Valley engineering by strain in Kekulé-distorted graphene

Physica E: Low-dimensional Systems and Nanostructures, 2010

We study the effect of uniaxial strain on the electronic band structure of gapped graphene. We consider two types of gapped graphene, one which breaks the symmetry between the two triangular sublattices (staggered model), and another which alternates the bonds on the honeycomb lattice (Kekulé model). In the staggered model, the effect of strains below a critical value is only a shift of the band gap location. In the Kekulé model, as strain is increased, band gap location is initially pinned to a corner of the Brillouin zone while its width diminishes, and after gap closure the location of the contact point begins to shift. Analytic and numerical results are obtained for both the tight-binding and Dirac fermion descriptions of gapped graphene.

2013

The behavior of electrons in strained graphene is usually described using effective pseudomagnetic fields in a Dirac equation. Here we consider the particular case of a spatially constant strain. Our results indicate that lattice corrections are easily understood using a strained reciprocal space, in which the whole energy dispersion is simply shifted and deformed. This leads to a directional dependent Fermi velocity without producing pseudomagnetic fields. The corrections due to atomic wavefunction overlap changes tend to compensate such effects. Also, the analytical expressions for the shift of the Dirac points as well as the corresponding Dirac equation are found. In view of the former results, we discuss the range of applicability of the usual approach of considering pseudomagnetic fields in a Dirac equation derived from the old Dirac points of the unstrained lattice. Such considerations are important if a comparison is desired with experiments or numerical simulations.

Phys. Rev. B, 2019

Graphene's electronic structure can be fundamentally altered when a substrate- or adatom-induced Kekulé superlattice couples the valley and isospin degrees of freedom. Here, we show that the band structure of Kekulé-textured graphene can be re-engineered through layer stacking. We predict a family of Kekulé graphene bilayers that exhibit band structures with up to six valleys, and room-temperature Dirac quasiparticles whose masses can be tuned electrostatically. Fermi velocities half as large as in pristine graphene put this system in the strongly coupled regime, where correlated ground states can be expected.

Physical Review B, 2009

We present an in-depth analysis of the electronic and vibrational band structure of uniaxially strained graphene by ab-initio calculations. Depending on the direction and amount of strain, the Fermi crossing moves away from the K-point. However, graphene remains semimetallic under small strains. The deformation of the Dirac cone near the K-point gives rise to a broadening of the 2D Raman mode. In spite of specific changes in the electronic and vibrational band structure the strain-induced frequency shifts of the Raman active E2g and 2D modes are independent of the direction of strain. Thus, the amount of strain can be directly determined from a single Raman measurement.

Physical Review B

One of the unique properties of graphene is its extremely high mechanical strength. Several studies have shown that the mechanical failure of graphene sheet under a tensile strain is due to the enhancement of the Kohn anomaly of the zone boundary transverse optical phonon modes. In this work, we derive an analytical expression of the Kohn anomaly parameter α K of these phonons in graphene deformed by a uniaxial strain along the armchair direction. We show that, the tilt of Dirac cones, induced by the strain, contributes to the enhancement of the Kohn anomaly under a tensile deformation and gives rise to a dominant contribution of the so-called outer intervalley mediated phonon processes. Moreover, the Kohn anomaly is found to be anisotropic with respect to the phonon wave vectors around the K point. This anisotropy may be at the origin of the light polarization dependence of the Raman 2D band of the strained graphene. Our results uncover, not only, the role of the Kohn anomaly in the anisotropic mechanical failure of the graphene sheet, under strains applied along the armchair and zigzag directions, but shed also light on the doping induced strengthening of strained graphene.

Physical Review Letters

Mechanical deformations of graphene induce a term in the Dirac Hamiltonian which is reminiscent of an electromagnetic vector potential. Strain gradients along particular lattice directions induce local pseudomagnetic fields and substantial energy gaps as indeed observed experimentally. Expanding this analogy, we propose to complement the pseudomagnetic field by a pseudoelectric field, generated by a time dependent oscillating stress applied to a graphene ribbon. The joint Hall-like response to these crossed fields results in a strain-induced charge current along the ribbon. We analyze in detail a particular experimental implementation in the (pseudo) quantum Hall regime with weak intervalley scattering. This allows us to predict an (approximately) quantized Hall current which is unaffected by screening due to diffusion currents.

Physical Review B, 2009

We analyze the effect of tensional strain in the electronic structure of graphene. In the absence of electron-electron interactions, within linear elasticity theory, and a tight-binding approach, we observe that strain can generate a bulk spectral gap. However this gap is critical, requiring threshold deformations in excess of 20%, and only along preferred directions with respect to the underlying lattice. The gapless Dirac spectrum is robust for small and moderate deformations, and the gap appears as a consequence of the merging of the two inequivalent Dirac points, only under considerable deformations of the lattice. We discuss how strain-induced anisotropy and local deformations can be used as a means to affect transport characteristics and pinch off current flow in graphene devices.

Physical Review B, 2015

Theory predicts that graphene under uniaxial compressive strain in an armchair direction should undergo a topological phase transition from a semimetal into an insulator. Due to the change of the hopping integrals under compression, both Dirac points shift away from the corners of the Brillouin zone towards each other. For sufficiently large strain, the Dirac points merge and an energy gap appears. However, such a topological phase transition has not yet been observed in normal graphene (due to its large stiffness) neither in any other electronic system. We show numerically and analytically that such a merging of the Dirac points can be observed in electronic artificial graphene created from a two-dimensional electron gas by application of a triangular lattice of repulsive antidots. Here, the effect of strain is modeled by tuning the distance between the repulsive potentials along the armchair direction. Our results show that the merging of the Dirac points should be observable in a recent experiment with molecular graphene.

Physical Review B

The effect of Rashba spin-orbit interaction and anisotropic elastic strain on the electronic, optical and thermodynamic properties of artificial graphene-like superlattice composed of InAs/GaAs quantum dots has been considered theoretically. The electronic energy dispersions have been obtained using Green's function formalism in combination with the Fourier transformation to the reciprocal space and an exact diagonalization technique. We have observed a splitting of Dirac points and appearance of additional Dirac-like points due to the Rashba spin-orbit interaction. Breaking of the hexagonal symmetry of the dispersion surfaces caused by the strain anisotropy is observed as well. It is shown that both the spin-orbit interaction and strain anisotropy have a qualitative impact on the measurable characteristics of the considered structure and can be used as effective tools to control the performance of devices based on artificial graphene.

Physical Review B, 2011

Energy gap in graphene is crucial for many applications, especially computing devices. Its realization is a challenging problem due to the transformation of electrons into holes i.e. Klein tunneling. In this letter, we show that when the pseudomagnetic fields created by long wavelength deformations is appropriately coupled with a scalar electric potential, a significant energy gap can emerge. Of particular technological importance, this gap is tunable through electrostatic gates, allowing for the design of electronic devices not realizable with other materials. Ramifications of this effect are examined through the study of various strain geometries commonly seen in experiments.