Abstract: Using the continuum model, we investigate the electronic properties of two types of bilayer graphene (BLG) quantum ring (QR) geometries: (i) An isolated BLG QR and (ii) a monolayer graphene (MLG) with a QR put on top of an infinite graphene sheet (hybrid BLG QR). Solving the Dirac-Weyl equation in the presence of a perpendicular magnetic field and applying the infinite mass boundary condition at the ring boundaries, we obtain analytical results for the energy levels and corresponding wave spinors for both structures. In the case of isolated BLG QR, we observe a sizable and magnetically tunable band gap which agrees with the tight-binding transport simulations. Our analytical results also show the intervalley symmetry EeK (m) = ???EK??? h (m) between the electron (e) and the hole (h) states (m is the angular momentum quantum number) for the energy spectrum of the isolated BLG QR. The presence of interface boundary in a hybrid BLG QR modifies drastically the energy levels as compared with that of an isolated BLG QR. Its energy levels are tunable from MLG dot to isolated BLG QR and to MLG Landau energy levels as the magnetic field is varied. Our predictions can be verified experimentally using different techniques such as by magnetotransport measurements.

Abstract: Using the tight-binding approach coupled with mean-field Hubbard model, we theoretically study the effect of mechanical deformations on the magnetic properties of bilayer graphene (BLG) quantum dots (QDs). Results are obtained for AA-and AB(Bernal)-stacked BLG QDs, considering different geometries (hexagonal, triangular and square shapes) and edge types (armchair and zigzag edges). In the absence of strain, our results show that (i) the magnetization is affected by taking different dot sizes only for hexagonal BLG QDs with zigzag edges, exhibiting different critical Hubbard interactions, and (ii) the magnetization does not depend on the interlayer hopping energies, except for the geometries with zigzag edges and AA stacking. In the presence of in-plane and uniaxial strain, for all geometries we obtain two different magnetization regimes depending on the applied strain amplitude. The appearance of such different regimes is due to the breaking of layer and sublattice symmetries in BLG QDs.

Abstract: By performing density functional theory-based ab initio calculations, Raman-active phonon modes of single-layer two-dimensional (2D) materials and the effect of in-plane biaxial strain on the peak frequencies and corresponding activities of the Raman-active modes are calculated. Our findings confirm the Raman spectrum of the unstrained 2D crystals and provide expected variations in the Raman-active modes of the crystals under in-plane biaxial strain. The results are summarized as follows: (i) frequencies of the phonon modes soften (harden) under applied tensile (compressive) strains; (ii) the response of the Raman activities to applied strain for the in-plane and out-of-plane vibrational modes have opposite trends, thus, the built-in strains in the materials can be monitored by tracking the relative activities of those modes; (iii) in particular, the A peak in single-layer Si and Ge disappears under a critical tensile strain; (iv) especially in mono-and diatomic single layers, the shift of the peak frequencies is a stronger indication of the strain rather than the change in Raman activities; (v) Raman-active modes of single-layer ReX2 (X = S, Se) are almost irresponsive to the applied strain. Strain-induced modifications in the Raman spectrum of 2D materials in terms of the peak positions and the relative Raman activities of the modes could be a convenient tool for characterization.

Abstract: We investigate scattering of the topological surface state of a three-dimensional time-reversal invariant topological insulator when graphene is deposited on the topological-insulator surface. Specifically, we consider the (111) surface of a Bi2Se3-like topological insulator. We present a low-energy model for the graphene-topological insulator heterostructure and we calculate the transmission probability at zigzag and armchair edges of the deposited graphene, and the conductance through graphene nanoribbon barriers, and show that its features can be understood from antiresonances in the transmission probability.

Abstract: A strong in-plane magnetic field drastically alters the low-energy spectrum of bilayer graphene by separating the parabolic energy dispersion into two linear Dirac cones. The effect of this dramatic change on the transport properties strongly depends on the orientation of the in-plane magnetic field with respect to the propagation direction of the charge carriers and the angle at which they impinge on the electrostatic potentials. For magnetic fields oriented parallel to the potential boundaries an additional propagating mode that results from the splitting into Dirac cones enhances the transmission probability for charge carriers tunneling through the potentials and increases the corresponding conductance. Our results show that the chiral suppression of transmission at normal incidence, reminiscent of bilayer graphene's 2 pi Berry phase, is turned into a chiral enhancement when the magnetic field increases, thus indicating a transition from a bilayer to a monolayer-like system at normal incidence. Further, we find that the typical transmission resonances stemming from confinement in a potential barrier are shifted to higher energy and are eventually transformed into antiresonances with increasing magnetic field. For magnetic fields oriented perpendicular to the potential boundaries we find a very pronounced transition from a bilayer system to two separated monolayer-like systems with Klein tunneling emerging at certain incident angles symmetric around 0, which also leaves a signature in the conductance. For both orientations of the magnetic field, the transmission probability is still correctly described by pseudospin conservation. Finally, to motivate the large in-plane magnetic field, we show that its energy spectrum can be mimicked by specific lattice deformations such as a relative shift of one of the layers. With this equivalence we introduce the notion of an in-plane pseudomagnetic field.

