Spin defects in hexagonal boron nitride as two-dimensional strain sensors

Abstract

Lattice deformation is a powerful way to engineer the properties of two-dimensional (2D) materials, making their precise measurement an important challenge for both fundamental science and technological applications. Here, we demonstrate that boron-vacancy (V$_\text{B}^-$) color centers in hexagonal boron nitride (hBN) enable quantitative strain sensing with sub-micrometer spatial resolution. Using this approach, we precisely quantify the strain-induced shift of the E$_{\rm 2g}$ Raman mode in a multilayer hBN flake under uniaxial stress, establishing V$_\text{B}^-$ centers as a new tool for strain metrology in van der Waals heterostructures. Beyond strain sensing, our work also highlights the unique multimodal sensing functionalities offered by V$_\text{B}^-$ centers, which will be valuable for future studies of strain-engineered 2D materials.

Figures (4)

• Figure 1: (a) Principle of the experiment. V$_\text{B}^-$ spin defects in a thin hBN flake deposited on a strain-transmitting substrate are incorporated into a strain cell, and employed as local strain sensors. The 100-nm thick Au coating is omitted for clarity. (b) Optical image of the sample placed into the strain cell. (c) PL raster scan recorded around the gap of the sample, revealing the PL signal produced by V$_\text{B}^-$ centers in hBN. The green laser excitation power is set to $1$ mW. The stretching directions are indicated by the white arrows.
• Figure 2: (a) Energy level structure of the V$_\text{B}^-$ center's spin triplet ground state illustrating the impact of tensile strain. (b) ODMR spectra recorded at the center of the hBN flake [see Fig. 1(c)] for different voltages applied to the strain cell. The solid lines are data fitting with Lorentzian functions from which the parameters $D_\varepsilon$ and $E$ are extracted. (c) Strain $\varepsilon_{\rm tot}$ (right axis) transferred to the hBN flake when the voltage applied to the strain cell gradually increases from $0$ to $5$ V (black markers) and then returns back to $0$ V (red markers). Strain values are obtained by converting measurements of the zero-field splitting parameter $D_\varepsilon$ (left axis) into strain using $g_{1}=-245$ MHz/% and $D_0=3.47$ GHz. The error bars correspond to the uncertainty on the strain values, which mainly arise from the uncertainty ($\sim 4\%$) on the coupling parameter $g_1$. The dashed lines is data fitting with a linear function. The inset shows the evolution of the orthorhombic splitting $E$ with voltage.
• Figure 3: Strain ($\varepsilon_{\rm tot}$) profiles measured along the linecut shown in the PL scan (left panel) for different voltages applied to the strain cell. The dashed lines are data fitting with a linear function from which we extract a strain gradient of about $\sim5\times10^{-3}$ %/$\mu$m for the three strain profiles.
• Figure 4: (a) Evolution of the strain $\varepsilon_{\rm tot}$ (right axis) in the hBN flake when the voltage applied to the strain cell gradually increases from $0$ to $10.5$ V (black markers) and then returns back to $0$ V (red markers). These values are obtained by converting measurements of the zero-field splitting parameter $D_\varepsilon$ (left axis) into strain using $g_{1}=-245$ MHz/% and $D_0=3.47$ GHz. The error bars correspond to the uncertainty on the strain values, which mainly arise from the uncertainty ($\sim 4\%$) on the coupling parameter $g_1$. (b) Frequency of the E$_{\rm 2g}$ Raman mode in hBN as a function of in-plane strain $\varepsilon_{\rm tot}$. Data fitting with a linear function (red dashed line) yields a strain-induced shift of the E$_{\rm 2g}$ Raman-mode of $-24.9(2)$ cm$^{-1}/\%$. The inset shows typical Raman spectra recorded for two different values of $\varepsilon_{\rm tot}$. The width of the Raman signal ($\sim 15$ cm$^{-1}$) is not significantly modified with applied stress.