Density dependence of the excitation gaps in an undoped Si/SiGe double-quantum-well heterostructure

We report low-temperature magneto-transport measurements of an undoped Si/SiGe asymmetric double quantum well heterostructure. The density in both layers is tuned independently utilizing a top and a bottom gate, allowing the investigation of quantum wells at both imbalanced and matched densities. Integer quantum Hall states at total filling factor $\nu_{\text{T}} = 1$ and $\nu_{\text{T}} = 2$ are observed in both density regimes, and the evolution of their excitation gaps is reported as a function of density. The $\nu_{\text{T}} = 1$ gap evolution departs from the behavior generally observed for valley splitting in the single layer regime. Furthermore, by comparing the $\nu_{\text{T}} = 2$ gap to the single particle tunneling energy, $\Delta_{\text{SAS}}$, obtained from Schr\"{o}dinger-Poisson (SP) simulations, evidence for the onset of spontaneous inter-layer coherence (SIC) is observed for a relative filling fraction imbalance smaller than ${\sim}50\%$