Abstract: We address the nature of the disordered state that results from the adsorption of adatoms in graphene. For adatoms that sit at the center of the honeycomb plaquette, as in the case of most transition metals, we show that the ones that form a zero-energy resonant state lead to Anderson localization in the vicinity of the Dirac point. Among those, we show that there is a symmetry class of adatoms where Anderson localization is suppressed, leading to an exotic metallic state with large and rare charge droplets, that localizes only at the Dirac point. We identify the experimental conditions for the observation of the Anderson transition for adatoms in graphene.

Abstract: The electronic properties of a triaxially strained hexagonal graphene flake with either armchair or zigzag edges are investigated using molecular dynamics simulations and tight-binding calculations. We found that (i) the pseudomagnetic field in strained graphene flakes is not uniform neither in the center nor at the edge of zigzag terminated flakes, (ii) the pseudomagnetic field is almost zero in the center of armchair terminated flakes but increases dramatically near the edges, (iii) the pseudomagnetic field increases linearly with strain, for strains lower than 15% but increases nonlinearly beyond it, (iv) the local density of states in the center of the zigzag hexagon exhibits pseudo-Landau levels with broken sublattice symmetry in the zeroth pseudo-Landau level, and in addition there is a shift in the Dirac cone due to strain induced scalar potentials, and (v) there is size effect in pseudomagnetic field. This study provides a realistic model of the electronic properties of inhomogeneously strained graphene where the relaxation of the atomic positions is correctly included together with strain induced modifications of the hopping terms up to next-nearest neighbors.

Abstract: We utilize an exact variational numerical procedure to calculate the ground-state properties of a polaron in the presence of Rashba and linear Dresselhaus spin-orbit coupling. We find that when the linear Dresselhaus spin-orbit coupling approaches the Rashba spin-orbit coupling, the Van Hove singularity in the density of states will be shifted away from the bottom of the band and finally disappear when the two spin-orbit couplings are tuned to be equal. The effective mass will be suppressed; the trend will become more significant for low phonon frequency. The presence of two dominant spin-orbit couplings will make it possible to tune the effective mass with more varied observables.

Abstract: We numerically investigate the spin-orbit (SO) coupling effect on the magnetic flux evolution of energy and supercurrent in mesoscopic d-wave superconducting loops by solving the spin-generalized Bogoliubov-de Gennes equations self-consistently. It is found that the energy spectrum splits when the SO interaction is involved and the Majorana zero mode can be realized in the [100] edges of square systems for an appropriate SO coupling strength. Superconducting phase transitions appear when the energy gap closes, accompanied by energy jumps between different energy parabolas in the ground state, which provides a possible mechanism to support fractional flux periodicity of supercurrent. Moreover, in the case of rectangular loops with SO coupling, the jumps of the ground-state energy gradually disappear by increasing the ratio of length to height of the sample, and a paramagnetic response with opposite direction of the screening current around zero flux value can occur in such systems.

Abstract: Recent scanning tunneling microscopy (STM) measurements of the proximity effect in Au/La2−xSrxCuO4 and La1.55Sr0.45CuO4/La2−xSrxCuO4 bilayers showed a proximity-induced pseudogap [O. Yuli, I. Asulin, Y. Kalcheim, G. Koren, and O. Millo, Phys. Rev. Lett. 103, 197003 (2009)]. We describe the proximity effect in mesoscopic superconductor/normal-metal bilayers by using the Bogoliubov-de Gennes equations for a tight-binding Hamiltonian with competing antiferromagnetic and d-wave superconductivity orders. The temperature-dependent local density of states is calculated as a function of the distance from the interface. Bound state due to both d-wave and spin-density wave gaps are formed in the normal metal for energies less than the respective gaps. If there is a mismatch between the Fermi velocities in the two layers we observe that these states will shift in energy when spin-density wave order is present, thus inducing a minigap at finite energy. We conclude that the STM measurement in the proximity structures is able to distinguish between the two scenarios proposed for the pseudogap (competing or precursor to superconductivity).

