Topological Insulator in the Presence of Spatially Correlated Disorder

We investigate the effect of spatially correlated disorder on two-dimensional topological insulators and on the quantum spin Hall effect which the helical edge states in these systems give rise to. Our work expands the scope of previous investigations which found that uncorrelated disorder can induce a nontrivial phase called the topological Anderson insulator (TAI). In extension of these studies, we find that spatial correlations in the disorder can entirely suppress the emergence of the TAI phase. We show that this phenomenon is associated with a quantum percolation transition and quantify it by generalizing an existing effective medium theory to the case of correlated disorder potentials. The predictions of this theory are in good agreement with our numerics and may be crucial for future experiments.Comment: 8 pages, 5 figures; final version including additional data on percolation transitio

Graphene quantum dot on boron nitride: Dirac cone replica and Hofstadter butterfly

Graphene flakes placed on hexagonal boron nitride feature in the presence of a magnetic field a complex electronic structure due to a hexagonal moir\'e potential resulting from the van der Waals interaction with the substrate. The slight lattice mismatch gives rise to a periodic supercell potential. Zone folding is expected to create replica of the original Dirac cone and Hofstadter butterflies. Our large-scale tight binding simulation reveals an unexpected coexistence of a relativistic and non-relativistic Landau level structure. The presence of the zeroth Landau level and its associated butterfly is shown to be the unambiguous signature for the occurrence of Dirac cone replica.Comment: 8 pages, 6 figure

Percolating States in the Topological Anderson Insulator

We investigate the presence of percolating states in disordered two-dimensional topological insulators. In particular, we uncover a close connection between these states and the so-called topological Anderson insulator (TAI), which is a topologically non-trivial phase induced by the presence of disorder. The decay of this phase could previously be connected to a delocalization of bulk states with increasing disorder strength. In this work we identify this delocalization to be the result of a percolation transition of states that circumnavigate the hills of the bulk disorder potential.Comment: 8 pages, 5 figures, to appear in Phys. Rev.

Graphene nanoribbons with wings

We have investigated electronic transport in graphene nanoribbon devices with additional bar-shaped extensions ("wings") at each side of the device. We find that the Coulomb-blockade dominated transport found in conventional ribbons is strongly modified by the presence of the extensions. States localized far away from the central ribbon contribute significantly to transport. We discuss these findings within the picture of multiple coupled quantum dots. Finally, we compare the experimental results with tight-binding simulations which reproduce the experiment both qualitatively and quantitatively

Transport through graphene nanoribbons: suppression of transverse quantization by symmetry breaking

We investigate transport through nanoribbons in the presence of disorder scattering. We show that size quantization patterns are only present when SU(2) pseudospin symmetry is preserved. Symmetry breaking disorder renders transverse quantization invisible, which may provide an explanation for the necessity of suspending graphene nanoconstrictions to obtain size quantization signatures in very recent experiments. Employing a quasi-classical Monte-Carlo simulation, we are able to reproduce and explain key qualitative features of the full quantum-mechanical calculations.Comment: 5 figure

Magneto-optical response of graphene: probing substrate interactions

Magneto-optical transitions between Landau levels can provide precise spectroscopic information on the electronic structure and excitation spectra of graphene, enabling probes of substrate and many-body effects. We calculate the magneto-optical conductivity of large-size graphene flakes using a tight-binding approach. Our method allows us to directly compare the magneto-optical response of an isolated graphene flake with one aligned on hexagonal boron nitride giving rise to a periodic superlattice potential. The substrate interaction induces band gaps away from the Dirac point. In the presence of a perpendicular magnetic field Landau-level like structures emerge from these zero-field band gaps. The energy dependence of these satellite structures is, however, not easily accessible by conventional probes of the density of states by varying the back-gate voltage. Here we propose the magneto-optical probing of the superlattice perturbed spectrum. Our simulation includes magneto-excitonic effects in first-order perturbation theory. Our approach yields a quantitative explanation of recently observed Landau-level dependent renormalizations of the Fermi velocity.Comment: 8 pages, 3 figure

Electron-Hole Crossover in Graphene Quantum Dots

We investigate the addition spectrum of a graphene quantum dot in the vicinity of the electron-hole crossover as a function of perpendicular magnetic field. Coulomb blockade resonances of the 50 nm wide dot are visible at all gate voltages across the transport gap ranging from hole to electron transport. The magnetic field dependence of more than 50 states displays the unique complex evolution of the diamagnetic spectrum of a graphene dot from the low-field regime to the Landau regime with the n=0 Landau level situated in the center of the transport gap marking the electron-hole crossover. The average peak spacing in the energy region around the crossover decreases with increasing magnetic field. In the vicinity of the charge neutrality point we observe a well resolved and rich excited state spectrum.Comment: 4 pages, 3 figure

Negative quantum capacitance in graphene nanoribbons with lateral gates

We present numerical simulations of the capacitive coupling between graphene nanoribbons of various widths and gate electrodes in different configurations. We compare the influence of lateral metallic or graphene side gate structures on the overall back gate capacitive coupling. Most interestingly, we find a complex interplay between quantum capacitance effects in the graphene nanoribbon and the lateral graphene side gates, giving rise to an unconventional negative quantum capacitance. The emerging non-linear capacitive couplings are investigated in detail. The experimentally relevant relative lever arm, the ratio between the coupling of the different gate structures, is discussed.Comment: 8 pages, 6 figure

Coherent transport through graphene nanoribbons in the presence of edge disorder

We simulate electron transport through graphene nanoribbons of experimentally realizable size (length L up to 2 micrometer, width W approximately 40 nm) in the presence of scattering at rough edges. Our numerical approach is based on a modular recursive Green's function technique that features sub-linear scaling with L of the computational effort. We identify the influence of the broken A-B sublattice (or chiral) symmetry and of K-K' scattering by Fourier spectroscopy of individual scattering states. For long ribbons we find Anderson-localized scattering states with a well-defined exponential decay over 10 orders of magnitude in amplitude.Comment: 8 pages, 6 Figure

Impact of Many-Body Effects on Landau Levels in Graphene

We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier density-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magneto-phonon resonances, we extract the charge carrier density dependence of the Landau level transition energies and the associated effective Fermi velocity $v_\mathrm{F}$. In contrast to the logarithmic divergence of $v_\mathrm{F}$ at zero magnetic field, we find a piecewise linear scaling of $v_\mathrm{F}$ as a function of charge carrier density, due to a magnetic field-induced suppression of the long-range Coulomb interaction. We quantitatively confirm our experimental findings by performing tight-binding calculations on the level of the Hartree-Fock approximation, which also allow us to estimate an excitonic binding energy of $\approx$ 6 meV contained in the experimentally extracted Landau level transitions energies.Comment: 10 pages, 6 figure