Spatiotemporal Mapping of Photocurrent in a Monolayer Semiconductor Using a Diamond Quantum Sensor

The detection of photocurrents is central to understanding and harnessing the interaction of light with matter. Although widely used, transport-based detection averages over spatial distributions and can suffer from low photocarrier collection efficiency. Here, we introduce a contact-free method to spatially resolve local photocurrent densities using a proximal quantum magnetometer. We interface monolayer MoS2 with a near-surface ensemble of nitrogen-vacancy centers in diamond and map the generated photothermal current distribution through its magnetic field profile. By synchronizing the photoexcitation with dynamical decoupling of the sensor spin, we extend the sensor's quantum coherence and achieve sensitivities to alternating current densities as small as 20 nA per micron. Our spatiotemporal measurements reveal that the photocurrent circulates as vortices, manifesting the Nernst effect, and rises with a timescale indicative of the system's thermal properties. Our method establishes an unprecedented probe for optoelectronic phenomena, ideally suited to the emerging class of two-dimensional materials, and stimulates applications towards large-area photodetectors and stick-on sources of magnetic fields for quantum control.


Introduction
The extraordinary features of two-dimensional van der Waals (2D vdW) systems have opened new directions for tailoring the interaction of light with matter, with potential to impact technologies for imaging, communications, and energy harvesting. The detection of photo-induced carriers is critical to realizing practical photosensing and photovoltaic devices [1][2][3] , as well as to characterizing novel photo-responses, including optical manipulation of spin and valley indices 4,5 , circular 6-8 and shift 9,10 photocurrents driven by non-trivial Berry curvature and scattering-protected photocurrents at a Dirac point 11 . Transport-based detection of photocurrents in 2D materials is susceptible to inefficient photocarrier extraction, requiring light to be directed near junctions with strong built-in electric field, and thus complicates the scale-up of devices to practical sizes [1][2][3] . To expand our understanding of light-matter interaction and overcome existing technical limitations, new photodetection approaches that offer high spatial and temporal resolution are needed.
In this work, we demonstrate a novel technique using an embedded quantum magnetometer [12][13][14] to detect and spatially resolve photocurrent densities via their local magnetic field signature. We transfer a monolayer MoS 2 (1L-MoS 2 ) sheet grown by metal-organic chemical vapor deposition 15 (MOCVD) onto a diamond chip hosting a near-surface ensemble of nitrogenvacancy (NV) centers. The magnetic field due to photocurrents, driven in this case by the photothermoelectric effect (PTE) 16,17 , modifies the quantum precession of the NV center spin, inducing a phase that can be optically detected [18][19][20] . Due to the near-field nature of our probe, our method does not require remote carrier extraction, and thus eliminates the need for electrical contacts and avoids challenges due to carrier trapping and potential fluctuations in large-area devices 2 . Moreover, in contrast to scanning photocurrent microscopy [6][7][8][9][10][11]16 , our technique provides diffraction-limited spatial resolution for both excitation and detection (Fig. 1a). This enables detailed spatial information to be extracted even when the net photocurrent between two contacts in a conventional measurement is zero.
With wide phase space applicability and potential nanoscale spatial resolution, NV magnetometry has emerged as a premier tool for probing current distributions in materials 13 , revealing insights on the structure of vortices in high-T c superconductors 21,22 and the effect of microscopic inhomogeneity on transport in graphene 23 and nanowires 24 . These demonstrations all probed direct current (dc) flow and were accordingly limited in sensitivity by the inhomogeneous dephasing time T 2 * of the NV center. Here, we leverage the ability to control the timing of the photoexcitation to implement for the first time a "quantum lock-in" protocol to isolate alternating photocurrents. This protocol simultaneously decouples the NV center from wideband magnetic noise, extending its coherence time to the homogeneous T 2 limit, and achieves a sensitivity of 20 nA/µm for alternating current (ac) densities, fifty times smaller than previous work on dc current sensing in graphene (~1 µA/µm in Ref. 23 ). Moreover, in contrast to dc sensing, our ac technique opens the investigation of the dynamics of photocarrier generation. Through changing the repetition rate of the photo-excitation pulses, we can resolve non-equilibrium response over a temporal bandwidth spanning from 1 ⁄~ 10 kHz to an upper range of ~10 MHz, set by achievable driving speeds on the NV center spin 25 .  nm excitation partially overlaps the NV emission spectrum and overwhelms the signal of single NV centers, precluding their identification upon coverage (Fig. 1e). To increase the NV signal and facilitate arbitrary spatial mapping, we instead utilize an engineered diamond sample hosting an ensemble of near-surface NV centers (~40 nm deep; ~85 NV centers per focused optical spot).

