Reentrant phase behavior in binary topological flocks with nonreciprocal alignment

We study a binary metric-free Vicsek model involving two species of self-propelled particles aligning with their Voronoi neighbors, focusing on a weakly nonreciprocal regime, where species <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>A</a:mi></a:math> aligns with both <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>A</b:mi></b:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>B</c:mi></c:math>, but species <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>B</d:mi></d:math> does not align with either. Using agent-based simulations, we find that even with a small fraction of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>B</e:mi></e:math> particles, the phase behavior of the system can be changed qualitatively, which becomes reentrant as a function of noise strength: traveling bands arise not only near the flocking transition, but also in the low-noise regime, separated in the phase diagram by a homogeneous polar liquid regime. We find that the ordered bands in the low-noise regime travel through an background, in contrast to their metric counterparts. We develop a coarse-grained field theory, which can account for the reentrant phase behavior qualitatively, provided the higher-order angular modes are taken into consideration.