We demonstrate the anomalous Hall effect (AHE) in single-layer graphene exchange-coupled to an atomically flat yttrium iron garnet (YIG) ferromagnetic thin film.The anomalous Hall conductance has magnitude of ~0.09(2e 2 /h) at low temperatures and is measurable up to ~ 300 K. Our observations indicate not only proximity-induced ferromagnetism in graphene/YIG with large exchange interaction, but also enhanced spin-orbit coupling which is believed to be inherently weak in ideal graphene. The proximity-induced ferromagnetic order in graphene can lead to novel transport phenomena such as the quantized AHE which are potentially useful for spintronics.

Graphene is described at low energy by a massless Dirac equation whose eigenstates have definite chirality. We show that the tendency of Coulomb interactions in lightly doped graphene to favor states with larger net chirality leads to suppressed spin and charge susceptibilities. Our conclusions are based on an evaluation of graphene's exchange and random-phase-approximation correlation energies. The suppression is a consequence of the quasiparticle chirality switch which enhances quasiparticle velocities near the Dirac point.

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As the only non-carbon elemental layered allotrope, few-layer black phosphorus or phosphorene has emerged as a novel two-dimensional (2D) semiconductor with both high bulk mobility and a band gap. Here we report fabrication and transport measurements of phosphorene-hexagonal BN (hBN) heterostructures with one-dimensional (1D) edge contacts. These transistors are stable in ambient conditions for >300 hours, and display ambipolar behavior, a gate-dependent metalinsulator transition, and mobility up to 4000 cm 2 /Vs. At low temperatures, we observe gatetunable Shubnikov de Haas (SdH) magneto-oscillations and Zeeman splitting in magnetic field with an estimated g-factor ~2. The cyclotron mass of few-layer phosphorene holes is determined to increase from 0.25 to 0.31 m e as the Fermi level moves towards the valence band edge. Our results underscore the potential of few-layer phosphorene (FLP) as both a platform for novel 2D physics and an electronic material for semiconductor applications. *

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