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Register a new userLandau Level Splitting in Graphene in High Magnetic Fields
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Y. Zhang
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The quantum Hall (QH) effect in two-dimensional (2D) electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors $ u=0,pm 1,pm 4$ are discovered at magnetic fields $B>$20 T, indicating the lifting of the four-fold degeneracy of the previously observed QH states at $ u=pm(|n|+1/2)$, where $n$ is the Landau level index. In particular, the presence of the $ u=0, pm 1$ QH plateaus indicates that the Landau level at the charge neutral Dirac point splits into four sublevels, lifting sublattice and spin degeneracy. The QH effect at $ u=pm 4$ is investigated in tilted magnetic field and can be attributed to lifting of the spin-degeneracy of the $n=1$ Landau level.
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Landau level gaps are important parameters for understanding electronic interactions and symmetry-broken processes in bilayer graphene (BLG). Here we present transport spectroscopy measurements of LL gaps in double-gated suspended BLG with high mobilities in the quantum Hall regime. By using bias as a spectroscopic tool, we measure the gap {Delta} for the quantum Hall (QH) state at filling factor { u}={pm}4 and -2. The single-particle gap for { u}=4 scales linearly with magnetic field B and is independent of the out-of-plane electric field E. For the symmetry-broken { u}=-2 state, the measured values of gap are 1.1 meV/T and 0.17 meV/T for singly-gated geometry and dual-gated geometry at E=0, respectively. The difference between the two values arises from the E-dependence of the gap, suggesting that the { u}=-2 state is layer polarized. Our studies provide the first measurements of the gaps of the broken symmetry QH states in BLG with well-controlled E, and establish a robust method that can be implemented for studying similar states in other layered materials.
We present magneto-Raman scattering studies of electronic inter Landau level excitations in quasi-neutral graphene samples with different strengths of Coulomb interaction. The band velocity associated with these excitations is found to depend on the dielectric environment, on the index of Landau level involved, and to vary as a function of the magnetic field. This contradicts the single-particle picture of non-interacting massless Dirac electrons, but is accounted for by theory when the effect of electron-electron interaction is taken into account. Raman active, zero-momentum inter Landau level excitations in graphene are sensitive to electron-electron interactions due to the non-applicability of the Kohn theorem in this system, with a clearly non-parabolic dispersion relation.
The Landau level spectrum of graphene superlattices is studied using a tight-binding approach. We consider non-interacting particles moving on a hexagonal lattice with an additional one-dimensional superlattice made up of periodic square potential barriers, which are oriented along the zig-zag or along the arm-chair directions of graphene. In the presence of a perpendicular magnetic field, such systems can be described by a set of one-dimensional tight-binding equations, the Harper equations. The qualitative behavior of the energy spectrum with respect to the strength of the superlattice potential depends on the relation between the superlattice period and the magnetic length. When the potential barriers are oriented along the arm-chair direction of graphene, we find for strong magnetic fields that the zeroth Landau level of graphene splits into two well separated sublevels, if the width of the barriers is smaller than the magnetic length. In this situation, which persists even in the presence of disorder, a plateau with zero Hall conductivity can be observed around the Dirac point. This Landau level splitting is a true lattice effect that cannot be obtained from the generally used continuum Dirac-fermion model.
The quantum Hall effect near the charge neutrality point in bilayer graphene is investigated in high magnetic fields of up to 35 T using electronic transport measurements. In the high field regime, the eight-fold degeneracy in the zero energy Landau level is completely lifted, exhibiting new quantum Hall states corresponding filling factors $ u=$0, 1, 2, & 3. Measurements of the activation energy gap in tilted magnetic fields suggest that the Landau level splitting at the newly formed $ u=$1, 2, & 3 filling factors are independent of spin, consistent with the formation of a quantum Hall ferromagnet. In addition, measurements taken at the $ u$ = 0 charge neutral point show that, similar to single layer graphene, the bilayer becomes insulating at high fields.
We have investigated tunneling current through a suspended graphene Corbino disk in high magnetic fields at the Dirac point, i.e. at filling factor $ u$ = 0. At the onset of the dielectric breakdown the current through the disk grows exponentially before ohmic behaviour, but in a manner distinct from thermal activation. We find that Zener tunneling between Landau sublevels dominates, facilitated by tilting of the source-drain bias potential. According to our analytic modelling, the Zener tunneling is strongly affected by the gyrotropic force (Lorentz force) due to the high magnetic field
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