Abstract: Within a minimal model, we present analytical expressions for the eigenstates and eigenvalues of carriers confined in quantum rings in monolayer and bilayer graphene. The calculations were performed in the context of the continuum model by solving the Dirac equation for a zero width ring geometry, i.e., by freezing out the carrier radial motion. We include the effect of an external magnetic field and show the appearance of Aharonov-Bohm oscillations and of a nonzero gap in the spectrum. Our minimal model gives insight on the energy spectrum of graphene-based quantum rings and models different aspects of finite width rings.

Abstract: Within a tight-binding approach, we investigate the effect of twisting angle on the energy levels of circular bilayer graphene (BLG) quantum dots (QDs) in both the absence and presence of a perpendicular magnetic field. The QDs are defined by an infinite-mass potential, so that the specific edge effects are not present. In the absence of magnetic field (or when the magnetic length is larger than the moire length), we show that the low-energy states in twisted BLG QDs are completely affected by the formation of moire patterns, with a strong localization at AA-stacked regions. When magnetic field increases, the energy gap of an untwisted BLG QD closes with the edge states, localized at the boundaries between the AA- and AB-stacked spots in a twisted BLG QD. Our observation of the spatial localization of the electrons in twisted BLG QDs can be experimentally probed by low-bias scanning tunneling microscopy measurements.

Abstract: The effect of the magnetic impurities on the charge transport in a magnetic topological ultra-thin film (MTF) is analytically investigated by applying the semi-classical Boltzmann framework through a modified relaxation-time approximation. Our results for the relaxation time of electrons as well as the charge conductivity of the system exhibit two distinct regimes of transport. We show that the generated charge current in a MTF is always dissipative and anisotropic when both conduction bands are involved in the charge transport. The magnetic impurities induce a chirality selection rule for the transitions of electrons which can be altered by changing the orientation of the magnetic impurities. On the other hand, when a single conduction band participates in the charge transport, the resistivity is isotropic and can be entirely suppressed due to the corresponding chirality selection rule. Our findings propose a method to determine an onset thickness at which a crossover from a three-dimensional magnetic topological insulator to a (two-dimensional) MTF occurs.

Abstract: We predict enhanced electron-hole superfluidity in two coupled electron-hole armchair-edge terminated graphene nanoribbons separated by a thin insulating barrier. In contrast to graphene monolayers, the multiple subbands of the nanoribbons are parabolic at low energy with a gap between the conduction and valence bands, and with lifted valley degeneracy. These properties make screening of the electron-hole interaction much weaker than for coupled electron-hole monolayers, thus boosting the pairing strength and enhancing the superfluid properties. The pairing strength is further boosted by the quasi one-dimensional quantum confinement of the carriers, as well as by the large density of states near the bottom of each subband. The latter magnifies superfluid shape resonances caused by the quantum confinement. Several superfluid partial condensates are present for finite-width nanoribbons with multiple subbands. We find that superfluidity is predominately in the strongly-coupled BEC and BCS-BEC crossover regimes, with large superfluid gaps up to 100 meV and beyond. When the gaps exceed the subband spacing, there is significant mixing of the subbands, a rounding of the shape resonances, and a resulting reduction in the one-dimensional nature of the system.

Abstract: Recently proposed accurate correlation energies are used to determine the phase diagram of strongly coupled electron-hole graphene bilayers. The control parameters of the phase diagram are the charge carrier density and the insulating barrier thickness separating the bilayers. In addition to the electron-hole superfluid phase we find two new inhomogeneous ground states, a one dimensional charge density wave phase and a coupled electron-hole Wigner crystal. The elementary crystal structure of bilayer graphene plays no role in generating these new quantum phases, which are completely determined by the electrons and holes interacting through the Coulomb interaction. The experimental parameters for the new phases lie within attainable ranges and therefore coupled electron-hole bilayer graphene presents itself as an experimental system where novel emergent many-body phases can be realized.

Abstract: We study the effect of structural inversion asymmetry, induced by the presence of substrates or by external electric fields, on charge transport in magnetic topological ultra-thin films. We consider general orientations of the magnetic impurities. Our results are based on the Boltzmann formalism along with a modified relaxation time scheme. We show that the structural inversion asymmetry enhances the charge transport anisotropy induced by the magnetic impurities and when only one conduction subband contributes to the charge transport a dissipationless charge current is accessible. We demonstrate how a substrate or gate voltage can control the effect of the magnetic impurities on the charge transport, and how this depends on the orientation of the magnetic impurities.

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: Using the effective continuum model, the electron energy spectrum of gated bilayer graphene with a step-like region of decoupled graphene layers at the edge of the sample is studied. Different types of coupled-decoupled interfaces are considered, i.e., zigzag (ZZ) and armchair junctions, which result in significant different propagating states. Two non-valley-polarized conducting edge states are observed for ZZ type, which are mainly located around the ZZ-ended graphene layers. Additionally, we investigated both BA-BA and BA-AB domain walls in the gated bilayer graphene within the continuum approximation. Unlike the BA-BA domain wall, which exhibits gapped insulating behaviour, the domain walls surrounded by different stackings of bilayer regions feature valley-polarized edge states. Our findings are consistent with other theoretical calculations, such as from the tight-binding model and first-principles calculations, and agree with experimental observations. Published by AIP Publishing.

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.