Abstract: Using the four-band continuum model we derive a general expression for the infinite-mass boundary condition in bilayer graphene. Applying this new boundary condition we analytically calculate the confined states and the corresponding wave functions in a bilayer graphene quantum dot in the absence and presence of a perpendicular magnetic field. Our results for the energy spectrum show an energy gap between the electron and hole states at small magnetic fields. Furthermore the electron (e) and hole (h) energy levels corresponding to the K and K' valleys exhibit the E-K(e(h)) (m) = E-K'(e(h)) (m) symmetry, where m is the angular momentum quantum number. (C) 2014 Elsevier Ltd. All rights reserved.

Abstract: We investigate the energy levels and optical properties of a circular graphene quantum dot in the presence of an external magnetic field perpendicular to the dot. Based on the Dirac-Weyl equation and assuming zero outward current at the edge of the dot we present the results for two different types of boundary conditions, i.e. infinite-mass (IMBC) and zigzag boundary conditions. We found that the dot with zigzag edges displays a zero-energy state in the energy spectra while this is not the case for the IMBCs. For both boundary conditions, the confinement becomes dominated by the magnetic field, where the energy levels converge to the Landau levels as the magnetic field increases. The effect of boundary conditions on the electron-and hole-energy states is found to affect the interband absorption spectra, where we found larger absorption in the case of IMBCs. The selection rules for interband optical transitions are determined and discussed for both boundary conditions.

Abstract: We investigate the effect of an external magnetic field on the carrier states that are localized at a potential kink and a kink-antikink in bilayer graphene. These chiral states are localized at the interface between two potential regions with opposite signs.

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: Recently it was found that bilayer graphene may exhibit regions with and without van der Waals coupling between the two layers. We show that such structures can exhibit a strong layer selectivity when current flows through the coupled region and that this selectivity can be tuned by means of electrostatic gating. Analysing how this effect depends on the type of bilayer stacking, the potential on the gates and the smoothness of the boundary between the coupled and decoupled regions, we show that nearly perfect layer selectivity is achievable in these systems. This effect can be further used to realise a tunable layer switch.

Abstract: We propose a new system where electron and hole states are electrostatically confined into a quantum ring in bilayer graphene. These structures can be created by tuning the gap of the graphene bilayer using nanostructured gates or by position-dependent doping. The energy levels have a magnetic field (B0) dependence that is strikingly distinct from that of usual semiconductor quantum rings. In particular, the eigenvalues are not invariant under a B0 ¨ −B0 transformation and, for a fixed total angular momentum index m, their field dependence is not parabolic, but displays two minima separated by a saddle point. The spectra also display several anticrossings, which arise due to the overlap of gate-confined and magnetically confined states.

Abstract: In the Comment, the authors state that the separation of the relative and center of mass variables in our work is not correct. Here we point out that there is a typographical error, i.e., qi instead of -e, in two of our equations which, when corrected, makes the Comment redundant. Within the ansatzes mentioned in our paper all our results are correct, in contrast to the claims of the Comment.

Abstract: Electrically gating of trilayer graphene (TLG) opens a band gap offering the possibility to electrically engineer TLG quantum dots. We study the energy levels of such quantum dots and investigate their dependence on a perpendicular magnetic field B and different types of stacking of the graphene layers. The dots are modeled as circular and confined by a truncated parabolic potential which can be realized by nanostructured gates or position-dependent doping. The energy spectra exhibit the intervalley symmetry E-K(e) (m) = -E (h)(K') (m) for the electron (e) and hole (h) states, where m is the angular momentum quantum number and K and K' label the two valleys. The electron and hole spectra for B = 0 are twofold degenerate due to the intervalley symmetry E-K (m) = E-K' [-(m + 1)]. For both ABC [alpha = 1.5 (1.2) for large (small) R] and ABA (alpha = 1) stackings, the lowest-energy levels show approximately a R-alpha dependence on the dot radius R in contrast with the 1/R-3 one for ABC-stacked dots with infinite-mass boundary. As functions of the field B, the oscillator strengths for dipole-allowed transitions differ drastically for the two types of stackings.

Abstract: The influence of a perpendicular magnetic field on the binding energy and structural properties of excitons, trions, and biexcitons in monolayers of semiconducting transition metal dichalcogenides (TMDs) is investigated. The stochastic variational method (SVM) with a correlated Gaussian basis is used to calculate the different properties of these few-particle systems. In addition, we present a simplified variational approach which supports the SVM results for excitons as a function of magnetic field. The exciton diamagnetic shift is compared with recent experimental results, and we extend this concept to trions and biexcitons. The effect of a local potential fluctuation, which we model by a circular potential well, on the binding energy of trions and biexcitons is investigated and found to significantly increase the binding of those excitonic complexes.

Abstract: In a recent paper [Phys. Rev. B 89, 155403 (2014)], the authors investigated the spectrum of a Coulomb impurity in graphene in the presence of magnetic and electric fields using the coupled series expansion approach. In the first part of their paper, they investigated how Coulomb impurity states collapse in the presence of a perpendicular magnetic field. We argue that the obtained spectrum does not give information about the atomic collapse and that their interpretation of the spectrum regarding atomic collapse is not correct. We also argue that the obtained results are only valid up to the dimensionless charge vertical bar alpha vertical bar = 0.5 and, to obtain correct results for alpha > 0.5, a proper regularization of the Coulomb interaction is required. Here we present the correct numerical results for the spectrum for arbitrary values of alpha.

Abstract: We investigate the effect of the temperature dependence of many-body correlations on hole-hole Coulomb drag in strongly coupled GaAs/GaAlAs double quantum wells. For arbitrary temperatures, we obtained the correlations using the classical-map hypernetted-chain approach. We compare the temperature dependence of the resulting drag resistivities rho D(T) at different densities with rho D(T) calculated assuming correlations fixed at zero temperature. Comparing the results with those when correlations are completely neglected, we confirm that correlations significantly increase the drag. We find that the drag becomes sensitive to the temperature dependence of T greater than or similar to 2TF, twice the Fermi temperature. Our results show excellent agreement with available experimental data. Published under license by AIP Publishing.

Abstract: The Dirac equation is solved for triangular and hexagonal graphene quantum dots for different boundary conditions in the presence of a perpendicular magnetic field. We analyze the influence of the dot size and its geometry on their energy spectrum. A comparison between the results obtained for graphene dots with zigzag and armchair edges, as well as for infinite-mass boundary condition, is presented and our results show that the type of graphene dot edge and the choice of the appropriate boundary conditions have a very important influence on the energy spectrum. The single-particle energy levels are calculated as a function of an external perpendicular magnetic field that lifts degeneracies. Comparing the energy spectra obtained from the tight-binding approximation to those obtained from the continuum Dirac equation approach, we verify that the behavior of the energies as a function of the dot size or the applied magnetic field are qualitatively similar, but in some cases quantitative differences can exist.

Abstract: We study the influence of confinement on the atomic collapse due to a Coulomb impurity placed at the center of a graphene quantum dot of radius R. We apply the zigzag or infinite-mass boundary condition and consider both a point-size and a finite-size impurity. As a function of the impurity strength Za, the energy spectra are discrete. In the case of the zigzag boundary condition, the degenerate (with respect to the angular momentum m) zero-energy levels are pulled down in energy as Z alpha increases, and they remain below epsilon = – Z alpha. Our results show that the energy levels exhibit a 1/R dependence in the subcritical regime [Z alpha < |km + 1/2|, k = 1 (-1) for the K (K') valley]. In the supercritical regime (Z alpha > |km + 1/2|) we find a qualitatively very different behavior where the levels decrease as a function of R in a nonmonotonic manner. While the valley symmetry is preserved in the presence of the impurity, we find that the impurity breaks electron-hole symmetry. We further study the energy spectrum of zigzag quantum dots in gapped graphene. Our results show that as the gap increases, the lowest electron states are pushed into the gap by the impurity.

Abstract: A comparative study is made of the propagation of wave packets and fronts in three different meta-media, i.e. graphene, left-handed media (LHM) and transmission lines, using one-dimensional models. It is shown that a potential step in graphene influences only the frequency of the electronic wave, i.e., the particular spectrum branch (electron or hole) to which the wave belongs to, while the envelop function (the wave front or packet form) remains unchanged. Although the model for a vacuum and LHM interface is similar to that of the potential step in graphene, the solutions are quite different due to differences in the chirality of the waves. Comparing the propagation of wave fronts and packets in a standard transmission line and its meta-analog we demonstrate that the propagating packets in the meta-line are much more deformed as compared to the standard one, including broadening, asymmetry and even the appearance of fast moving precursors. This influence is seen not only in the case of packets with steep fronts but in soft Gaussian packets as well.

Abstract: The electronic and structural properties of excitons and trions in monolayer transition metal dichalcogenides are investigated using both a multiband and a single- band model. In the multiband model we construct the excitonic Hamiltonian in the product base of the single-particle states at the conduction and valence band edges. We decouple the corresponding energy eigenvalue equation and solve the resulting differential equation self-consistently, using the finite element method (FEM), to determine the energy eigenvalues and the wave functions. As a comparison, we also consider the simple single-band model which is often used in numerical studies. We solve the energy eigenvalue equation using the FEM as well as with the stochastic variational method (SVM) in which a variational wave function is expanded in a basis of a large number of correlated Gaussians. We find good agreement between the results of both methods, as well as with other theoretical works for excitons, and we also compare with available experimental data. For trions the agreement between both methods is not as good due to our neglect of angular correlations when using the FEM. Finally, when comparing the two models, we see that the presence of the valence bands in the mutiband model leads to differences with the single- band model when (interband) interactions are strong.