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Immersed in external magnetic fields ($B$), buckled graphene constitutes anideal tabletop setup, manifesting a confluence of time-reversal symmetry(${\mathcal T}$) breaking Abelian ($B$) and ${\mathcal T}$-preservingstrain-induced internal axial ($b$) magnetic fields. In such a system, here wenumerically compute two-terminal conductance ($G$), and four- as well assix-terminal Hall conductivity ($\sigma_{xy}$) for spinless fermions. On a flatgraphene ($b=0$), the $B$ field produces quantized plateaus at $G=\pm|\sigma_{xy}|=(2n+1) e^2/h$, where $n=0,1,2, \cdots$. The strain induced $b$field lifts the two-fold valley degeneracy of higher Landau levels and leads tothe formation of additional even-integer plateaus at $G=\pm |\sigma_{xy}|=(2,4,\cdots)e^2/h$, when $B>b$. While the same sequence of plateaus is observedfor $G$ when $b>B$, the numerical computation of $\sigma_{xy}$ in Hall bargeometries in this regime becomes unstable. A plateau at $G=\sigma_{xy}=0$always appears with the onset of a charge-density-wave order, causing astaggered pattern of fermionic density between two sublattices of the honeycomblattice.

Transport in strained graphene: Interplay of Abelian and axial magnetic fields