Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $q$th-root non-Hermitian Floquet topological insulators   Floquet phases of matter have attracted great attention due to their
dynamical and topological nature that are unique to nonequilibrium settings. In
this work, we introduce a generic way of taking any integer $q$th-root of the
evolution operator $U$ that describes Floquet topological matter. As a case
study, we apply our $q$th-rooting procedure to obtain the square- and
cubic-root first- and second-order non-Hermitian Floquet topological
insulators. There, we explicitly demonstrate the presence of multiple edge and
corner modes at fractional quasienergies $\pi/2$, $\pi/3$ and $2\pi/3$, whose
numbers can be large and are highly controllable. Notably, we observe
non-Hermiticity induced fractional-quasienergy corner modes and the coexistence
of non-Hermitian skin effect with fractional-quasienergy edge states. By
repeatedly applying the square- and cubic-rooting procedure, the resulting
$2^n$th- and $3^n$th-root systems are found to possess degenerate edge or
corner modes at quasienergies $\pm(0,1,...2^{n})\pi/2^{n}$ and
$\pm(0,1,...,3^{n})\pi/3^{n}$, respectively, whose numbers are determined by
the bulk topological invariants of the parent system $U$. Our findings thus
establish a framework of constructing an intriguing class of topological matter
in Floquet systems.

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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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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: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: econ