Abstract: The interplay between quantum Hall states and Cooper pairs is usually hindered by the suppression of the superconducting state due to the strong magnetic fields needed to observe the quantum Hall effect. From this point of view, graphene is special since it allows the creation of strong pseudomagnetic fields due to strain. We show that in a Josephson junction made of strained graphene, Cooper pairs will diffuse into the strained region. The pair correlation function will be sublattice polarized due to the polarization of the local density of states in the zero pseudo-Landau level. We uncover two regimes: (1) one in which the cyclotron radius is larger than the junction length, in which case the supercurrent will be enhanced, and (2) the long junction regime where the supercurrent is strongly suppressed because the junction becomes an insulator. In the latter case quantized Hall states form and Andreev scattering at the normal/superconducting interface will induce edge states. Our numerical calculation has become possible due to an extension of the Chebyshev-Bogoliubovde Gennes method to computations on video cards (GPUs).

Abstract: Using highly efficient simulations of the tight-binding Bogoliubov-de-Gennes model, we solved self-consistently for the pair correlation and the Josephson current in a superconducting-bilayer graphene-superconducting Josephson junction. Different doping levels for the non-superconducting link are considered in the short- and long-junction regimes. Self-consistent results for the pair correlation and superconducting current resemble those reported previously for single-layer graphene except at the Dirac point, where remarkable differences in the proximity effect are found, as well as a suppression of the superconducting current in the long-junction regime. Inversion symmetry is broken by considering a potential difference between the layers and we found that the supercurrent can be switched if the junction length is larger than the Fermi length.

Abstract: The time evolution of a wave packet in strained graphene is studied within the tight-binding model and continuum model. The effect of an external magnetic field, as well as a strain-induced pseudomagnetic field, on the wave-packet trajectories and zitterbewegung are analyzed. Combining the effects of strain with those of an external magnetic field produces an effective magnetic field which is large in one of the Dirac cones, but can be practically zero in the other. We construct an efficient valley filter, where for a propagating incoming wave packet consisting of momenta around the K and K' Dirac points, the outgoing wave packet exhibits momenta in only one of these Dirac points while the components of the packet that belong to the other Dirac point are reflected due to the Lorentz force. We also found that the zitterbewegung is permanent in time in the presence of either external or strain-induced magnetic fields, but when both the external and strain-induced magnetic fields are present, the zitterbewegung is transient in one of the Dirac cones, whereas in the other cone the wave packet exhibits permanent spatial oscillations.

Abstract: The mechanical and electronic properties of a graphene membrane placed on top of a triangular superlattice of nanopillars are investigated. We use molecular dynamics simulations to access the deformation fields and the tight-binding approaches to calculate the electronic properties. Ripples form in the graphene layer that span across the unit cell, connecting neighboring pillars, in agreement with recent experiments. We find that the resulting pseudo-magnetic field (PMF) varies strongly across the unit cell. We investigate the dependence of PMF on unit cell boundary conditions, height of the pillars, and the strength of the van der Waals interaction between graphene and the substrate. We find direct correspondence with typical experiments on pillars, showing intrinsic “slack” in the graphene membrane. PMF values are confirmed by the local density of states calculations performed at different positions of the unit cell showing pseudo-Landau levels with varying spacings. Our findings regarding the relaxed membrane configuration and the induced strains are transferable to other flexible 2D membranes.

Abstract: Two-dimensional atomic crystals can radically change their properties in response to external influences, such as substrate orientation or strain, forming materials with novel electronic structure(1-5). An example is the creation of weakly dispersive, 'flat' bands in bilayer graphene for certain 'magic' angles of twist between the orientations of the two layers(6). The quenched kinetic energy in these flat bands promotes electron-electron interactions and facilitates the emergence of strongly correlated phases, such as superconductivity and correlated insulators. However, the very accurate fine-tuning required to obtain the magic angle in twisted-bilayer graphene poses challenges to fabrication and scalability. Here we present an alternative route to creating flat bands that does not involve fine-tuning. Using scanning tunnelling microscopy and spectroscopy, together with numerical simulations, we demonstrate that graphene monolayers placed on an atomically flat substrate can be forced to undergo a buckling transition(7-9), resulting in a periodically modulated pseudo-magnetic field(10-14), which in turn creates a 'post-graphene' material with flat electronic bands. When we introduce the Fermi level into these flat bands using electrostatic doping, we observe a pseudogap-like depletion in the density of states, which signals the emergence of a correlated state(15-17). This buckling of two-dimensional crystals offers a strategy for creating other superlattice systems and, in particular, for exploring interaction phenomena characteristic of flat bands. Buckled monolayer graphene superlattices are found to provide an alternative to twisted bilayer graphene for the study of flat bands and correlated states in a carbon-based material.

