Pseudo-magnetic field distribution and pseudo-Landau levels in suspended graphene flakes

Combining the tight-binding approximation and linear elasticity theory for a planar membrane, we investigate stretching of a graphene flake assuming that two opposite edges of the sample are clamped by the contacts. We show that, depending on the aspect ratio of the flake and its orientation, gapped states may form in the membrane in the vicinity of the contacts. This gap in the pre-contact region should be biggest for the armchair orientation of the flake and width to length ratio of around 1.Comment: 7 pages + 3 figure

Landau levels in deformed bilayer graphene at low magnetic fields

We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ff=+-4 being the most stable in the quantum Hall effect measurement, instead of ff=+-8 in unperturbed bilayer at a weak magnetic field. To mention, in one of the strain regimes, the activation gap at ff=+-4 is, down to very low fields, weakly dependent on the strength of the magnetic field.Comment: 14 single-column pages, 5 figures, more details on material presented in arXiv:1104.502

Strained bilayer graphene: Band structure topology and Landau level spectrum

We show that topology of the low-energy band structure in bilayer graphene critically depends on mechanical deformations of the crystal which may easily develop in suspended graphene flakes. We describe the Lifshitz transition that takes place in strained bilayers upon splitting the parabollic bands at intermediate energies into several Dirac cones at the energy scale of few meV. Then, we show how this affects the electron Landau level spectra and the quantum Hall effect.Comment: slightly over 4 pages, 3 figures, updated discussion and references; almost identical to the published versio

Strain-induced modifications of transport in gated graphene nanoribbons

We investigate the effects of homogeneous and inhomogeneous deformations and edge disorder on the conductance of gated graphene nanoribbons. Under increasing homogeneous strain the conductance of such devices initially decreases before it acquires a resonance structure, and finally becomes completely suppressed at larger strain. Edge disorder induces mode mixing in the contact regions, which can restore the conductance to its ballistic value. The valley-antisymmetric pseudo-magnetic field induced by inhomogeneous deformations leads to the formation of additional resonance states, which either originate from the coupling into Fabry-Perot states that extend through the system, or from the formation of states that are localized near the contacts, where the pseudo-magnetic field is largest. In particular, the n=0 pseudo-Landau level manifests itself via two groups of conductance resonances close to the charge neutrality point.Comment: 10 pages, 6 figure

Spectroscopic Signatures of Electronic Excitations in Raman Scattering in Thin Films of Rhombohedral Graphite

Rhombohedral graphite features peculiar electronic properties, including persistence of low-energy surface bands of a topological nature. Here, we study the contribution of electron-hole excitations towards inelastic light scattering in thin films of rhombohedral graphite. We show that, in contrast to the featureless electron-hole contribution towards Raman spectrum of graphitic films with Bernal stacking, the inelastic light scattering accompanied by electron-hole excitations in crystals with rhombohedral stacking produces distinct features in the Raman signal which can be used both to identify the stacking and to determine the number of layers in the film.Comment: 15 pages in preprint format, 4 figures, accepted versio

Spectral features due to inter-Landau-level transitions in the Raman spectrum of bilayer graphene

We investigate the contribution of the low-energy electronic excitations towards the Raman spectrum of bilayer graphene for the incoming photon energy Omega >> 1eV. Starting with the four-band tight-binding model, we derive an effective scattering amplitude that can be incorporated into the commonly used two-band approximation. Due to the influence of the high-energy bands, this effective scattering amplitude is different from the contact interaction amplitude obtained within the two-band model alone. We then calculate the spectral density of the inelastic light scattering accompanied by the excitation of electron-hole pairs in bilayer graphene. In the absence of a magnetic field, due to the parabolic dispersion of the low-energy bands in a bilayer crystal, this contribution is constant and in doped structures has a threshold at twice the Fermi energy. In an external magnetic field, the dominant Raman-active modes are the n_{-} to n_{+} inter-Landau-level transitions with crossed polarisation of in/out photons. We estimate the quantum efficiency of a single n_{-} to n_{+} transition in the magnetic field of 10T as I_{n_{-} to n_{+}}~10^{-12}.Comment: 7 pages, 3 figures, expanded version published in PR

Electronic Raman Scattering in Twistronic Few-Layer Graphene

We study electronic contribution to the Raman scattering signals of two-, three- and four-layer graphene with layers at one of the interfaces twisted by a small angle with respect to each other. We find that the Raman spectra of these systems feature two peaks produced by van Hove singularities in moir\'{e} minibands of twistronic graphene, one related to direct hybridization of Dirac states, and the other resulting from band folding caused by moir\'{e} superlattice. The positions of both peaks strongly depend on the twist angle, so that their detection can be used for non-invasive characterization of the twist, even in hBN-encapsulated structures.Comment: 7 pages (including 4 figures) + 10 pages (3 figures) supplemen

Anomalous sequence of quantum Hall liquids revealing tunable Lifshitz transition in bilayer graphene

Fermi surface topology plays an important role in determining the electronic properties of metals. In bulk metals, the Fermi energy is not easily tunable at the energy scale needed for reaching conditions for the Lifshitz transition - a singular point in the band structure where the connectivity of the Fermi surface changes. Bilayer graphene is a unique system where both Fermi energy and the low-energy electron dispersion can be tuned using the interplay between trigonal warping and a band gap opened by a transverse electric field. Here, we drive the Lifshitz transition to experimentally controllable carrier densities by applying large transverse electric fields through a h-BN-encapsulated bilayer graphene structure, and detect it by measuring the degeneracies of Landau levels. These degeneracies are revealed by filling factor -3 and -6 quantum Hall effect states of holes at low magnetic fields reflecting the existence of three maxima on the top of the valence band dispersion. At high magnetic fields all integer quantum Hall states are observed, indicating that deeper in the valence band the constant energy contours are singly-connected. The fact that we observe ferromagnetic quantum Hall states at odd-integer filling factors testifies to the high quality of our sample, and this enables us to identify several phase transitions between correlated quantum Hall states at intermediate magnetic fields, in agreement with the calculated evolution of the Landau level spectrum.Comment: 5 pages, 3 figure

Moiré miniband features in the angle-resolved photoemission spectra of graphene/hBN heterostructures

We identify features in the angle-resolved photoemission spectra (ARPES) arising from the periodic pattern characteristic for graphene heterostructure with hexagonal boron nitride (h BN). For this, we model ARPES spectra and intensity maps for five microscopic models used previously to describe moire superlattice in graphene/h BN systems. We show that detailed analysis of these features can be used to pin down the microscopic mechanismof the interaction between graphene and h BN. We also analyze how the presence of a moire-periodic strain in graphene or scattering of photoemitted electrons off h BN can be distinguished from the miniband formation

Directional approach to spatial structure of solutions to the Navier-Stokes equations in the plane

We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity $u_\infty$ at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of $u_\infty$. Furthermore a spacial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the directino of the flow as \emph{time} direction. The analysis is done in framework of the Fourier transform taken in one (perpendicular) direction and a special choice of function spaces which take into account the inhomogeneous character of the symbol of the Oseen system. From that point of view our technique can be used as an effective tool in examining spatial asymptotics of solutions to other systems modeled by elliptic equations