  We have studied the breakdown of the integer quantum Hall (QH) effect with
fully broken symmetry, in an ultra-high mobility graphene device sandwiched
between two single crystal hexagonal boron nitride substrates. The evolution
and stabilities of the QH states are studied quantitatively through the
nonlinear transport with dc Hall voltage bias. The mechanism of the QH
breakdown in graphene and the movement of the Fermi energy with the electrical
Hall field are discussed. This is the first study in which the stabilities of
fully symmetry broken QH states are probed all together. Our results raise the
possibility that the v=6 states might be a better target for the quantum
resistance standard.
