Direct imaging of magnetotransport at graphene-metal interfaces with a single-spin quantum sensor

Abstract

Magnetotransport underlines many important phenomena in condensed matter physics, such as the Hall effect and magnetoresistance (MR) effect. Thus far, most magnetotransport studies are based on bulk resistance measurements without direct access to microscopic details of the spatial transport pattern. Here, we report nanoscale imaging of magnetotransport using a scanning single-spin quantum magnetometer, which is demonstrated in a graphene-metal hybrid device at room temperature. By visualizing the current flow at elevated magnetic fields (~0.5 T), we directly observe the Lorentz deflection of current near the graphene-metal interface, which is a hallmark of magnetotransport. Combining the local current distribution with global resistance measurements, we reveal that transport properties of the hybrid are governed by a complex interplay of intrinsic MR around the Dirac cone, carrier hydrodynamics, interface resistance, and the nanoscale device geometry. Furthermore, accessing the local transport pattern across the interface enables quantitative mapping of spatial variations in contact resistance, which is commonly present in electronic devices made from two-dimensional materials yet non-trivial to characterize. Our work demonstrates the potential of nanoscale current imaging techniques for studying complex electronic transport phenomena that are difficult to probe by resistance-based measurements.

Figures (4)

• Figure 1: Concept of the experiment and the graphene-metal hybrid device.a, Hall effect in a uniform semiconductor. No current deflection occurs because the Lorentz force and opposing Hall potential gradient are exactly balanced. $B_\mathrm{ext}$ is the out-of-plane external magnetic field. b, In a semiconductor-metal hybrid, current is attracted to the metal disc at low field (left panel) while being deflected at elevated field (right panel). c, Topography of the sample, showing the van-der-Pauw geometry with an inner metal disc (radius $r$), outer graphene ring (radius $R$), and eight contacts labeled P to W. Dashed contours mark the edge of the graphene sheet. Scale bar, $1\,\mathrm{\,\mu{\rm m}}$. d, Experimental arrangement for imaging current flow through the device using a scanning NV microscope. e, Measured two-terminal resistance $R$ (contacts Q-V) and computed magnetoresistance $\textit{MR}$ (see text), plotted as a function of the out-of-plane magnetic bias field $B_\mathrm{ext}$. The dotted line indicates the zero-field resistance and the dashed line represents the simulated resistances supplementary.
• Figure 2: Imaging of current flow for various source-drain configurations at zero bias field around charge neutrality ($V_\mathrm{BG}=0$).a, Schematic of source-drain configurations. Thick red (thin green) arcs indicate a high (low) contact resistance between the metal disc and the graphene annulus. See Fig. S10 for a quantitative model. b, Measured magnetic field maps (out-of-plane component $B_z$) induced by a current (amplitude $I_0$) for $\{180^\circ, 135^\circ,90^\circ\}$ contact configurations. c, Current density magnitude ($J=\sqrt{J_x^2+J_y^2}$) computed from the measured $B_z$. d, Simulated current density maps using the quantitative model of Fig. S10 and Tables S1 and S2. Scale bars, $1\,\mathrm{\,\mu{\rm m}}$.
• Figure 3: Lorentz-force-induced deflection and current redistribution under an applied bias field around charge neutrality ($V_\mathrm{BG}=0$). a,b, $B_z$ maps and corresponding $J$ maps measured at $B_\mathrm{ext} = -0.53\,\mathrm{T}$ (top), $-0.01\,\mathrm{T}$ (center) and $+0.53\,\mathrm{T}$ (bottom). The dataset at $B_\mathrm{ext}\sim 0$ is replotted from Fig. \ref{['fig2']}. Scale bars, $1~\mathrm{\,\mu{\rm m}}$. c, Detail of $B_z$ (dashed square in panel a) revealing Lorentz-induced current deflection. Dashed contours show the device boundaries. The gray curves are the center streamlines of the injected current (see text). Scale bars, $200\,\mathrm{nm}$. d, Deflection of the center streamline (color) together with the Hall angle tangent $\tan\theta_\mathrm{H}$ (gray), permitting a direct spatial measurement of the carrier mobility $\mu$. e, Fraction of the current flowing through the graphene ring, obtained by integrating the normal component of the current density along the dashed line in panel b (Methods). Circles are the experimental data and the dashed line corresponds to simulations in the diffusive regime. The cross corresponds to a simulation in the hydrodynamic regime at $B_\mathrm{ext}=0$.
• Figure 4: Electron hydrodynamics and carrier dependence of magnetotransport.a, Experimental data (second dataset measured at $B_\mathrm{ext}\sim 0$) together with hydrodynamic ($D_\nu=0.1\,\mathrm{\,\mu{\rm m}}$) and diffusive transport simulations. The arrow indicates enhanced flow in the graphene ring for the hydrodynamic case. b, Two-terminal resistance $R$ for the P-R source-drain configuration as a function of the back-gate voltage $V_\mathrm{BG}$ and the corresponding carrier density $n$. Dots are the experimental data. Curves represent finite element simulations based on a two-carrier model supplementary using the parameters of Tables S1 and S2. The CNP is at $V_\mathrm{BG}\approx0.175~\mathrm{V}$ (vertical dashed line). The gray area shows the region of electron-hole coexistence around the Dirac cone where the Fermi energy is less than the thermal energy, $|E_\mathrm{F}|<k_{\rm B}T$. c, Corresponding $\textit{MR} = R(0.54\,\mathrm{T})/R(0.04\,\mathrm{T})-1$ computed from the simulation (includes $2.2\,\mathrm{k\Omega}$P-R contact resistance). d, Measured current density maps near zero field (upper row) and at $B_\mathrm{ext}=0.54\,\mathrm{T}$ (lower row) for hole doping ($V_\mathrm{BG}=-0.4\,\mathrm{V}$), near charge neutrality ($V_\mathrm{BG}=0$) and for electron doping ($V_\mathrm{BG}=1.0\,\mathrm{V}$). The current in the graphene ring is enhanced for single carrier doping (arrows). Some current leakage occurs at contact S. Corresponding simulated current density maps in the diffusive regime are given in Fig. S14. The full dataset including other $B_\mathrm{ext}$ and $V_\mathrm{BG}$ is given in Figs. S15-S17. Scale bars, $1\,\mathrm{\,\mu{\rm m}}$.