Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High Chern number quantum anomalous Hall phases in graphene ribbons with
  Haldane orbital coupling   We investigate possible phase transitions among the different quantum
anomalous Hall (QAH) phases in a zigzag graphene ribbon under the influence of
the exchange field. The effective tight-binding Hamiltonian for graphene is
made up of the hopping term, the Kane-Mele and Rashba spin-orbit couplings as
well as the Haldane orbital term. We find that the variation of the exchange
field results in bulk gap-closing phenomena and phase transitions occur in the
graphene system. If the Haldane orbital coupling is absent, the phase
transition between the chiral (anti-chiral) edge state $\nu=+2$ ($\nu=-2$) and
the pseudo-quantum spin Hall state ($\nu=0$) takes place. Surprisingly, when
the Haldane orbital coupling is taken into account, an intermediate QSH phase
with two additional edge modes appears in between phases $\nu=+2$ and $\nu=-2$.
This intermediate phase is therefore either the hyper-chiral edge state of high
Chern number $\nu=+4$ or anti-hyper-chiral edge state of $\nu=-4$ when the
direction of exchange field is reversed. We present the band structures, edge
state wave functions and current distributions of the different QAH phases in
the system. We also report the critical exchange field values for the QAH phase
transitions.

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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph