Imaging the Local Charge Environment of Nitrogen-Vacancy Centers in Diamond

Characterizing the local internal environment surrounding solid-state spin defects is crucial to harnessing them as nanoscale sensors of external fields. This is especially germane to the case of defect ensembles which can exhibit a complex interplay between interactions, internal fields, and lattice strain. Working with the nitrogen-vacancy (NV) center in diamond, we demonstrate that local electric fields dominate the magnetic resonance behavior of NV ensembles at a low magnetic field. We introduce a simple microscopic model that quantitatively captures the observed spectra for samples with NV concentrations spanning more than two orders of magnitude. Motivated by this understanding, we propose and implement a novel method for the nanoscale localization of individual charges within the diamond lattice; our approach relies upon the fact that the charge induces a NV dark state which depends on the electric field orientation.

Figure 1

(a) Typical optically detected magnetic resonance (ODMR) spectrum of an electron-irradiated and annealed type-Ib diamond sample ($S1$) at zero magnetic field. The spectrum exhibits heavy tails which cannot be reproduced by either a double Lorentzian or a Gaussian (orange fit) profile. The blue theory curve is obtained via our microscopic charge model. (Left inset) A typical zero-field spectrum for a single NV center shows only a single resonance. (Right inset) Schematic depicting an equal density of positive (e.g., ${\mathrm{N}}^{+}$) and negative (e.g., NV) charges, which together create a random local electric field at each NV center’s position. (b) Nanoscale localization ($\sim 5\mathrm{nm}$) of a single positive charge via dark-state spectroscopy of an isolated NV center. The shaded regions indicate the probable location of the charge, with darker areas indicating a higher likelihood. The percentages shown correspond to the confidence intervals of the dark and light regions, respectively. (c) Analogous localization of a more proximal charge defect ($\sim 2\mathrm{nm}$) for a different NV center.

Figure 2

ODMR spectra at zero magnetic field for (a) a type-Ib untreated diamond sample ($S5$) and (b) a type-IIa electron-irradiated and annealed sample ($S3$). The spectra portray the two qualitative regimes one expects based upon the average electric field strength, as shown schematically in the right panel of Fig. 3. The blue theory curve is obtained via our microscopic charge model. (Inset) The spectrum for $S3$ at a magnetic field $\sim 45\mathrm{G}$ exhibits three identical hyperfine resonances.

Figure 3

Both strain and electric fields lead to (a) shifting ${\mathrm{\Pi }}_z$ and (b) splitting $2{\mathrm{\Pi }}_{\perp }$ of the $|m_s=\pm 1⟩$ manifold. (c) When averaged over an ensemble of NV centers, random local strain fields lead to a single broad spectral feature (at large strain). (d) By contrast, random local electric fields lead to two distinct spectral regimes: at small electric fields, the center hyperfine resonance splits, leading to a total of four resolvable features ($S3$); at large electric field, one obtains the characteristic split resonance seen in typical high-density NV ensembles ($S1$, $S5$).

Figure 4

Charge localization via dark-state spectroscopy. (a) Single NV ODMR spectra (untreated type-Ib diamond) for two different microwave polarizations, ${\varphi }_{\mathrm{MW}}$, depicting the reversal of the split-peak imbalance. The data correspond to the localized charge shown in Fig. 1. (Inset) Top view through the NV axis ($\widehat{z}$), where ${\varphi }_E$ and ${\varphi }_{\mathrm{MW}}$ are defined with respect to $\widehat{x}$ (along a carbon-vacancy bond). (b) Analogous split-peak imbalance data corresponding to the localized charge shown in Fig. 1. (c) By changing the microwave polarization, ${\varphi }_{\mathrm{MW}}$, one can directly control the coupling strength between the $|0⟩$ and $|\pm ⟩$ states. (d) Measuring the change in the imbalance as a function of ${\varphi }_{\mathrm{MW}}$ allows one to extract the orientation of the electric field. Dashed lines indicate the polarizations plotted in (a).