Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Confinement in bilayer graphene via intra- and inter-layer interactions   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 $2\times2$ Dirac-type Hamiltonians and auxiliary interactions.
We show that it is possible to find localized states by solving an effective
Schr\"odinger 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.

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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin