  Negative compressibility is a sign of thermodynamic instability of open or
non-equilibrium systems. In quantum materials consisting of multiple mutually
coupled subsystems, the compressibility of one subsystem can be negative if it
is countered by positive compressibility of the others. Manifestations of this
effect have so far been limited to low-dimensional dilute electron systems.
Here we present evidence from angle-resolved photoemission spectroscopy (ARPES)
for negative electronic compressibility (NEC) in the quasi-three-dimensional
(3D) spin-orbit correlated metal (Sr1-xLax)3Ir2O7. Increased electron filling
accompanies an anomalous decrease of the chemical potential, as indicated by
the overall movement of the deep valence bands. Such anomaly, suggestive of
NEC, is shown to be primarily driven by the lowering in energy of the
conduction band as the correlated bandgap reduces. Our finding points to a
distinct pathway towards an uncharted territory of NEC featuring bulk
correlated metals with unique potential for applications in low-power
nanoelectronics and novel metamaterials.
