Interband State Transfer in Double-Gated Bilayer Graphene at High Electric Field

The band structure of Bernal-stacked bilayer graphene can be tuned using double-gated transistors to apply a perpendicular electric field that generates an interlayer potential energy difference $\Delta$. Dielectric breakdown limits the operation of conventional devices to the $\Delta \ll t_\perp \simeq 360$ meV regime. We employ double ionic gating to reach fields past $1$ V/nm, for which $\Delta > t_\perp$. We find that for $\Delta \simeq t_\perp$, the evolution of the longitudinal resistance ($R_{xx}$) peak as a function of applied gate voltages undergoes a sharp change in slope, exhibiting a pronounced "knee". Increasing $\Delta$ past the "knee" results in an unusual evolution transport properties: the peak in $R_{xx}$ decreases in magnitude, it exhibits a splitting concomitant with multiple sign reversals of the Hall resistance, and hysteresis in the peak position emerges. We explain the observed phenomenology in terms of in-gap bound states, whose energy strongly depends on the perpendicular electric field, and crosses the mid-gap level for sufficiently large $\Delta > t_\perp$. The phenomenon causes large changes in the electronic density of in-gap states that profoundly affect the evolution of the chemical potential. Our experimental results and their interpretation reveal unique aspects of the physics of in-gap states in Bernal bilayer graphene and demonstrate that double ionic gating enables investigating the large-$\Delta$ regime, which has remained experimentally inaccessible so far.