We perform low temperature transport measurements on dual-gated suspended Bernal-stacked(ABA) and Rhombohedral-stacked(ABC) trilayer graphene in the quantum Hall (QH) regime. In ABA Bernal stacking order trilayer, we observe QH plateaus at filling factors ν=-8, -2, 2, 6, and 10, in agreement with the full-parameter tight binding calculations. In high magnetic fields, odd integer plateaus are also resolved, indicating almost complete lifting of the 12-fold degeneracy of the lowest Landau levels (LL). Under an out-of-plane electric field E⊥, we observe degeneracy breaking and transitions between QH plateaus. Interestingly, depending on its direction, E⊥ selectively breaks the LL degeneracies in the electron-doped or hole-doped regimes. In ABC Rhombohedral stacking order trilayer, we observe QH plateaus at filling factors ν=0, 1, 2 and 3 in a high magnetic field.

A worldwide effort is underway to build devices that take advantage of the remarkable electronic properties of graphene and other two-dimensional crystals. An outstanding question is how stacking two or a few such crystals affects their joint electronic behavior. This talk concerns “twisted bilayer graphene (TBG),” that is, two graphene layers azimuthally misoriented. Applying angle-resolved photoemission spectroscopy and density functional theory, we have found van Hove singularities (vHs) and associated mini-gaps in the TBG electronic spectrum, which represent unambiguous proof that the layers interact. Of particular interest is that the measured and calculated electronic dispersions reflect the periodicity of the moiré superlattice formed by the twist. Thus, there are vHs not just where the Dirac cones of the two layers overlap, but also at the boundaries of the moiré superlattice Brillouin zone. Such changes in the electronic dispersion also manifest themselves in TBG’s optical properties. The result is that the material’s color varies depending on the twist angle, and can be seen under optical microscope. Moirés, ubiquitous in hybrid solids based on two-dimensional crystals, accordingly present themselves as tools for manipulating the electronic behavior.

This work is carried out in collaboration with J. T. Robinson, S. W. Schmucker, J. P. Long, J. C. Culbertson, A. L. Friedman at Naval Research Laboratory, P. J. Feibelman, T. E. Beechem, B. Diaconescu, G. L. Kellogg at Sandia National Laboratories, and A. Bostwick, E. Rotenberg at Lawrence Berkeley National Laboratory. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Ultraviolet photoemission spectroscopy measurements of fluorinated epitaxial graphene on the carbon face of silicon carbide show that there are changes in the electron density of states in the valence band near the Fermi level with applied electrical bias. The strong modification of density of states may be due to doping or piezoelectric effects. The experimentally observed changes in the electronic structure are compared to analysis using first principles density-functional theory including interlayer Van der Waals interactions. The results indicate that the p-doping inherent with the fluorination strongly effects the changes in the electronic band structure near the valence band maximum of the joint density of states region.

Low-frequency current fluctuations with the spectral density S(f)~1/f (f is the frequency) is a ubiquitous phenomenon observed in a wide variety of electronic materials and devices. Low-frequency 1/f noise limits the sensitivity of sensors and makes the main contribution to the phase-noise of communication systems via its up-conversion. For this reason, practical applications of every new material system require a thorough investigation of specific features of the low-frequency noise in this material and developing methods for its reduction. It has already been demonstrated that the low-frequency current fluctuations in graphene [1-3] and thin films of van der Waals materials [4] reveal unusual gate bias dependence, which cannot be described with conventional Hooge parameter or McWhorter model. In this talk, I will review state-of-the-art in the 1/f noise field in graphene and van der Waals materials, and describe possibilities for deeper understanding of 1/f noise offered by availability of continuous atomically thin films. A long-standing question of importance for electronics is whether 1/f noise is generated on the surface of conductors or inside their volumes. Using graphene multilayers we were able to directly address this fundamental problem of the noise origin. Unlike the thickness of metal or semiconductor films, the thickness of graphene multilayers can be continuously and uniformly varied all the way down to a single atomic layer of graphene – the actual surface. We found that 1/f noise becomes dominated by the volume noise when the thickness exceeds ~7 atomic layers (~2.5 nm). The 1/f noise is the surface phenomenon below this thickness [5]. We investigated experimentally the effect of the electron-beam irradiation on the level of the low-frequency 1/f noise in graphene devices. It was found unexpectedly that 1/f noise in graphene reduces with increasing concentration of defects induced by irradiation [6]. The bombardment of graphene devices with 20-keV electrons reduced the noise spectral density by an order-of magnitude at the radiation dose of 10⁴ m C/cm². The noise reduction can be explained within the mobility fluctuation mechanism. The obtained results are important for the proposed applications of graphene and van der Waals materials in sensors and communications.

[1] G. Liu, et al., Appl. Phys. Lett., 95, 033103 (2009); [2] S. Rumyantsev, et al., J. Phys.: Cond. Matter, 22, 395302 (2010); [3] G. Liu, et al., Appl. Phys. Lett., 100, 033103 (2012); [4] M.Z. Hossain, et al., ACS Nano, 5, 2657 (2011); [5] G. Liu, et al., Appl. Phys. Lett., 102, 093111 (2013); [6] M. Z. Hossain, et al. Appl. Phys. Lett., 102, 153512 (2013).

The symmetry of the extended 5-5-8 line defect discovered in graphene in 2010 provides many interesting properties that could potentially be exploited in graphene-based electronic applications. Intrinsically, this line defect is approximately semitransparent, meaning that about 50% of carriers transmit through the line defect with the remaining 50% being subject to specular reflection. Another feature is that the transmission probability depends strongly on the valley of the incident carriers, making the line defect a valley filter, an essential component for valley-based electronics. Numerical simulations suggest that the line defect might offer ferromagnetically aligned local moments, which could also have implications for spin-based devices.

The properties of the line defect could be dramatically altered through chemical decoration. By turning sp2 bonds into sp3 bonds, the transmission probability is significantly reduced. Structures with two such line defects in a parallel configuration therefore exhibit confined graphene states, closely related to the states in zigzag nanoribbons. Unlike the nanoribbons, the railroad track structure formed by two parallel line defects allows carrier transport not only along the structure but also across it. The latter transverse transport occurs within resonance bands that closely trace the dispersion of the bands within the confinement. Owing to a dimensional crossover, the resonance bands must terminate, which leaves behind a transport gap. This transport gap could be used in lateral graphene-based resonant tunneling transistors.

This work was supported by the Office of Naval Research, directly and through the Naval Research Laboratory.

In this talk, we discuss results from some recent theoretical studies on the electronic and optical properties of graphene, monolayer MoS₂, and surface states of topological insulators. Owing to their reduced dimensionality and unique electronic structure, these systems present opportunities for study of unusual manifestation of concepts/phenomena that may not be so prominent or have not been seen in bulk materials. Many-body effects and symmetry play a critical role in shaping both qualitatively and quantitatively their spectroscopic properties. Several phenomena will be discussed: 1) Excitonic effects in the optical spectra of graphene, in the form of a strong resonant (hyperbolic) exciton, and how they are altered by carrier doping and quasiparticle lifetime are predicted. 2) The physical origin of the intriguing satellite structures seen in angle-resolved photoemission spectra of graphene is explained. 3) The optical response of monolayer MoS₂ is shown to be very rich in features and is dictated by excitonic states with huge binding energies of ~1 eV. 4) For topological insulators, we show that the spin orientation of photoelectrons from the topologically protected surface states in general can be very different from that of the initial states and is controlled by the photon polarization.

This work is supported in part by the National Science Foundation, U.S. Department of Energy, and the Office of Naval Research.