  High-temperature superconductivity in cuprates emerges upon doping the parent
Mott insulator. Robust signatures of the low-doped electronic state include a
Hall carrier density that initially tracks the number of doped holes and the
emergence of an anisotropic pseudogap; the latter characterised by disconnected
Fermi arcs, closure at a critical doping level $p^* \approx 0.19$, and, in some
cases, a strongly enhanced carrier effective mass. In Sr$_2$IrO$_4$, a
spin-orbit-coupled Mott insulator often regarded as a 5$d$ analogue of the
cuprates, surface probes have revealed the emergence of an anisotropic
pseudogap and Fermi arcs under electron doping, though neither the
corresponding $p^*$ nor bulk signatures of pseudogap closing have as yet been
observed. Here, we report electrical transport and specific heat measurements
on Sr$_{2-x}$La$_x$IrO$_4$ over an extended doping range 0 $\leq x \leq$ 0.20.
The effective carrier density $n_{\rm H}$ at low temperatures exhibits a
crossover from $n_{\rm H} \approx x$ to $n_{\rm H} \approx 1+x$ near $x$ =
0.16, accompanied by \textcolor{blue}{a five-orders-of-magnitude increase in
conductivity} and a six-fold enhancement in the electronic specific heat. These
striking parallels in the bulk pseudogap phenomenology, coupled with the
absence of superconductivity in electron-doped Sr$_2$IrO$_4$, disfavour the
pseudogap as a state of precursor pairing and thereby narrow the search for the
key ingredient underpinning the formation of the superconducting condensate in
doped Mott insulators.
