Session V26: Focus Session: Graphene XIV: Magnetism and Bilayers

Defect-induced magnetism in graphene nanoflakes

The interaction between electron spin and the magnetic moments of vacancies in graphene could open new opportunities for spintronic and quantum computation. In that direction, we have studied the magnetic properties of graphene nanoflakes (C$_{6n2}$H$_{6n})$ with vacancies within the framework of density functional theory, using the pseudopotential LCAO method with a Generalized Gradient Approximation (GGA) for the exchange-correlation energy functional. In particular, we have calculated the magnetic moment of graphene nanoflakes of different diameters with a simple vacancy. We have found that the total spin-polarization of the graphene nanoflakes with a simple vacancy decreases as the diameter increases. In particular, we show that the vacancy induces the appereance of a midgap state at Fermi level. Thus, the spin degeneracy is broken, being only one of the spin channels of the midgap state occupied, the other being empty. This feature could be exploited for future spintronic applications. This research was supported by Consejo Nacional de Ciencia y Tecnolog\'{\i}a (Conacyt) under Grant No. 83604.   

Magnetism in Nanopatterned Graphene and Graphite Film

We report first-principles calculations of magnetic properties of nanopatterned graphene-based nanostructures (GBNs) and nanopatterned graphite films (NPGFs). We introduce a simple geometric rule to design several novel magnetic GBNs: 0D FM nanodots with the highest possible magnetic moments, 1D FM nanoribbons, and 2D magnetic superlattices, whose predicted ground-sate magnetic ordering is confirmed by first-principles calculations. Furthermore, we show that nanopatterned graphite films (NPGFs) can exhibit magnetism similar to GBNs. In particular, graphite films with patterned nanoscale triangular holes and channels with zigzag edges all have ferromagnetic ground states.   

Tunable band structure in double gated trilayer graphene

Graphene based materials are promising candidates for nano electronic applications. It is currently unclear which layer thickness is better suited for a given application, as only the properties of monolayers and bilayers have been investigated systematically. For the optimization of future devices, it is important to understand how the electronic properties of graphene based materials evolve from Dirac particles, in monolayer, to massive particles in bulk graphite. We experimentally address this question by investigating trilayer graphene, the thinnest few layer graphene system in which all the parameters determining the band structure of graphite are first found. Contrary to monolayer and bilayer (which are both zero gap semiconductors), we find that trilayer is a semimetal with a finite overlap of conduction and valence bands. We show that the low energy band structure of trilayer graphene can be tuned by a large amount by means of an external perpendicular electric field, achieving 100{\%} change in band overlap a property not known to occur in any other semimetal.   

Can Carbon Be Ferromagnetic?

While conventional wisdom says that magnetic materials have to contain some metallic atoms, the possibility of intrinsic magnetic order in pure metal free carbon materials is of fundamental interest because of the role of carbon as an elemental building block of organic as well as inorganic matter and last but not least of the tremendous interest in the electronic properties of graphene based structures. The common controversy raised across all disciplines in this matter is whether the magnetism of carbon is intrinsic or induced by other elements. We address this controversy by providing clear experimental evidence that metal free carbon can be ferromagnetic at room temperature using dichroism x-ray absorption spectro-microscopy. For this purpose we acquired soft x-ray microscopy images of magnetic structures on a thin carbon film that have been produced by irradiation with a focused 2.25MeV proton beam. Our element specific magnetic probe shows no indication of magnetically ordered Fe, Co or Ni impurities in these samples. Combination of the microscopy data with element specific spectroscopy and hysteresis measurements shows furthermore that only the carbon $\pi$-electronic states contribute to the long range ferromagnetic order of the sample.   

Low-frequency magnetooptical spectra of bilayer Bernal graphene

The low-frequency magnetoabsorption spectra of bilayer Bernal graphene are investigated within the gradient approximation. The interlayer interactions significantly alter the Landau- level energies, state wave function, and thus enrich the ptical excitation spectra. There exist four kinds of absorption peaks, mainly owing to the optical transitions between two groups of Landau levels with valence and conduction states. The number, intensity, and frequency of absorption peaks strongly depend on the field strength. Such features quite differ from those of monolayers.   

Tunneling Measurements in Single- and Multi-layer Graphene

We have fabricated novel single- and multi-layer graphene devices with both normal metal ohmic contacts and superconducting tunnel probes. The superconducting gap of the tunnel probes in the graphene devices is well formed at 250 mK, showing that the probes are good for tunneling spectroscopy studies of graphene electronic structure. We have observed oscillations as a function of bias and gate voltages, possibly due to electron phase interference among the layers and/or tunnel probe interfaces. Those oscillations die out in the presence of magnetic fields. Unexpectedly, two distinct and symmetric peaks, which have weak dependence on gate voltages, exist in the superconducting gap.   

Resistance noise in electrically biased bilayer graphene

The growing interest in bilayer graphene (BLG) is fueled by the ability to control the energy gap between its valence and conduction bands through external means. Here, we demonstrate experimentally that the low-frequency resistance fluctuations, or noise, in bilayer graphene is strongly connected to its band structure, and displays a minimum when the gap between the conduction and valence band is zero. Using double-gated bilayer graphene devices we have tuned the zero gap and charge neutrality points independently, which offers a unique mechanism to investigate the low-energy band structure, charge localization and screening properties of bilayer graphene. We show: (1) the noise to be minimum when band gap ($\Delta _{g})$ = 0 even if it corresponds to a nonzero carrier density (n), (2) the evidence of localized states near the band tails even at $\Delta _{g}$ = 0, with a mobility edge that strongly depends on the external electric field E, and finally, (3) a method to directly determine the dielectric properties of BLG in both electron and hole-doped regimes.   

Ab-initio study of doped bilayer graphene

The recent discovery that the application of an external electric field induces a band gap opening in bilayer graphene [1], attracted a lot of interest on this system, due to important applications in nanoelectronics. By means of ab-initio calculations, we investigated the electronic properties of doped bilayer graphene, in presence of different bottom and top gate. In particular, the dependence of the band gap on the doping, on the average external electric field and temperature has been analysed. We find that our ab-initio results differ with respect to those obtained with standard Tigth Binding (TB) calculations [2]. In particular, we show important charge effects, which are crucial for the description of the electronic properties of bilayer graphene, and which are not included in TB models. Moreover, we compare our results with experimental measurements of the band gap, cyclotron mass and work function. [1] Ohta et al., Science v.313 , 951 (2006). [2] Castro Neto et al., Pys. Rev. Lett. v.99, 216802 (2007).   

Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate

A real-space lattice formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly-quantized vortex in the condensate binds exactly one zero mode per valley index of the bilayer. In the full lattice model the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties, including their fractional exchange statistics.   

Ultrafast electroic-state dynamics of graphite probed by time-resolved photoemission spectroscopy

Time-resolved photoemission spectroscopy (250-kHz repetition of 1.5-eV pump and 5.9 eV probe pulses with durations of $\sim $170 fs) using a hemisphereical electron-energy analyzer (VG Scienta SES2002) is employed to investigate the ultrafast electronic-state dynamics of highly oriented pyrolytic graphite. We directly observe electrons excited to 0.75 eV above the Fermi level within 0.1 ps after the pump, reflecting the conical dispersion of graphite about the Fermi level [1]. The excited state decays over $\sim $20 ps with at least two time scales. The longer time scale shows little pump-power dependence, indicating that the decay is independent of the excitation population. We also find a peculiar increase of the spectral weight at the Fermi level throughout the transient state, which can be modeled by a dynamical broadening of the electronic states due to hot optical phonons generated by the pump [2]. [1] S.Y. Zhou \textit{et al.}, \textit{Nature Phys.} \textbf{2}, 595 (2006). [2] T. Krampfrath \textit{et al.}, \textit{Phys. Rev. Lett.} \textbf{95}, 187403 (2005); D. Sun \textit{et al.}, \textit{Phys. Rev. Lett.} \textbf{101}, 157402 (2008).   

Plasmon Dispersion and Damping in Electrically-isolated Two-dimensional Charge Sheets

Using high resolution reflection electron-energy-loss- spectroscopy (HREELS), we compare experimental results for the wavevector-dependent behavior of plasmons in a graphene sheet on SiC(0001) with that due to a filled band of surface states on semiconducting silicon. There are significant differences in behavior between the two systems, and the behavior predicted for a classical two-dimensional sheet of electrons. In particular, the damping increases with wavevector independent of any obvious inelastic scattering channel. The results illustrate the importance of finite-momentum, non-local potential effects for the dynamical behavior of electrically- isolated charge sheets.\footnote{Y. Liu, et al. Phys. Rev. B 78, 201403(R)(2008)}   

Edge Phonons of Graphene from Tight-Binding.

Edge-states in graphene can affect the band-gap and carrier group velocities in narrow ( $<$ 5 nm) graphene nanoribbons. As a first, tight-binding approximation from simple nearest-neighbor hopping, it is shown that armchair nanoribbons have large band-gaps compared to zigzag nanoribbons, which are metallic, unless certain crucial effects are included in the calculation, e.g. magnetic- , quasiparticle- , charge-self-consistent- and/or relaxation- based degeneracy lifting. All of these effects open a small band gap, and the interplay between relaxation and electronic-structure may be examined by calculating the edge phonons of graphene. To this end, we expand on our previous, all-neighbor tight-binding Hamiltonian [\textit{Phys. Rev. B} \textbf{76}, 121405(R) (2007)] and include charge self-consistency at the edge of a zigzag nanoribbon. By allowing charge transfer and structural-relaxation at zigzag edges, we are able to remove imaginary phonons and verify the opening of a small band-gap in zigzag ribbons, which is characterized by the phonon density-of-states and normal modes of carbon-hydrogen edge bonds. These calculations are relevant to ribbons cut along non-ideal directions, as well, and we will discuss edge-disorder.   

Optical Conductivity and quasiparticle properties of Bilayer graphene

The low energy properties of Bernal stacked bilayer graphene can be adequately described by chiral quasiparticles exhibiting a Berry phase of $2 \pi$ with a parabolic dispersion. When the Fermi energy lies at the neutrality point the Fermi surface consists of a pair of points where dominant inter-band excitations determine the effect on electronic correlations. The particle-hole continuum due to the inter-band excitations is given by $\Omega > q^2/(4m)$ in frequency-momentum space. The full wavevector and frequency dependent polarization bubble and optical conductivity is calculated within the RPA. We also calculate the quasiparticle properties for short-ranged interactions and comment on the breakdown of Fermi liquid theory.