Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topical Review on Skyrmions and Hall Transport   We review recent progresses towards an understanding of the Skyrmion Hall
transport in insulating as well as conducting materials. First, we consider a
theoretical breakthrough based on the quantum field theory Ward identity, a
first principle analysis, relying on symmetries and conservation laws. Broken
parity (inversion) symmetry plays a crucial role in Skyrmion Hall transport. In
addition to the well known thermal and electric Hall conductivities, our
analysis has led us to the discovery of a new and unforeseen physical quantity,
Hall viscosity - an anti-symmetric part of the viscosity tensor. We propose a
simple way to confirm the existence of Hall viscosity in the measurements of
Hall conductivity as a function of momentum. We provide various background
materials to assist the readers to understand the quantum field theory Ward
identity.
  In the second part, we review recent theoretical and experimental
advancements of the Skyrmion Hall effects and the topological (Magnon) Hall
effects for conducting (insulting) magnets. For this purpose, we consider two
enveloping themes: spin torque and thermo-electromagnetic effect. First, we
overview various spin torques, such as spin transfer torque, spin-orbit torque,
and spin Hall torque, and generalized Landau-Lifshitz-Gilbert equations and
Thiele equations using a phenomenological approach. Second, we consider
irreversible thermodynamics to survey possible thermo-electromagnetic effects,
such as Seebeck, Peltier and Thompson effects in the presence of the electric
currents, along with the Hall effects in the presence of a background magnetic
field. Recently developed spin Seebeck effects are also a significant part of
the survey. We also accommodate extensive background materials to make this
review self-contained. Finally, we revisit the Skyrmion Hall transport from the
Ward identity view point.

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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th