Flow coupling alters topological phase transition in nematic liquid crystals

We investigate how coupling to fluid flow influences defect-mediated transitions in two-dimensional passive and active nematic fluids using fluctuating nematohydrodynamic simulations. The system is driven by tuning the fluctuation strength, with increasing (decreasing) fluctuations defining the forward (backward) protocol through the defect creation temperature threshold where defects spontaneously nucleate. In the absence of flow coupling, the transition follows the Berezinskii--Kosterlitz--Thouless (BKT) scenario, governed by reversible binding and unbinding of $\pm 1/2$ defect pairs. When hydrodynamics is included, the outcome is controlled by the flow--alignment parameter. For non-aligning nematics ($\lambda=0$), the transition remains consistent with BKT. By contrast, for strain-rate--coupled nematics ($\lambda\neq 0$), bend--splay walls emerge, lowering the defect nucleation threshold and preventing sustained recombination: once created, defects remain unbound across the full range of fluctuation strengths in both forward and backward protocols. In active nematics,
self-generated flows produce the same effect, with defects remaining unbound irrespective of alignment.
These findings demonstrate that coupling to flow, whether through strain-rate alignment or
activity, fundamentally alters defect-mediated phase transitions and suggest that the canonical BKT transition emerges only in the absence of flow coupling.