Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zero modes of the Kitaev chain with phase-gradients and longer range
  couplings   We present an analytical solution for the full spectrum of Kitaev's
one-dimensional p-wave superconductor with arbitrary hopping, pairing amplitude
and chemical potential in the case of an open chain. We also discuss the
structure of the zero-modes in the presence of both phase gradients and next
nearest neighbor hopping and pairing terms. As observed by Sticlet et al., one
feature of such models is that in a part of the phase diagram, zero-modes are
present at one end of the system, while there are none on the other side. We
explain the presence of this feature analytically, and show that it requires
some fine-tuning of the parameters in the model. Thus as expected, these
`one-sided' zero-modes are neither protected by topology, nor by symmetry.

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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat