Pseudo-zero-mode Landau levels and collective excitations in bilayer graphene

Shizuya, K.

doi:10.1103/physrevb.79.165402

Cited by 44 publications

(60 citation statements)

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“…The resulting density 13 schematics shown as the line profiles in Fig. 4d naturally result in the potential asymmetries and local fields reversing in sign from electron to hole puddles.Even though we observe a non-zero energy gap when E D crosses E F , it is not clear whether the observed asymmetries are related to the broken symmetry states predicted in recent models 11,17,19,40,41 , or are the result of the broken symmetry related to the substrate interactions.In contrast, the existence of the subgaps in electron puddles when LL (0,+);(1,+) crosses E F is likely related to the recent theoretical predictions of spontaneously broken symmetry states, as correlated electron behavior is expected and most easily observed when the LLs are close to E F 28 . At present, we are not able to identify the exact quantum numbers of the split LL (0,+);(1,+) levels.…”

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confidence: 56%

“…1d) enables us to determine both the sign and the value of ΔU. Each quartet of the LL (0,±);(1,±) manifold remains degenerate at each layer, but electron-electron interactions can further lift this degeneracy and enhance the splitting of this level as pointed out in theoretical analyses 11,17,19 .A rich set of spectral features is observed in the STS spectra in bilayer graphene in the quantum Hall regime. Figure 3c shows the gate map at the location of the P1 electron puddle ( we examine the magnetic field dependence of the dI/dV spectra and LL peak positions as shown in Fig.…”

mentioning

confidence: 92%

“…With an applied electric field this degeneracy is partially lifted and a band gap is opened in the low energy bands. Accordingly, the Landau level energies are modified as 3,11,12 ,with the potential energy difference (or asymmetry) ΔU = U 2 -U 1 , where U 2 and U 1 are the onsite energies of the top and bottom graphene layers, respectively (Fig. 1c), and z is a term relating to the B 2 /A 1 dimer sites given by z = 2ħω c / γ 1 << 1.…”

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confidence: 99%

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Microscopic polarization in bilayer graphene

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Bilayer graphene has drawn significant attention due to the opening of a band gap in its low energy electronic spectrum, which offers a promising route to electronic applications. The gap can be either tunable through an external electric field or spontaneously formed through an interaction-induced symmetry breaking. Our scanning tunneling measurements reveal the microscopic nature of the bilayer gap to be very different from what is observed in previous macroscopic measurements or expected from current theoretical models. The potential difference between the layers, which is proportional to charge imbalance and determines the gap value, shows strong dependence on the disorder potential, varying spatially in both magnitude and sign on a microscopic level. Furthermore, the gap does not vanish at small charge densities. Additional interaction-induced effects are observed in a magnetic field with the opening of a subgap when the zero orbital Landau level is placed at the Fermi energy.Bilayer graphene consists of two graphene sheets overlaid in the Bernal stacking orientation where A 2 atoms of the top layer lie on top of the B 1 atoms of the bottom layer (see * These authors contributed equally to this work.§ To whom correspondence should be addressed: nikolai.zhitenev@nist.gov, joseph.stroscio@nist.gov.2 Fig. 1a), connected by the interlayer coupling 1 γ , thus breaking the A/B sublattice symmetry in the individual graphene layers. This results in massive chiral fermions where the electronic energy dispersion is hyperbolic in momentum, in contrast to the linear dispersion that leads to massless carriers in single layer graphene 1,2 . In bilayer graphene the energy bands still meet at the charge neutrality point (E D ) in the absence of an electric field between the layers (neglecting interaction effects) (Fig. 1b). In an applied electric field a potential asymmetry is developed between the layers, resulting in the opening of an energy band gap between the low lying bands making bilayer graphene of intense interest in electronic applications ( Fig. 1b) [2][3][4][5][6][7][8][9][10] . Bilayer graphene also differs from single layer graphene in its magnetic quantization in the quantum Hall regime. At E D , the four-fold degenerate Landau level (LL) in single layer graphene becomes eight-fold degenerate in the bilayer due to the additional layer degeneracy 3,11,12 . When the gap is opened this manifold splits into two four-fold degenerate quartets polarized on each layer at low energies. Lifting of these degeneracies have been observed in recent measurements [13][14][15][16] .Theoretical studies 17,18 suggest the existence of interaction-driven band gaps, which are even possible in zero applied field with corresponding quantum Hall ferromagnetic states 17,19 .The energy band gap in bilayer graphene has been studied by optical measurements such as angle resolved photoemission spectroscopy 20 and infrared spectroscopy [4][5][6]21 , which demonstrate that the gap is externally tunable and can reach values up to ≈ 250 meV...

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confidence: 99%

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Microscopic polarization in bilayer graphene

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“…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. 10 To complement these studies, here we address the issue of the inter-Landau level excitations of bilayer graphene in the quantum Hall regime.…”

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confidence: 89%

Theory of inter-Landau-level magnetoexcitons in bilayer graphene

Sári

Tőke

2013

Phys. Rev. B

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If bilayer graphene is placed in a strong perpendicular magnetic field, several quantum Hall plateaus are observed at low enough temperatures. Of these, the σxy = 4ne 2 /h sequence (n = 0) is explained by standard Landau quantization, while the other integer plateaus arise due to interactions. The low-energy excitations in both cases are magnetoexcitons, whose dispersion relation depends on single-and many-body effects in a complicated manner. Analyzing the magnetoexciton modes in bilayer graphene, we find that the mixing of different Landau level transitions not only renormalizes them, but essentially changes their spectra and orbital character at finite wave length. These predictions can be probed in inelastic light scattering experiments.

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“…In the presence of Zeeman coupling, Coulomb interactions, etc., these zeroenergy levels evolve into a variety of pseudo-zero-mode (PZM) levels, or broken-symmetry states, as discussed theoretically. [9][10][11] The interplay of orbital degeneracy and Coulomb interactions brings about a new realm of quantum phenomena 9,[12][13][14][15][16] in the PZM sector, such as orbital mixing and orbital-pseudospin waves.…”

Section: Introductionmentioning

confidence: 99%

Orbital Lamb shift and mixing of the pseudo-zero-mode Landau levels inABC-stacked trilayer graphene

Shizuya

2013

Phys. Rev. B

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In a magnetic field graphene trilayers support a characteristic multiplet of 12 zero(-energy)-mode Landau levels with a threefold degeneracy in Landau orbitals. It was earlier noted for bilayer graphene that Coulombic vacuum fluctuations, specific to graphene, lift the orbital degeneracy of such zero-energy modes and that these "Lamb-shfted" orbital modes, with filling, get mixed via the Coulomb interaction. It is pointed out that analogous orbital Lamb shift and mixing of zero-mode levels can also take place, with an enriched symmetry content, in ABC-stacked trilayer graphene; and its consequences are discussed in the light of experimental results.

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Pseudo-zero-mode Landau levels and collective excitations in bilayer graphene

Cited by 44 publications

References 43 publications

Microscopic polarization in bilayer graphene

Microscopic polarization in bilayer graphene

Theory of inter-Landau-level magnetoexcitons in bilayer graphene

Orbital Lamb shift and mixing of the pseudo-zero-mode Landau levels inABC-stacked trilayer graphene

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