Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical Solutions for the Surface States of Bi$_{1-x}$Sb$_x$ ($0\le x
  \lesssim 0.1$)   Analytical solutions for the surface state (SS) of an extended Wolff
Hamiltonian, which is a common Hamiltonian for strongly spin-orbit coupled
systems, are obtained both for semi-infinite and finite-thickness boundary
conditions. For the semi-infinite system, there are three types of SS
solutions: (I-a) linearly crossing SSs in the direct bulk band gap, (I-b) SSs
with linear dispersions entering the bulk conduction or valence bands away from
the band edge, and (II) SSs with nearly flat dispersions entering the bulk
state at the band edge. For the finite-thickness system, a gap opens in the SS
of solution I-a. Numerical solutions for the SS are also obtained based on the
tight-binding model of Liu and Allen [Phys. Rev. B, 52, 1566 (1995)] for
Bi$_{1-x}$Sb$_x$ ($0\le x \le 0.1$). A perfect correspondence between the
analytic and numerical solutions is obtained around the $\bar{M}$ point
including their thickness dependence. This is the first time that the character
of the SS numerically obtained is identified with the help of analytical
solutions. The size of the gap for I-a SS can be larger than that of bulk band
gap even for a "thick" films ($\lesssim 200$ bilayers $\simeq 80$ nm) of pure
bismuth. Consequently, in such a film of Bi$_{1-x}$Sb$_x$, there is no apparent
change in the SSs through the band inversion at $x\simeq 0.04$, even though the
nature of the SS is changed from solution I-a to I-b. Based on our theoretical
results, the experimental results on the SS of Bi$_{1-x}$Sb$_x$ ($0\le x
\lesssim 0.1$) are discussed.

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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas