Microscopic polarization in bilayer graphene

Abstract

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...

Strain and curvature induced evolution of electronic band structures in twisted graphene bilayer

“…is the cyclotron frequency, B S is the pseudomagnetic field, m * ¼ 0.03m e with m e the mass of electron and E g B0.32 eV is the band gap) 16,18 . The energy of the pseudo-LLs as a function of the orbital and valley index (N, x) are plotted in Fig.…”

“…The energies of these LLs follow the progression of LLs of massless Dirac Fermions, which suggest a possible route to realize zero-field quantum Hall effects in the strained graphene [11][12][13][14][15] . Compared with single-layer graphene, graphene bilayers, including AA stacked, AB stacked (Bernal) and twisted graphene bilayer, display even more complex electronic band structures and intriguing properties because of the interplay of quasiparticles between the Dirac cones on each layer [16][17][18][19][20][21][22][23][24][25][26][27][28] . Recently, several groups addressed the physics of the strained graphene bilayer (either AA-or AB-stacked graphene bilayer) theoretically and obtained many interesting results [29][30][31][32][33][34] .…”

Configuration-enriched magneto-electronic spectra of AAB-stacked trilayer graphene

“…The exceptionally high peak at the Fermi level is a superposition of three peaks corresponding to the Dirac points; its intensity is proportional to the number of graphene layers. The essential differences of the DOS can be verifed by STS [86][87][88][89]; those profiles can then be used as a tool to identify the stacking configuration of graphene sheets.…”

“…The discrete LLs lead to many symmetric delta-function-like peaks in the DOS, where the peak intensities are proportional to the LL degeneracy [86,87].…”

Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride

“…Impurities can also contribute to in-gap states and lead to a smaller gap size. In bilayer graphene, it has been suggested that the gap extracted from transport or STM measurements can be underestimated due to additional conductive channels created by defects and charge impurities 27 , and this may also affect the gap size measured in graphene/h-BN. Second, although the maximum gap at the equilibrium layer separation for a perfectly lattice matched heterostructure is predicted to be approximately 50 meV (ref.…”