  We theoretically investigate the interaction between magnons and a
Skyrmion-textured domain wall in a two-dimensional antiferromagnet and
elucidate the resultant properties of magnon transport. Using supersymmetric
quantum mechanics, we solve the scattering problem of magnons on top of the
domain wall and obtain the exact solutions of propagating and bound magnon
modes. Then, we find their properties of reflection and refraction in the
Skyrmion-textured domain wall, where magnons experience an emergent magnetic
field due to its non-trivial spin texture-induced effective gauge field. Based
on the obtained scattering properties of magnons and the domain wall, we show
that the thermal transport decreases as the domain wall's chirality increases.
Our results suggest that the thermal transport of an antiferromagnet is tunable
by modulating the Skyrmion charge density of the domain wall, which might be
useful for realizing electrically tunable spin caloritronic devices.
