transport phenomena will also be anomalous. Graphene Bilayer Landau Levels-When trigonal warping [11] and Zeeman coupling are neglected, the low energy properties of Bernal stacked unbalanced bilayer graphene are determined by electron-electron interactions and by a band Hamiltonian [8] H = H 0 + H ext where

Quantum anomalous Hall state in bilayer graphene

“…In this section we show that within the often-used approximation where the difference between interlayer and intra-layer interactions is neglected [4][5][6]13,14 , the interacting Hamiltonian is invariant under rotations in a suitably defined four-dimensional flavor subspace. Specifically, we perform a unitary transformation by exchanging the sublattices A and B in one of the valleys, upon which the single particle Hamiltonian becomes identical for all spin and valley species, while the layer and sublattice blind interactions are left unchanged.…”

“…Another experimental signature is a phase transition at filling factor ν = 0 and finite B from a QAH state to the Quantum Hall Ferromagnet (QHF) states that are expected to form at large magnetic fields 13 . Such a phase transition would not be seen if the dominant state at small B was of (2,2) type, since the (2,2) states are smoothly connected to the QHF state.…”

Theory of inter-Landau-level magnetoexcitons in bilayer graphene

“…The minimization of the interaction energy results in gapped states which break either spin rotation or pseudospin (valley) rotation symmetry, or both. 17,33,35,49,60,61,74 If either the Zeeman energy ∆ Z or the interlayer energy difference u is present, they affect the order how the Landau levels are filled, but exchange energy considerations are more crucial in most cases. 17,68 The most convenient basis in pseudospin space may differ; we may introducê a nSσp = cos θ 2â n,ξ=1,σp + sin θ 2 e iφâ n,ξ=−1,σp ,…”

“…11 Further broken symmetry states have been observed [12][13][14][15][16] in the central Landau band at ν = 0, ±1, ±2 and ±3, and by careful tilted-field measurements it has been shown that they arise predominantly from many-body effects, i.e., from quantum Hall ferromagnetism (QHF). 17 Quantum Hall states with broken symmetry have also been found in the n = −2 Landau level 18 , and there is also some evidence for a fractional quantum Hall plateau.…”

“…At odd integers in the central Landau band (ν = ±1, ±3) the degeneracy of the n = 0, 1 Landau orbitals causes fluctuations with an in-plane electric dipole character, which gives rise to unusual collective modes. 17,60,61 At even integers in the central Landau band (ν = ±2, 0) orbital degeneracy does not play a similar role, and the intra-level excitations are still magnetoexcitons. 35,62 For inter-LL excitations, the many-body corrections to cyclotron resonance has been calculated by renormalization 55 including the possi-ble particle-hole symmetry-breaking terms but using the unscreened Coulomb interaction, with partial agreement with experiments.…”