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: Due to its strong bonds graphene can stretch up to 25% of its original size without breaking. Furthermore, mechanical deformations lead to the generation of pseudo-magnetic fields (PMF) that can exceed 300 T. The generated PMF has opposite direction for electrons originating from different valleys. We show that valley-polarized currents can be generated by local straining of multi-terminal graphene devices. The pseudo-magnetic field created by a Gaussian-like deformation allows electrons from only one valley to transmit and a current of electrons from a single valley is generated at the opposite side of the locally strained region. Furthermore, applying a pressure difference between the two sides of a graphene membrane causes it to bend/bulge resulting in a resistance change. We find that the resistance changes linearly with pressure for bubbles of small radius while the response becomes non-linear for bubbles that stretch almost to the edges of the sample. This is explained as due to the strong interference of propagating electronic modes inside the bubble. Our calculations show that high gauge factors can be obtained in this way which makes graphene a good candidate for pressure sensing.

Abstract: The interaction of monolayer graphene with specific substrates may break its sublattice symmetry and results in unidirectional chiral states with opposite group velocities in the different Dirac cones (Zarenia et al 2012 Phys. Rev. B 86 085451). Taking advantage of this feature, we propose a valley filter based on a transversal mass kink for low energy electrons in graphene, which is obtained by assuming a defect region in the substrate that provides a change in the sign of the substrate-induced mass and thus creates a non-biased channel, perpendicular to the kink, for electron motion. By solving the time-dependent Schrodinger equation for the tight-binding Hamiltonian, we investigate the time evolution of a Gaussian wave packet propagating through such a system and obtain the transport properties of this graphene-based substrate-induced quantum point contact. Our results demonstrate that efficient valley filtering can be obtained, provided: (i) the electron energy is sufficiently low, i.e. with electrons belonging mostly to the lowest sub-band of the channel, and (ii) the channel length (width) is sufficiently long (narrow). Moreover, even though the transmission probabilities for each valley are significantly affected by impurities and defects in the channel region, the valley polarization in this system is shown to be robust against their presence.

Abstract: http://dx.doi.org/doi:10.1103/PhysRevLett.70.2146

Abstract: Magnetotransport properties of a pseudomorphic GsAs/Ga0.8In0.2As/Ga0.75Al0.25As heterostructure are investigated in pulsed magnetic fields up to 50 T and at temperatures of T = 1.4 and 4.2 K. The structure studied consists of a Si delta layer parallel to a Ga0.8In0.2As quantum well (QW). The dark electron density of the structure is n(c) = 1.67 x 10(16) m(-2). By illumination the density can be increased up to a factor of 4; this way the second subband in the Ga0.08In0.2As QW can become populated as well as the Si delta layer. The presence of electrons in the delta layer results in drastic changes in the transport data, especially at magnetic fields beyond 30 T. The phenomena observed are interpreted as (i) magnetic freeze-out of carriers in the delta layer when a low density of electrons is present in the delta layer, and (ii) quantization of the electron motion in the two-dimensional electron gases in both the Ga0.8In0.2As QW and the Si delta layer in the case of high densities. These conclusions are corroborated by the numerical results of our theoretical model. We obtain satisfactory agreement between model and experiment.

Abstract: The nonlinear Schrodinger equation is solved on an infinitesimal thin ring or circle. We obtained the exact real wave functions with their corresponding energies for the ground state and the excited states. Critical values of the circle perimeter are found at which the ground state changes its structure and additional higher excited states appear. Also, the complex wave functions that correspond to energy levels with finite angular momentum are studied.