Electrically tuning many-body states in a Coulomb-coupled InAs/InGaSb double layer

We study the transport properties of an electron-hole double layer consisting of barrier-separated InAs/InGaSb quantum wells. We focus on measurements of four-terminal resistivity of a Hall-bar sample as a function of electron $(n)$ and hole $(p)$ density, that are being tuned by a pair of top and bottom gates. In zero magnetic field, we clearly observe an insulating phase which occurs at a charge neutral point, below a critical carrier density $n=p<1\phantom{\rule{4pt}{0ex}}\ifmmode\times\else\texttimes\fi{}{10}¹¹\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$. This phase is characterized by a narrow and thermally activated resistance peak and an anomalous Hall resistance. This observation reinforces our previous finding of an excitonic insulator. Remarkably, when the layer densities are being tuned into imbalance, here $p\ensuremath{\gg}n$, a broader resistance peak emerges. We discuss this phase with respect to a possible (theoretically predicted) charge density wave ground state. Both phases can persist above \ensuremath{\sim}25 K, indicating robust correlations in the electron-hole double layers.