Extended Data Fig. 8: Time reversal invariant pseudo-PHE.
From: Hall effects in artificially corrugated bilayer graphene without breaking time-reversal symmetry
a, The planar Hall resistivities ρyx (see top insets in b for measurement setup) and ρxy (see c, top insets) measured as a function of Vg at zero external magnetic field B = 0. Although the current directions and measurement setups for ρyx and ρxy are very different with respect to the corrugation and device geometry, the fact the ρxy = ρyx indicates that the resistivity is a symmetric tensor and the observed pseudo-PHE is indeed time reversal symmetric. b, c, Colour rendition of ρyx(B, Vg) (b) and ρxy(B, Vg) (c). The top insets show representative current trajectories for each region labelled in the colour plot. Interplay between the pseudo-PHE and the HE results in an asymmetric overall Hall resistivity, for example, the Hall resistivity ρyx(B = + 0.9T) (region labelled ii in b) is completely different to ρyx(B = − 0.9T) (region labelled iii in b). However, ρyx(B = + 0.9T) (region labelled ii in b) is nearly the same as ρxy(B = − 0.9T) (region labelled iii in c). d, ρyx(B = + 0.9T) and ρxy(B = − 0.9T) are explicitly plotted as a function of Vg to demonstrate the equivalence.
