Electric field induced transition between spin to valley polarized $\nu $=0 quantum Hall state in dual-gated graphene bilayers*

Graphene bilayers in Bernal stacking exhibit a transverse electric field dependent energy gap, thanks to the on-site electron energy asymmetry between the two layers. In a perpendicular magnetic field, the applied transverse electric field ($E)$ will induce a quantum Hall state (QHS) at the charge neutrality point (filling factor $\nu $=0) marked by a insulating behavior of the longitudinal resistance ($\rho _{xx})$, and a plateau in the Hall conductivity. Using dual-gated graphene bilayers, we investigate here the $E$-field dependence of the $\nu $=0 QHS in high perpendicular magnetic fields ($B)$, up to 30T. The temperature dependence of $\rho _{xx}$ measured at $\nu $=0 shows an insulating behavior, which is strongest in the vicinity of $E$=0 as well as at large $E$-fields. At a fixed $B$-field, as a function of the applied $E$-field the $\nu $=0 QHS undergoes a transition, marked by a $\rho _{xx }$minimum, as well as a temperature independent $\rho _{xx}$ at a finite $E$-field value. This observation can be explained by a transition from a spin polarized $\nu $=0 QHS at small $E$-fields, to a valley (layer) polarized $\nu $=0 QHS at large $E$-fields. The $E$-field value at which the transition occurs follows a linear dependence on the applied perpendicular magnetic field, with a slope of $\sim $18 mV/nm$\cdot $T.