I. Hybrid NV-MoS 2 Photosensing Platform
Additionally, we band-pass filter the detected PL between 690 nm and 830 nm to predominantly isolate NV center emission, as shown in the room-temperature PL spectra of monolayer MoS 2 and a typical ensemble NV sample (Fig. 1f). Importantly, the excitation wavelength for photocarriers in MoS 2 must be sufficiently longer than the zero-phonon line of the NV center (637 nm) to minimize thermally-assisted absorption 28 by the NV center during the photocurrent sensing duration. Excitation and subsequent decay of the NV center will decohere the spin superposition, leading to reduced read-out contrast and sensitivity 29 . We excite at 661 nm, but have verified that our effects persist for longer excitation wavelength (see Supplementary Section 5.1).
Our photocurrent sensing protocol is based on an XY8-N dynamical decoupling sequence commonly used for the NV-based detection of ac fields from the precession of remote nuclei [18][19][20] .
However, in contrast to applications in nuclear magnetic resonance, here we directly control both the frequency and the phase of the targeted oscillating field through the timing of the photoexcitation pulses (Fig. 2a). This enables us to sweep the phase of the oscillating field relative to the NV sensing sequence and examine the full dependence, increasing sensitivity compared to measuring an averaged response over random phases. We prepare the superposition state | ⟩ 1 √2 ⁄ |0⟩ | 1⟩) and allow it to evolve to | 1 √2 ⁄ |0⟩ | 1⟩) under the influence of photo-excitation and the XY8-N rephasing pulses (N repetitions of 8 -pulses). We first match the spacing between the -pulses to a half period of the photo-excitation frequency ( 1 2 ⁄ here) and probe the acquired phase for varying relative delays between the start of the -pulses and the photo-excitation (Fig. 2a). The X and Y-projections cos and sin , respectively, of the final state | are optically detected after an appropriate projection pulse on the NV center.
In essence, the delay of our "quantum lock-in" protocol plays the analogous role to the relative phase between the signal and reference oscillator in a classical lock-in measurement. If photoexcitation generates an instantaneous, square pulse current density ⃗ in the MoS 2 monolayer, then the phase accumulated by the NV center will be maximized for an optimal delay 0°. We denote this maximal accumulated phase as Φ, with its amplitude and sign determined by the amplitude and direction of the local current density. Alternatively, if the photocurrent rises and falls with a characteristic timescale (purple trace in Fig. 2a), maximum phase accumulation will occur for nonzero optimal delay ( 0°) (see Supplementary Section 4.1). For a current density ⃗ with sinusoidal time-dependence, the accumulated phase will depend on as Φ cos ). This form represents a good approximation to our data due to the smoothing effect of the photocurrent rise and fall times. In Fig. 2b, we plot the analytical behaviors for and under this model as a function of the delay and the maximal phase Φ.

