  The fate of the low-temperature conductance at the charge-neutrality (Dirac)
point in a single sheet of graphene is investigated down to 20 mK. As the
temperature is lowered, the peak resistivity diverges with a power-law behavior
and becomes as high as several Megohms per square at the lowest temperature, in
contrast with the commonly observed saturation of the conductivity. As a
perpendicular magnetic field is applied, our device remains insulating and
directly transitions to the broken-valley-symmetry, nu=0 quantum Hall state,
indicating that the insulating behavior we observe at zero magnetic field is a
result of broken valley symmetry. Finally we discuss the possible origins of
this effect.
