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 $300\mathrm{nm}$. 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.

Figure 1

(a) AFM image of our graphene device. The width $w$ and length $L$ of the Hall bar, and the configuration of current $I_{\mathrm{NL}}$ and voltage probes $V_{\mathrm{NL}}$ for measurement of the nonlocal resistance are indicated. (b) The conductivity ${\sigma }_{\mathrm{xx}}$ versus gate voltage $V_g$ for $L/w=2.9$ for as-fabricated graphene and at three different Au coverages. Here $1\mathrm{ML}=1.4\times {10}^{15}\mathrm{c}{\mathrm{m}}^{-2}$ for Au(111). (c) The shift of gate voltage of minimum conductivity $-\mathrm{\Delta }{V}_{g,\min }$ as a function of Au coverage. The inset shows the $-\mathrm{\Delta }{V}_{g,\min }$ versus inverse mobility; here all $-\mathrm{\Delta }{V}_{g,\min }$ values are offset by 10 V to account for initial disorder. Lines correspond to the theory in [Ref. 20]. (d) Temperature dependence of ${\rho }_{\mathrm{xx}}$ at $V_g=V_{g,\min }$ for Au-decorated graphene.

Figure 2

(a) Nonlocal resistance $R_{\mathrm{NL}}$ versus $V_g$ curves for as-fabricated and Au-decorated graphene with $L/w=2.9$. The dashed and solid black curves correspond to as-fabricated graphene at 300 and $7\mathrm{K}$, respectively. (b) The ratio of $\frac{R_{\mathrm{NL}}}{{\rho }_{xx}}$ as a function of shifted gate voltage $V_g-V_{g,\min }$ for as-fabricated and Au-decorated graphene with $L/w=2.9$. The solid lines are a fit to a Breit-Wigner-Fano function as described in text.

Figure 3

(a–c) The parameters of the Breit-Wigner-Fano function $A_1\left(a\right), q\left(b\right)$, and $\mathrm{\Gamma }\left(c\right)$ as a function of mobility at various $L/w$ ratios. Parameters are described in text. (d) The fitting parameter $A_1$ for three different as-fabricated graphene devices as a function of length.

Figure 4

$R_{\mathrm{NL}}$ for as-fabricated graphene device with $L=1.4\mathrm{um}$ and $w=0.9\mathrm{um}$ at $V_g-{V_g}_{,\min }=5\mathrm{V}$ as a function of parallel magnetic field $B_{\left|\right|}$. The squares and black line are the measured data, the dotted black line is the calculated Ohmic contribution, and the red lines are calculated Hanle precession for ${\lambda }_s=300\mathrm{nm}, {\tau }_s=1.2\mathrm{ps}$ (solid red line); and ${\lambda }_s=3000\mathrm{nm}, {\tau }_s=100\mathrm{ps}$ (dashed red line).