Charge Neutral Dirac Point Research Articles

Effect of MeV Electron Beam Irradiation on Graphene Grown by Thermal Chemical Vapor Deposition

We explored the effect of MeV electron beam irradiation (MEBI) under ambient conditions on the growth of graphene by thermal chemical vapor deposition. X-ray photoelectron spectroscopy and Raman spectroscopy clearly revealed that the propagation of irradiation mediated-defects and oxidation on graphene transferred onto SiO2 (300 nm)/Si(001) occurred simultaneously after MEBI. In addition, a positive shift in the charge-neutral Dirac point (CNDP) and suppression of electrical conductivity near the CNDP were observed by electrical transport measurements, indicating p-type doping and the opening of a band-gap of graphene after MEBI.

Intrinsic plasmons in two-dimensional Dirac materials

We consider theoretically, using the random phase approximation (RPA), low-energy intrinsic plasmons for two-dimensional (2D) systems obeying Dirac-like linear chiral dispersion with the chemical potential set precisely at the charge neutral Dirac point. The "intrinsic Dirac plasmon" energy has the characteristic $q^{1/2}$ dispersion in the 2D wave-vector $q$, but vanishes as $T^{1/2}$ in temperature for both monolayer and bilayer graphene. The intrinsic plasmon becomes overdamped for a fixed $q$ as $T -> 0$ since the level broadening (i.e. the decay of the plasmon into electron-hole pairs due to Landau damping) increases as $T^{-1/2}$ as temperature decreases, however, the plasmon mode remains well-defined at any fixed $T$ (no matter how small) as $q -> 0$. We find the intrinsic plasmon to be well-defined as long as $q < k_B T/e^2$. We give analytical results for low and high temperatures, and numerical RPA results for arbitrary temperatures, and consider both single-layer and double-layer intrinsic Dirac plasmons. We provide extensive comparison and contrast between intrinsic and extrinsic graphene plasmons, and critically discuss the prospects for experimentally observing intrinsic Dirac point graphene plasmons.

Quantum Hall States near the Charge-Neutral Dirac Point in Graphene

We investigate the quantum Hall (QH) states near the charge-neutral Dirac point of a high mobility graphene sample in high magnetic fields. We find that the QH states at filling factors nu=+/-1 depend only on the perpendicular component of the field with respect to the graphene plane, indicating that they are not spin related. A nonlinear magnetic field dependence of the activation energy gap at filling factor nu=1 suggests a many-body origin. We therefore propose that the nu=0 and +/-1 states arise from the lifting of the spin and sublattice degeneracy of the n=0 Landau level, respectively.

Quantum Hall effect in graphene

The quantum Hall (QH) effect in two-dimensional electron and hole gas is studied in high quality graphene samples. Graphene samples whose lateral size ∼10 μm were fabricated into mesoscopic devices for electrical transport measurement in magnetic fields. In an intermediate field range of up to 10 T, a distinctive half-integer QH effect is discovered with QH plateaus appearing at a filling factor sequence, ν = 4 ( n + 1 / 2 ) , where n is the Landau level (LL) index. As the magnetic field increases to the extreme quantum limit, we observe additional QH plateaus at filling factors ν = 0 , ± 1 , ± 4 . Further detailed investigations show that the presence of the ν = 0 , ± 1 QH states indicates the n = 0 LL at the charge neutral Dirac point splits into four sublevels. This lifts both the sublattice and the spin degeneracy, while the QH states at ν = ± 4 can be attributed to lifting of the spin degeneracy of the LLs. Above 30 T of magnetic field, the large quasiparticle gaps between the n = 0 and n = ± 1 LLs lead to the QH effect that can be observed even at room temperature.

Electric Field Effect Tuning of Electron-Phonon Coupling in Graphene

Gate-modulated low-temperature Raman spectra reveal that the electric field effect (EFE), pervasive in contemporary electronics, has marked impacts on long-wavelength optical phonons of graphene. The EFE in this two-dimensional honeycomb lattice of carbon atoms creates large density modulations of carriers with linear dispersion (known as Dirac fermions). Our EFE Raman spectra display the interactions of lattice vibrations with these unusual carriers. The changes of phonon frequency and linewidth demonstrate optically the particle-hole symmetry about the charge-neutral Dirac point. The linear dependence of the phonon frequency on the EFE-modulated Fermi energy is explained as the electron-phonon coupling of massless Dirac fermions.

GRAPHENE IN EXTREMELY HIGH MAGNETIC FIELDS

We have studied the quantum Hall (QH) effect in two-dimensional electrons and holes in high quality graphene samples in strong magnetic fields up to 45 T. A distinctive half-integer QH effect is discovered at high magnetic fields, with QH plateaus appearing at filling factors ν = ±4(|n| + 1/2), where n is the Landau level (LL) index. This finding is consistent with theoretical predictions. In addition, in the extreme magnetic quantum limit with magnetic fields up to 45 T, we observe LL splittings in graphene at filling factors ν = 0,±1,±4. Further detailed investigation shows that the presence of the ν = 0,±1 QH states indicates the n = 0 LL at the charge neutral Dirac point splits into four sublevels, lifting both the sublattice and the spin degeneracy, while the QH states at ν = ±4 can be attributed to lifting of the spin degeneracy of the n = ±1 LLS.

Landau-Level Splitting in Graphene in High Magnetic Fields

The quantum Hall (QH) effect in two-dimensional electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors nu = 0, +/-1, +/-4 are discovered at magnetic fields B > 20 T, indicating the lifting of the fourfold degeneracy of the previously observed QH states at nu = +/-4(absolute value(n) + 1/2), where n is the Landau-level index. In particular, the presence of the nu = 0, +/-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 nu = +/-4 is investigated in a tilted magnetic field and can be attributed to lifting of the spin degeneracy of the n = 1 Landau level.