Coherent Spins in van der Waals Semiconductor GeS2 at Ambient Conditions

TL;DR

We report room-temperature optically active spin defects in the vdW semiconductor $β$-GeS$_2$ and demonstrate coherent control of these spins. The defects behave as spin-1/2 with no zero-field splitting, described by a weakly coupled spin-pair model; ODMR and Rabi data are captured by a Lindblad master equation, with $g = 2.000 \pm 0.007$ and kinetic parameters extracted from experiments. Coherence is extended from $T_2 \approx 64.5$ ns (Hahn echo) to $T_2 \approx 1.315$ μs via Carr-Purcell-Meiboom-Gill dynamical decoupling with $N = 32$, following a scaling $T_2 \propto a N^{0.691}$, while $T_1$ remains longer at $14.5 \pm 4.3$ μs; first-principles work identifies Ge$_S^{-1}$ and C$_S^{-1}$ as plausible spin-defect candidates with localized spin densities. These results establish $β$-GeS$_2$ as a promising 2D platform for room-temperature quantum sensing and spin-qubit studies, with clear pathways to longer coherence times in higher-quality crystals.

Abstract

Optically active spin defects in van der Waals (vdW) materials have recently emerged as versatile quantum sensors, enabling applications from nanoscale magnetic field detection to the exploration of novel quantum phenomena in condensed matter systems. Their ease of exfoliation and compatibility with device integration make them promising candidates for future quantum technologies. Here we report the observation and room-temperature coherent control of spin defects in the high-temperature crystalline phase of germanium disulfide ($β$-GeS2), a two-dimensional (2D) semiconductor with low nuclear spin density. The observed spin defects exhibit spin-1/2 behavior, and their spin dynamics can be explained by a weakly coupled spin-pair model. We implement dynamical decoupling techniques to extend the spin coherence time (T$_2$) by a factor of 20. Finally, we use density functional theory (DFT) calculations to estimate the structure and spin densities of two possible spin defect candidates. This work will help expand the field of quantum sensing with spin defects in van der Waals materials.

Figures (5)

• Figure 1: (a) The crystal structure of $\beta$-GeS$_2$. The black box in the top view denotes the unit cell and the lower figure denotes the side view of the lattice. (b) Microscope Images of the $\beta$-GeS$_2$ sample studied in the experiment. The scale bar is 10 $\mu$m. (c) Confocal scans of the sample under 532 nm excitation. The scale bar is 10 $\mu$m. (d) Photoluminescence spectrum of the spin defects under 532 nm laser excitation. The inset shows the Raman spectrum with a sharp peak at 360 cm$^{-1}$. (e) ODMR spectrum measured under 532 nm laser and 1 W of MW excitation. The black curves are fits of the data to a Lorentzian function. (f) Dependence of the ODMR peak frequency on an external magnetic field perpendicular to the sample surface.
• Figure 2: (a) Rabi Oscillations of the spin defects at different MW powers. The solid lines are fits to the spin-pair model predicted oscillations. The top schematic shows the laser and MW pulses used in the experiment. (b) Fitted Rabi frequency vs the square root of the MW power. The solid red line shows a linear fit of the data. (c) The spin pair model consisting of 2 spin defects located a distance of $\gtrsim$ 1 nm from each other. The 3 level system used to model the system is shown at the bottom. The singlet state with both electrons on the same defects is on the left side while the state with the electrons on different defects is on the right. $\Gamma_{10}, \Gamma_{20}$ are the rate constants from $\ket{S,T_0},\ket{T_\pm}$ to $\ket{S_0}$ respectively and $\gamma_\phi$ is the rate between $\ket{S,T_0}$ and $\ket{T_\pm}$. $\Omega$ is the Rabi driving frequency. (d) Simulated ODMR contrast from the spin pair model with different values of the $\Gamma_{10}, \Gamma_{20}$ and $\gamma_\phi$, showing how the model can simulate the various kinds of decay in the Rabi oscillations observed experimentally. All constants have units of $\mu$s$^{-1}$.
• Figure 3: (a) $T_1$ measurements and the pulse sequence schematic used in performing the $T_1$ experiment. The $\pi$ pulse duration is determined from the Rabi experiments as shown in Figure \ref{['figure_2']}. (b) Ramsey decay for the spin defects. Due to a slight detuning between the resonant frequency and the drive, some oscillations are visible. (c) Experimentally observed charged state dynamics for the spin defects. The top schematic shows the laser pulse sequence used in the experiment. Note that this measurement is performed without any MW applied, and hence only measures evolution of the polarized state with time.
• Figure 4: (a) Measurement of the coherence time $T_2$ of the spin defects in $\beta$-GeS$_2$ via the Hahn Echo pulse sequence as shown in the schematic. The red line shows a stretched exponential fit. (b) Extending the $T_2$ using the CPMG pulse sequence for different number N of $\pi$ pulses. The schematic shows the pulse sequence used in the experiment for each N. (c) The extended $T_2$ plotted as a function of number of pulses in the sequence and fitted to a power law $\propto a N^\gamma$ with $\gamma$ = 0.69.
• Figure 5: (a) Energy diagram showing the energy levels of the two possible defects in $\beta$-GeS$_2$ in the bandgap. (b), (c) Calculated spin density for the Ge$_S^{-1}$ and C$_S^{-1}$ defects in the lattice respectively.