Neutral-current Hall effects in disordered graphene

A nonlocal Hall bar geometry is used to detect neutral-current Hall effects in graphene on silicon dioxide. Disorder is tuned by the addition of $\mathrm{Au}$ or $\mathrm{Ir}$ adatoms in ultrahigh vacuum. A reproducible neutral-current Hall effect is found in both as-fabricated and adatom-decorated graphene. The Hall angle exhibits a complex but reproducible dependence on gate voltage and disorder, and notably breaks electron-hole symmetry. An exponential dependence on length between Hall and inverse Hall probes indicates a neutral-current relaxation length of approximately $300\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$. The short relaxation length and lack of precession in a parallel magnetic field suggest that the neutral currents are valley currents. No signature of the spin-orbit coupling induced spin Hall effect is observed in the $\mathrm{Au}$- or $\mathrm{Ir}$-decorated graphene. The near lack of temperature dependence from 7 to 300 K is unprecedented among reports of valley Hall effect in graphene, and promising for using controlled disorder for room temperature neutral-current electronics.