Black hole surrounded by perfect fluid dark matter with a background Kalb-Ramond field

With an intent to explore the interplay between the Lorentz symmetry breaking (LSB) and the presence of dark matter (DM), we obtain a static and spherically symmetric black hole (BH) solution in the background of nonminimally coupled Kalb-Ramond (KR) field surrounded by perfect fluid dark matter (PFDM). The KR field is frozen to a non-zero vacuum expectation value (VEV) that breaks the particle Lorentz symmetry spontaneously. We explore scalar invariants, Ricci Scalar, Ricci squared, and Kretschmann Scalar, to probe the nature of singularities in the obtained solution. We then study strong gravitational lensing in the background of our BH, i.e., KRPFDM BH, revealing the adverse impact of LSB parameter $\alpha$ and PFDM parameter $\beta$ on the lensing coefficients. The significant effect of our model parameters is evident in strong lensing observables. Bounds on the deviation from Schwarzschild, $\delta$, for supermassive BHs (SMBHs) $M87^*$ and $SgrA^*$ from the EHT, Keck, and VLTI observatories are then utilized to put our BH model to the test and extract possible values of model parameters $\alpha$ and $\beta$ that generate theoretical predictions in line with experimental observations within $1\sigma$ confidence level. Our study sheds light on the combined effect of LSB and PFDM and may be helpful in finding their signature.