Search for: All records

Immersed in external magnetic fields (B), buckled graphene constitutes an ideal tabletop setup, manifesting a confluence of time-reversal symmetry (T) breaking Abelian (B) and 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 (σxy) for spinless fermions. On a flat graphene (b=0), the B field produces quantized plateaus at G=±|σxy|=(2n+1)e2/h, where n=0,1,2,⋯. The strain-induced b field lifts the twofold valley degeneracy of higher Landau levels and leads to the formation of additional even-integer plateaus at G=±|σxy|=(2,4,⋯)e2/h, when B>b. While the same sequence of plateaus is observed for G when b>B, the numerical computation of σxy in Hall bar geometries in this regime becomes unstable. A plateau at G=σxy=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. 

Topological classification of quantum solids often (if not always) groups all trivial atomic or normal insulators (NIs) into the same featureless family. As we argue here, this is not necessarily the case always. In particular, when the global phase diagram of electronic crystals harbors topological insulators with the band inversion at various time-reversal invariant momenta KTIinv in the Brillouin zone, their proximal NIs display noninverted band-gap minima at KNImin=KTIinv. In such systems, once topological superconductors nucleate from NIs, the inversion of the Bogoliubov de Gennes bands takes place at KBdGinv=KNImin, inheriting from the parent state. We showcase this (possibly general) proposal for two-dimensional time-reversal symmetry-breaking insulators. Then, distinct quantized thermal Hall conductivity and responses to dislocation lattice defects inside the paired states (tied with KBdGinv or KNImin), in turn, unambiguously identify different parent atomic NIs.