Abstract: An effective tight-binding (TB) Hamiltonian for monolayer GeSnH2 is constructed which has an inversion-asymmetric honeycomb structure. The low-energy band structure of our TB model agrees very well with previous ab initio calculations even under biaxial tensile strain. Our model predicts a phase transition at 7.5% biaxial tensile strain in agreement with DFT calculations. Upon 8.5% strain the system exhibits a band gap of 134 meV, suitable for room temperature applications. It is shown that an external applied magnetic field produces a special phase which is a combination of the quantum Hall (QH) and quantum spin Hall (QSH) phases; and at a critical magnetic field strength the QSH phase completely disappears. The topological nature of the phase transition is confirmed from: (1) the calculation of the Z(2) topological invariant, and (2) quantum transport properties of disordered GeSnH2 nanoribbons which allows us to determine the universality class of the conductance fluctuations. The application of an external applied magnetic field reduces the conductance fluctuations by a factor of root 2.

Abstract: Fabry-Pérot resonances in the transmission through single and double, graphene-based barriers (of height V) and wells are investigated and their dependence on an applied perpendicular magnetic field. For rectangular barriers the conductance decreases with increasing magnetic field while the resonances weaken (become more pronounced) with increasing magnetic field for EF<V (EF>V). The position of the resonances exhibit a linear shift with magnetic field which move to lower (higher) energy for EF<V (EF>V). Compared to semielliptic- or Gaussian-shaped barriers they show a smaller number of resonances in the absence of a magnetic field and an overall lower conductance but the resonant structure is more pronounced. The conductance of asymmetric double barriers show two major regions of resonances while the symmetric ones show one, that of three asymmetric barriers three, and so on.

Abstract: Topological insulators are attracting considerable interest due to their potential for technological applications and as platforms for exploring wide-ranging fundamental science questions. In order to exploit, fine-tune, control, and manipulate the topological surface states, spectroscopic tools which can effectively probe their properties are of key importance. Here, we demonstrate that positrons provide a sensitive probe for topological states and that the associated annihilation spectrum provides a technique for characterizing these states. Firm experimental evidence for the existence of a positron surface state near Bi2Te2Se with a binding energy of E-b = 2.7 +/- 0.2 eV is presented and is confirmed by first-principles calculations. Additionally, the simulations predict a significant signal originating from annihilation with the topological surface states and show the feasibility to detect their spin texture through the use of spin-polarized positron beams.

Abstract: We investigate the effect of Rashba and intrinsic spin-orbit couplings on the electronic properties and spin configurations of Dirac fermions confined in: (i) a flat graphene sheet, (ii) a graphene wire with p-n-p structure, and (iii) a superlattice of graphene wires. The interplay between the spin-orbit interaction mechanisms breaks the electron-hole symmetry and the spin configuration induced by Rashba spin-orbit coupling lacks inversion symmetry in k space. We show that the Rashba spin-orbit interaction doubles the Fabry-Perot resonant modes in the transmission spectrum of a graphene wire and opens new channels for the electron transmission. Moreover, it leads to the appearance of spin split extra Dirac cones in the energy spectrum of a graphene superlattice. It is shown that the spin of the electrons and holes confined in a flat graphene sheet is always perpendicular to their motion while this is not the case for the other nanostructures.

Abstract: The spectrum of a Coulomb impurity in bilayer graphene is investigated as function of the strength of a perpendicular magnetic field for different values of the angular quantum number m and for different values of the gate voltage. We point out fundamental differences between the results from the two-band and four-band model. The supercritical instability and fall-to-center phenomena are investigated in the presence of a magnetic field. We find that in the four-band model the fall-to-center phenomenon occurs as in monolayer graphene, while this is not the case in the two-band model. We find that in a magnetic field the supercritical instability manifests itself as a series of anticrossings in the hole part of the spectrum for states coming from the low-energy band. However, we also find very distinct anticrossings in the electron part of the spectrum that continue into the hole part, which are related to the higher energy band of the four-band model. At these anticrossings, we find a very sharp peak in the probability density close to the impurity, reminiscent for the fall-to-center phenomenon. In this paper, these peculiar and interesting effects are studied for different magnetic field, interlayer coupling, and bias potential strengths.

Abstract: A unified theory of phonon dispersions and piezoelectricity in bulk and multilayers of hexagonal boron nitride (h-BN) is derived. The dynamical matrix is calculated on the basis of an empirical force constant model of intralayer valence and interlayer van der Waals interactions. Coulomb interactions are calculated by Ewalds method, adapted for the three-dimensional (3D) and the multilayer case. The deformation of the ionic charge distribution with long-wave lattice displacements is taken into account. Special attention is devoted to the nonanalytic long-range Coulomb contribution to the dynamical matrix which is different for the 3D crystal and the multilayer case. Consequently there is a splitting of the transverse optical (TO) and longitudinal optical (LO) phonon branches of E1u symmetry and a discontinuity of the A2u branch at the Γ point in 3D h-BN. No such splitting and discontinuity at Γ are present in multilayer crystals with a finite number N of layers. There a diverging bundle of N overbending optical phonon branches emerges from Γ. Borns long-wave theory is applied and extended for the study of piezoelectricity in layered crystals. While 3D h-BN and h-BN multilayers with an even number of layers (symmetry D6h) are not piezoelectric, multilayers with an uneven number of Nu layers (symmetry D3h) are piezoelectric; the piezoelectric coefficient e1,11 is inversely proportional to Nu.

Abstract: Trions and biexcitons in anisotropic two-dimensional materials are investigated within an effective mass theory. Explicit results are obtained for phosphorene and arsenene, materials that share features such as a direct quasiparticle gap and anisotropic conduction and valence bands. Trions are predicted to have remarkably high binding energies and an elongated electron-hole structure with a preference for alignment along the armchair direction, where the effective masses are lower. We find that biexciton binding energies are also notably large, especially for monolayer phosphorene, where they are found to be twice as large as those for typical monolayer transition metal dichalcogenides.