Abstract: We perform the wavepacket dynamics simulation of a graphene-based device where propagating electron trajectories are tamed by an applied magnetic field toward a normal/superconductor interface. The magnetic field controls the incidence angle of the incoming electronic wavepacket at the interface, which results in the tunable electron-hole ratio in the reflected wave function due to the angular dependence of the Andreev reflection. Here, mapped control of the quasiparticle trajectories by the external magnetic field not only defines an experimental probe for fundamental studies of the Andreev reflection in graphene but also lays the foundation for further development of magnetic focusing devices based on nanoengineered superconducting two-dimensional materials.

Abstract: The flexoelectric and electronic properties of zig-zag graphene nanoribbons are explored under mechanical bending using state of the art first principles calculations. A linear dependence of the bending induced out of plane polarization on the applied strain gradient is found. The inferior flexoelectric properties of graphene nanoribbons can be improved by more than two orders of magnitude by hydrogen and fluorine functionalization (CH and CF nanoribbons). A large out of plane flexoelectric effect is predicted for CF nanoribbons. The origin of this enhancement lies in the electro-negativity difference between carbon and fluorine atoms, which breaks the out of plane charge symmetry even for a small strain gradient. The flexoelectric effect can be further improved by co-functionalization with hydrogen and fluorine (CHF Janus-type nanoribbon), where a spontaneous out of plane dipole moment is formed even for flat nanoribbons. We also find that bending can control the charge localization of valence band maxima and therefore enables the tuning of the hole effective masses and band gaps. These results present an important advance towards the understanding of flexoelectric and electronic properties of hydrogen and fluorine functionalized graphene nanoribbons, which can have important implications for flexible electronic applications. (C) 2020 Elsevier Ltd. All rights reserved.

Abstract: The moire pattern observed in stacked noncommensurate crystal lattices, such as heterobilayers of transition metal dichalcogenides, produces a periodic modulation of their band gap. Excitons subjected to this potential landscape exhibit a band structure that gives rise to a quasiparticle dubbed the moire exciton. In the case of MoS2/WSe2 heterobilayers, the moire trapping potential has honeycomb symmetry and, consequently, the moire exciton band structure is the same as that of a Dirac-Weyl fermion, whose mass can be further tuned down to zero with a perpendicularly applied field. Here we show that, analogously to other Dirac-like particles, the moire exciton exhibits a trembling motion, also known as Zitterbewegung, whose long timescales are compatible with current experimental techniques for exciton dynamics. This promotes the study of the dynamics of moire excitons in van der Waals heterostructures as an advantageous solid-state platform to probe Zitterbewegung, broadly tunable by gating and interlayer twist angle.

Abstract: When using hexagonal boron-nitride (hBN) as a substrate for graphene, the resulting moire pattern creates secondary Dirac points. By encapsulating a multilayer graphene within aligned hBN sheets the controlled moire stacking may offer even richer benefits. Using advanced tight-binding simulations on atomistically-relaxed heterostructures, here we show that the gap at the secondary Dirac point can be opened in selected moire-stacking configurations, and is independent of any additional vertical gating of the heterostructure. On the other hand, gating can broadly tune the gap at the principal Dirac point, and may thereby strongly compress the first moire mini-band in width against the moire-induced gap at the secondary Dirac point. We reveal that in hBN-encapsulated bilayer graphene this novel mechanism can lead to isolated bands flatter than 10 meV under moderate gating, hence presenting a convenient pathway towards electronically-controlled strongly-correlated states on demand.

Abstract: A wave-packet time evolution method, based on the split-operator technique, is developed to investigate the scattering of quasiparticles at a normal-superconductor interface of arbitrary profile and shape. As a practical application, we consider a system where low-energy electrons can be described as Dirac particles, which is the case for most two-dimensional materials, such as graphene and transition-metal dichalcogenides. However, the method is easily adapted for other cases such as electrons in few-layer black phosphorus or any Schrodinger quasiparticles within the effective mass approximation in semiconductors. We employ the method to revisit Andreev reflection in mono-, bi-, and trilayer graphene, where specular-and retro-reflection cases are observed for electrons scattered by a steplike superconducting region. The effect of opening a zero-gap channel across the superconducting region on the electron and hole scattering is also addressed, as an example of the versatility of the technique proposed here.