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Register a new userLocal and Global Screening Properties of Graphene Revealed through Landau Level Spectroscopy
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One-atom thick crystalline layers and their vertical heterostructures carry the promise of designer electronic materials that are unattainable by standard growth techniques. In order to realize their potential it is necessary to isolate them from environmental disturbances in particular those introduced by the substrate. But finding and characterizing suitable substrates, and minimizing the random potential fluctuations they introduce, has been a persistent challenge in this emerging field. Here we show that Landau-level (LL) spectroscopy is exquisitely sensitive to potential fluctuations on both local and global length scales. Harnessing this technique we demonstrate that the insertion of an intermediate graphene layer provides superior screening of substrate induced disturbances, more than doubling the electronic mean free path. Furthermore, we find that the proximity of hBN acts as a nano-scale vacuum cleaner, dramatically suppressing the global potential fluctuations. This makes it possible to fabricate high quality devices on standard SiO2 substrates.
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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.
We describe an infrared transmission study of a thin layer of bulk graphite in magnetic fields up to B = 34 T. Two series of absorption lines whose energy scales as sqrtB and B are present in the spectra and identified as contributions of massless holes at the H point and massive electrons in the vicinity of the K point, respectively. We find that the optical response of the K point electrons corresponds, over a wide range of energy and magnetic field, to a graphene bilayer with an effective inter-layer coupling 2gamma_1, twice the value for a real graphene bilayer, which reflects the crystal ordering of bulk graphite along the c-axis. The K point electrons thus behave as massive Dirac fermions with a mass enhanced twice in comparison to a true graphene bilayer.
We demonstrate that surface relaxation, which is insignificant in trilayer graphene, starts to manifest in Bernal-stacked tetralayer graphene. Bernal-stacked few-layer graphene has been investigated by analyzing its Landau level spectra through quantum capacitance measurements. We find that in trilayer graphene, the interlayer interaction parameters were similar to that of graphite. However, in tetralayer graphene, the hopping parameters between the bulk and surface bilayers are quite different. This shows a direct evidence for the surface relaxation phenomena. In spite of the fact that the Van der Waals interaction between the carbon layers is thought to be insignificant, we suggest that the interlayer interaction is an important factor in explaining the observed results and the symmetry-breaking effects in graphene sublattice are not negligible.
Scanning tunneling spectroscopy is used to study the real-space local density of states (LDOS) of a two-dimensional electron system in magnetic field, in particular within higher Landau levels (LL). By Fourier transforming the LDOS, we find a set of n radial minima at fixed momenta for the nth LL. The momenta of the minima depend only on the inverse magnetic length. By comparison with analytical theory and numerical simulations, we attribute the minima to the nodes of the quantum cyclotron orbits, which decouple in Fourier representation from the random guiding center motion due to the disorder. This robustness of the nodal structure of LL wave functions should be viewed as a key property of quantum Hall states.
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.
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