Understanding Surface-Induced Decoherence of NV Centers in Diamond

TL;DR

The paper develops a first-principles, multi‑scale framework to understand surface-induced NV decoherence in diamond by combining DFT-derived atomistic surface models with an extended cluster‑correlation expansion approach that incorporates both dissipative baths and hopping of surface spins. By systematically varying surface orientation, termination, and unpaired-electron density, the authors quantify the contributions of nuclear spins, static surface electrons, spin relaxation, and hopping dynamics to the Hahn-echo coherence time $T_2$, revealing orientation- and depth-dependent regimes and the critical role of hopping in reproducing experimental trends. Key findings include that H and F terminations strongly degrade $T_2$ at shallow depths, O and N terminations preserve bulk-like coherence beyond a few nanometers, and surface-spin hopping is essential to explain depth-dependent decoherence, with motional narrowing capable of restoring bulk-like behavior under fast spin dynamics. The work offers actionable surface-engineering guidelines and provides public access to ME-CCE codes, advancing the design of NV-based quantum sensors and information processors.

Abstract

Nitrogen vacancy centers (NV) in proximity to diamond surfaces are promising nanoscale quantum sensors. However, their coherence properties are negatively affected by magnetic and electric surface noise, whose origin and detailed impact have remained elusive. Using atomistic models of diamond surfaces derived with density functional theory, together with decoherence time calculations with cluster correlation expansion methods, we quantify the effects of surface crystallographic orientation and functionalization, and of the density of unpaired electrons on the NV Hahn-echo time $T_2$. We determine a crossover depth at which $T_2$ ceases to be limited by surface nuclear spins and recovers the bulk-limited value. We find that for static surface-electron baths, the ratio between the NV depth and the separation between surface electron spins determines a transition from fast-fluctuating to quasi-static noise, leading to a dependence of $T_2$ on orientation for specific surfaces. We also find that the modulation of $T_2$ by spin-phonon relaxations leads to motional-narrowing at sub-microsecond relaxation times. Importantly, our calculations show that it is only when accounting for surface-spin in-sequence hopping that measured $T_2$ values as a function of depth can be reproduced, thus highlighting the importance of hopping-mediated models to describe the surface spin noise affecting NV sensors. Overall, our work provides clear guidelines for engineering diamond surfaces to achieve enhanced NV coherence for quantum sensing and information processing applications.

Figures (15)

• Figure 1: Atomistic models of diamond surfaces. (a) Representative reconstructions of the (100) surface with different terminating species; Fluorine (green sphere), Oxygen (red sphere), and Nitrogen (brown sphere) were used to terminate a 2×1 reconstructed surface, while mixed hydroxyl/oxygen/hydrogen (OH/O/H) was used to terminate a 1×1 unreconstructed surface (b) Hydrogen‐terminated surfaces for four distinct crystallographic orientations: (100), (110), (111), and (113).
• Figure 2: Hahn-Echo T$_2$ at various NV depth from diamond surfaces with various terminations. (a) Result for (100) surfaces terminated with O, N, F, H are compared with those obtained for NV in bulk diamond and in the presence of a bare surface (see text). (b) Hahn echo T$_2$ for Fluorine (F) terminations across various surface orientations.
• Figure 3: Representative models of electron spins on diamond surfaces. (a-b). (100) and (111) surfaces with surface electron spins (black arrows) aligned to the NV quantization axis; the NV center is shown in orange and nearby $^{13}C$ nuclear spins in gray. (c). (100) surface electron in the presence of relaxation effects with relaxation time $T_1$(d). (100) surface electron spins subject to hopping, with rates $\Gamma_{hop}$; open circles indicate vacant sites. The direction of the external magnetic field $B_0$ is indicated in each case (see text).
• Figure 4: Computed Hahn echo T$_2$, for NV center for (100) and (111) surface against NV centers as a function of their depth from (100) (a) and (111) (b) surfaces, for various surface electron spin densities ($\rho$), as indicated in (b). Computed single stretched exponent of the Hahn-echo coherence function of NV centers as a function of their depth from (100) (c) and (111) (d) surfaces, for various surface electron spin densities ($\rho$), as indicated in (c). Log-log plot of the Hahn-echo coherence signal showing the temporal transition of the stretching factors at various depths of the NV center for (100) (e) and (111) (f) surface. $\mathcal{L}(t)$ indicates the computed coherence signal.
• Figure 5: Precession frequency $\omega$ of the most strongly coupled surface pseudo-spin as a function of NV center's depth for surface‐spin densities $\rho = 0.001\rm\ nm^{-2}$(a) and $\rho=0.01\rm\ nm^{-2}$(b). Computed Hahn–echo coherence time $T_{2}$ as a function of depth at $\rho=0.001\rm\ nm^{-2}$(c) and $\rho=0.01\rm\ nm^{-2}$(d). Solid brown lines indicate the results for (100) surface, and dashed orange lines for (111) surface. Vertical dashed lines indicate the characteristic depths at which the (111) surface exhibits its coherence “sweet spot.” (see text)