  The application of a mechanical strain to a 2D material can create
pseudo-magnetic fields and lead to a quantized valley Hall effect. However,
measuring valley-resolved effects remains a challenging task due to their
inherent fragility and dependence on the sample's proper design. Additionally,
non-local transport probes based on multiterminal devices have often proven to
be inadequate in yielding conclusive evidence of the valley Hall signal. Here,
we introduce an alternative way of detecting the quantized valley Hall effect,
which entirely relies on local density measurements, performed deep in the bulk
of the sample. The resulting quantized signal is a genuine Fermi sea response,
independent of the edge physics, and reflects the underlying valley Hall effect
through the Widom-St\v{r}eda formula. Specifically, our approach is based on
measuring the variation of the particle density, locally in the bulk, upon
varying the strength of the applied strain. This approach to the quantized
valley Hall effect is particularly well suited for experiments based on
synthetic lattices, where the particle density (or integrated density of
states) can be spatially resolved.
