Quantum imaging of current flow in graphene

Abstract

Since its first discovery in 2004, graphene has been found to host a plethora of unusual electronic transport phenomena, making it a fascinating system for fundamental studies in condensed matter physics as well as offering tremendous opportunities for future electronic and sensing devices. Typically, electronic transport in graphene has been investigated via resistivity measurements; however, these measurements are generally blind to spatial information critical to observing and studying landmark transport phenomena in real space and in realistic imperfect devices. We apply quantum imaging to the problem and demonstrate noninvasive, high-resolution imaging of current flow in monolayer graphene structures. Our method uses an engineered array of near-surface, atomic-sized quantum sensors in diamond to map the vector magnetic field and reconstruct the vector current density over graphene geometries of varying complexity, from monoribbons to junctions, with spatial resolution at the diffraction limit and a projected sensitivity to currents as small as 1 μA. The measured current maps reveal strong spatial variations corresponding to physical defects at the submicrometer scale. The demonstrated method opens up an important new avenue to investigate fundamental electronic and spin transport in graphene structures and devices and, more generally, in emerging two-dimensional materials and thin-film systems.

Keywords: Graphene devices; Nano-magnetometry; Nitrogen-vacancy center; graphene.

Fig. 1. Graphene ribbons on a diamond imaging platform.

(A) Schematic of the experiment. The diamond platform consists of a diamond chip hosting a layer of near-surface NV centers. The graphene devices are fabricated directly on the diamond chip, which is mounted on a coverslip equipped with an MW resonator. The NV centers’ PL under green laser and MW excitations is imaged on a camera to form the magnetic field image. (B) Optical micrograph of the final device. Apparent on the diamond are metallic contacts, and wire bonds, used for current injection in the graphene ribbons. (C) Bright-field image recorded with the camera, focused on a graphene ribbon (not visible). (D) PL image of the same area under laser excitation. The graphene ribbon is now visible because of PL quenching. (E) Line cut across the ribbon extracted from (D) (white dashed line). a.u., arbitrary units.

Fig. 2. Magnetic field imaging and reconstruction of the current density.

(A) PL image of the graphene ribbon under study, defining the xyz reference frame. (B) ODMR spectrum of the NV centers in a single pixel near the graphene under a positive (red dots) or negative (blue dots) applied current. Solid lines are data fit to a sum of eight Lorentzian functions. Inset: Energy levels of the electron spin of a single NV center, showing the Zeeman splitting 2γ_eB_∥ between m_s = ±1, where m_s is the spin projection along the NV axis, B_∥ is the magnetic field projection, and γ_e is the electron gyromagnetic ratio. The two electron spin resonances are indicated by green arrows. The experimental spectrum comprises eight resonances in total due to the four possible crystallographic orientations, allowing vector magnetometry. (C) Maps of the B_x (top), B_y (middle), and B_z (bottom) components of the magnetic field produced by a total current I = 0.8 mA. (D) Maps of the J_x (top) and J_y (middle) components of the current density reconstructed from (C). The bottom panel shows the norm of the current density, $|\vec{\mathit{J}}|$. The black arrows represent the vector $\vec{\mathit{J}}$ (length proportional to $|\vec{\mathit{J}}|$; threshold $|\vec{\mathit{J}}|$ > 30 A/m). Scale bars, 10 μm (C and D).

Fig. 3. Current flow near defects in graphene.

(A) Maps of the norm of the current density, $|\vec{\mathit{J}}|$, in two different graphene ribbons driven by a total current I = 0.8 mA. (B) Zooms of selected areas from (A). The black arrows represent the vector $\vec{\mathit{J}}$ (length proportional to $|\vec{\mathit{J}}|$; threshold $|\vec{\mathit{J}}|$ > 30 A/m). (C) PL images corresponding to the same areas as in (B). (D) Corresponding SEM images. Scale bars, 5 μm.

Fig. 4. Current flow near metallic contacts.

(A and B) SEM images of two junctions between Ti/Au electrodes and a graphene ribbon. The insets show the corresponding PL images. (C and D) Maps of the norm of the current density, $|\vec{\mathit{J}}|$, under a total current I = 0.8 mA, corresponding to the two junctions shown in (A) and (B). The black dashed lines indicate the edges of the metallic electrodes, as extracted from the PL images. The black arrows represent the vector $\vec{\mathit{J}}$ (length proportional to $|\vec{\mathit{J}}|$; threshold $|\vec{\mathit{J}}|$ > 30 A/m). Scale bars, 10 μm.