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We consider confinement of Dirac fermions in $AB$-stacked bilayer graphene by inhomogeneous on-site interactions, (pseudo-)magnetic field or inter-layer interaction. Working within the framework of four-band approximation, we focus on the systems where the stationary equation is reducible into two stationary equations with $2times2$ Dirac-type Hamiltonians and auxiliary interactions. We show that it is possible to find localized states by solving an effective Schrodinger equation with energy-dependent potential. We consider several scenarios where bilayer graphene is subject to inhomogneous (pseudo-)magnetic field, on-site interactions or inter-layer coupling. In explicit examples, we provide analytical solutions for the states localized by local fluctuations or periodicity defects of the interactions.
We present a full derivation of the interaction Hamiltonian for holes in Silicon within the six-band envelope-function scheme, which appropriately describes the valence band close to the $boldsymbol{Gamma}$ point. The full structure of the single-hol
Vertical plasmonic coupling in double-layer graphene leads to two hybridized plasmonic modes: optical and acoustic plasmons with symmetric and anti-symmetric charge distributions across the interlayer gap, respectively. However, in most experiments b
Interaction driven integer quantum Hall effects are anticipated in graphene bilayers because of the near-degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance
The Josephson effect is one of the most studied macroscopic quantum phenomena in condensed matter physics and has been an essential part of the quantum technologies development over the last decades. It is already used in many applications such as ma
The effects of the long range electrostatic interaction in twisted bilayer graphene are described using the Hartree-Fock approximation. The results show a significant dependence of the band widths and shapes on electron filling, and the existence of