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We derive semiclassical quantization equations for graphene mono- and bilayer systems where the excitations are confined by the applied inhomogeneous magnetic field. The importance of a semiclassical phase, a consequence of the spinor nature of the excitations, is pointed out. The semiclassical eigenenergies show good agreement with the results of quantum mechanical calculations based on the Dirac equation of graphene and with numerical tight binding calculations.
Resonant transmission through electronic quantum states that exist at the zero points of a magnetic field gradient inside a ballistic quantum wire is reported. Since the semiclassical motion along such a line of zero magnetic field takes place in for
The electronic states at graphene-SiO$_2$ interface and their inhomogeneity was investigated using the back-gate-voltage dependence of local tunnel spectra acquired with a scanning tunneling microscope. The conductance spectra show two, or occasional
The goal of this paper is to provide an intuitive and useful tool for analyzing the impurity bound state problem. We develop a semiclassical approach and apply it to an impurity in two dimensional systems with parabolic or Dirac like bands. Our metho
We present a tight-binding theory of triangular graphene quantum dots (TGQD) with zigzag edge and broken sublattice symmetry in external magnetic field. The lateral size quantization opens an energy gap and broken sublattice symmetry results in a she
We report on high-field magnetotransport (B up to 35 T) on a gated superlattice based on single-layer graphene aligned on top of hexagonal boron nitride. The large-period moire modulation (15 nm) enables us to access the Hofstadter spectrum in the vi