Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirac equation description on the electronic states and magnetic
  properties of a square graphene quantum dot   Electronic eigen-states of a square graphene quantum dot(GQD) terminated by
both zigzag and armchair edges are derived in the theoretical framework of
Dirac equation. We find that the Dirac equation can determine the eigen-energy
spectrum of a GQD with high accuracy even if its size is reduced to a few
nanometers. More importantly, from the Dirac equation description we can
readily work out the number and energy gap of the conjugate surface states,
which are intimately associated with the magnetic properties of the GQD. By
using the Hartree-Fock mean field approach, we study the size dependence of the
magnetic ordering formation in this square GQD. We find that there exists a
critical size of the width between the two zigzag edges to indicate the onset
of the stable magnetic ordering. On the other hand, when such a width increases
further, the magnetic ground state energy of a charge neutral GQD tends to a
saturated value. These results coincide with the previous results obtained from
the first principle calculation. Then, based on the Dirac equation solution
about the surface state, we establish a simple two-state model which can
quantitatively explain the size dependence of the magnetic ordering in the
square GQD.

6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
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The categories of this paper are: nlin
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol