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

Abstract

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

Published version in PRB: 7 pages, 4 figures: Supplemental Material as Ancillary file