The MeerKAT Massive Distant Clusters Survey: detection of diffuse radio emission in galaxy clusters at $z > 1$
Diffuse, low surface-brightness radio emission in merging galaxy clusters provides insights into cosmic structure formation, the growth of magnetic fields, and turbulence. This paper reports a search for diffuse radio emission in a pilot sample of six high-redshift ($1.01 < z < 1.31$) galaxy clusters from the MeerKAT Massive Distant Cluster Survey (MMDCS). These six clusters are selected as the most massive $(M_{\rm 500c} = 6.7\,- 8.5 \times 10^{14}~\rm{M_{\odot}})$ systems based on their Sunyaev-Zel'dovich mass from the full MMDCS sample of 30 ACT DR5 clusters, and were observed first to explore the high-mass, high-redshift regime. Diffuse radio emission is confidently detected in four clusters and tentatively identified in two, with $k$-corrected radio powers scaled to 1.4 GHz ranging from $(0.46 \pm 0.16)$ to $(4.51 \pm 1.68) \times 10^{24}\, \mathrm{WHz^{-1}}$ and linear sizes between 0.47 and 1.08 Mpc. Combining $Chandra$ X-ray data with MeerKAT radio data, we find that 80$\%$ of clusters with X-ray observations exhibit disturbed morphologies indicative of mergers. These $z > 1$ galaxy clusters scatter around the established radio power-mass scaling relation observed at lower redshifts, supporting turbulent re-acceleration models in high-redshift mergers. However, their radio spectra are predicted to steepen ($α< -1.5$) due to enhanced inverse Compton losses in the cosmic microwave background, rendering them under-luminous at 1.4 GHz and placing them below the correlation. Our results demonstrate that merger-driven turbulence can sustain radio halos even at $z > 1$ while highlighting MeerKAT's unique ability to probe non-thermal processes in the early universe.