II. Detection and Mapping of Photo-Nernst Currents
We first perform a photocurrent sensing protocol with N = 2 and = 7.6 s over an uncovered area of diamond (probe and excitation beams slightly offset). Consistent with negligible absorption by the NV center or bulk diamond at 661 nm, we cannot detect the presence of photoexcitation and measure 0 for all ( Supplementary Fig. S6). Remarkably, when we shift to an area where monolayer MoS 2 covers the diamond, we detect oscillations in and as is varied of the XY8 block, we can increase Φ linearly (Fig. 2f).
The maximum accumulated phase Φ represents a weighted time-integral of the ac magnetic field along the NV axis produced by the photocurrents. By modeling the pulse shape of ⃗ , we can estimate the final instantaneous field from the time-integrated field (Fig. 2a) via: where is a pulse shape dependent factor, Φ is measured in radians, and the factor of 0.5 stems from the 50% duty-cycle of the photo-excitation. The factor increases monotonically with from 1 for square pulses to 2 as → ∞ (see Supplementary Section 4.1). Unless otherwise stated, we utilize a constant factor 1.25, corresponding roughly to the range of our typical measurements ( = 7.6 s). In Fig. 2e, we resolve as small as 0.84 0.08 mG for about 2 hours of averaging time (0.14 0.05 mG for additional data shown in Supplementary Fig.   S8). From this, we assert a minimum sensitivity to a sheet current density of ~20 nA/µm flowing perpendicular to the NV axis (along the y-direction), which produces a field ~ 0. By scanning the probe beam relative to the excitation spot, we map the magnetic field distribution generated by the photo-Nernst vortex. In Fig. 3a and b, we present the measured for line scans along the x-and y-axes, respectively. Crucially, we show that changes sign as expected when the static magnetic field B is reversed, indicating that the chirality of the vortex also reverses (Fig. 3a). The solid lines in Fig. 3a  versus negative (Fig. 3a). For the y-direction, becomes slightly negative as we pass outside the ring of maximum current density and the z-component of the fringing field reverses ( Fig. 3b).
In Fig. 3c, we plot the current distribution ⃗ used to approximate the experimental field profile together with independent thermal modeling of the laser-induced temperature distribution in monolayer MoS 2 . The modeled ⃗ peaks at ~ 1.0 , in close agreement with the predicted location of the maximum thermal gradient (Supplementary Fig. S15). At our base temperature for the diamond substrate ( = 6 K), the photocurrent vortex is enhanced by the reduced thermal conductivity of monolayer MoS 2 and the large thermal interface resistance to the substrate, which permit large thermal gradients (~18 K/ max) and a spatial distribution significantly larger than the excitation spot size (Gaussian intensity with standard deviation 0.45 ). As increases, the thermal conductivity 32 and thermal interface conductance 33 both increase and we find that the detected at 0.95 diminishes, disappearing around 20 K (Supplementary Fig. S10).
Using ⃗ , we estimate that the integrated current for one side of the vortex is ~1.3 µA for an excitation power of 25 uW before the objective (85% transmission). This implies a Nernst photoresponsivity of ~60 mA/W for 226 G parallel to the NV axis (130 G perpendicular to the sample).
For the same magnetic field, this value for ungated monolayer MoS 2 is higher than the giant Nernst photo-responsivities reported for a graphene-hexagonal boron nitride heterostructure that is gatetuned to its van Hove singularities 31 . This enhancement in MoS 2 is consistent with its lower thermal conductivity and higher Seebeck coefficient stemming from a favorable density of states for its gapped band structure 16, 17 . In Supplementary Fig. S10, we verify that the Nernst photocurrent is linear in the external magnetic field and non-saturating up to 500 G, as expected for the low field regime 31 .
Our unique probe provides additional insight into the dynamics of photocarrier generation. In Fig. 3d, we examine the optimal delay between the NV driving and photoexcitation pulses as a function of , using a sequence with = 7.6 s. As the probe beam moves away from the excitation spot, increases. This effect can be explained if the rise time for the local photocurrent, which dominates the contribution to the local field, increases for larger | |. To corroborate this hypothesis, we map the leading edge of the photocurrent rise by varying the pulse spacing in the synchronized sensing protocol. To deduce , the value of the field at the end of the pulse, we need to account for variations in pulse shape as changes. For each set with different , we utilize the measured delay to infer the factor within our pulse shape model.
In Fig. 3e, we compare , for two different locations. We confirm an exponential rise to the photocurrent with a time constant ~ 1 s that increases for larger | |. The extracted rise times are sufficient to explain the measured , suggesting that no additional effects, such as carrier propagation from the excitation spot, contribute significantly to the delay (see Supplementary Section 5.5). Indeed, we find that is, to within error, independent of the external magnetic field, which would affect carrier propagation.
The rise times for can be compared to a model of system's transient thermal response.
Indeed, the rise time for the thermal gradient ⁄ increases for larger | | (Supplementary Section 6). This matches the qualitative experimental trend (Fig. 3c,d) and supports a picture of photocurrents generated locally by PTE. Interestingly, to approximate the microsecond-scale photocurrent rise times, we need to assume a heat capacity for monolayer MoS 2 that is significantly higher than theoretically predicted 34,35 . Our model estimates ~ 200 J/ kg * * for temperatures below ~50 K, while is generally taken 16 as 400 J/ kg * K for single crystal monolayer MoS 2 at 300 K. Even considering that we use polycrystalline MoS 2 , this discrepancy may suggest extrinsic contributions to the estimated . For example, excess heat capacity could arise from PMMA residue or a layer of cryopumped adsorbates, and the latter is known to significantly raise the measured low-temperature heat capacity of other low-dimensional materials 36,37 (see Supplementary Fig. S2). Further investigations under systematic outgassing and sample cleaning conditions are required to clarify this phenomena, as well as to explore potential applications toward the sensing of absorbed gases.
Finally, we demonstrate the ability to detect light without prior knowledge of its frequency or phase. Gating the light at a constant frequency with an independent controller, we examine the projection of the final state | as we scan the spacing of the XY8-8 sequence. When the frequency 1 2 ⁄ of the decoupling sequence matches to within a bandwidth Δ . 11⁄ , the average value of over random starting delays is diminished from its initial full projection, resulting in a resonant dip 19 . In Fig. 4, we demonstrate this unsynchronized detection scheme for three different frequencies = 65 kHz, 110 kHz, and 333 kHz. Due to the rise time of the PTE photocurrents, our sensitivity to optical power decreases for higher , necessitating stronger excitation to see the same contrast change. However, the NV sensing protocol itself is effective for frequencies up to several tens of MHz 25 and thus can be combined with faster photocurrent mechanisms for optimal photodetection.

Discussion
Our demonstration broaches wide-ranging opportunities for investigating fascinating opto-

Sample Fabrication
An NV center ensemble was created ~40 nm deep into an [001]-oriented diamond sample by 15  After optically initializing the NV spin into |0⟩, the XY8-N dynamical decoupling sequence applied to the NV center consists of 8N+2 qubit rotations:

2
Here, the subscript indicates the axis on the Bloch sphere for the qubit rotation, and { /2, indicates the rotation angle. The axis of the final /2 projection pulse determines which component , of the final spin superposition is rotated onto the |0⟩ (bright) state for readout.
The pulses are uniformly spaced by the interval , whereas the /2 pulses are spaced by /2.
The timing (frequency, delay) of the photoexcitation and NV microwave pulses can be synchronously controlled to nanosecond resolution using an arbitrary waveform generator.

Data Analysis and Modeling
All errorbars reported in our paper are 95% confidence intervals. Complete details of the data fitting, thermal modeling and stray field modeling are supplied in the Supplementary Information.