  It was proposed that a dilute semimetal is unstable against the formation of
an exciton insulator, however experimental confirmations have remained elusive.
We investigate the origin of bulk energy gap in inverted InAs/GaSb quantum
wells (QWs) which naturally host spatially-separated electrons and holes, using
charge-neutral point density (no~po) in gated-device as a tuning parameter. We
find two distinct regimes of gap formation, that for I), no >> 5x1010/cm2, a
soft gap opens predominately by electron-hole hybridization; and for II),
approaching the dilute limit no~ 5x1010/cm2, a hard gap opens leading to a true
bulk insulator with quantized edge states. Moreover, the gap is dramatically
reduced as the QWs are tuned to less dilute. We further examine the response of
gaps to in-plane magnetic fields, and find that for I) the gap closes at B// >
~ 10T, consistent with hybridization while for II) the gap opens continuously
for B// as high as 35T. Our analyses show that the hard gap in II) cannot be
explained by single-particle hybridization. The data are remarkably consistent
with the formation of a nontrivial exciton insulator in very dilute InAs/GaSb
QWs.
