Chiral Flat-Band Optical Cavity with Atomically Thin Mirrors

TL;DR

The study introduces a sub-wavelength planar cavity formed by two atomically thin MoSe$_2$ monolayer mirrors embedded in hBN, engineered to sustain a standing optical mode with flat dispersion. Using transfer matrix and FDTD simulations, the authors reproduce the experimental reflectance and dispersion, achieving a high quality factor of $Q\approx1060$ and an effective mode length of $L_{\text{eff}}\approx120$ nm. They demonstrate magnetically induced chirality via the valley Zeeman effect, extracting a g-factor of $g\approx-4.46$ and showing spin-polarized cavity modes that split with the magnetic field. The cavity mode is electrically and thermally tunable, with on/off switching and tunability on the order of 0.5 nm electrically and ~10 nm thermally (4–100 K). Overall, this work provides a scalable, 2D-platform for chiral cavity electrodynamics and spin–photon interfaces with potential for integration into nano-photonic systems.

Abstract

A fundamental requirement for photonic technologies is the ability to control the confinement and propagation of light. Widely utilized platforms include two-dimensional (2D) optical microcavities in which electromagnetic waves are confined between either metallic or distributed Bragg reflectors. Recently, transition metal dichalcogenides hosting tightly bound excitons with high optical quality have emerged as promising atomically thin mirrors. In this work, we propose and experimentally demonstrate a sub-wavelength 2D nano-cavity using two atomically thin mirrors with degenerate resonances. Angle-resolved measurements show a flat band, which sets this system apart from conventional photonic cavities. Remarkably, we demonstrate how the excitonic nature of the mirrors enables the formation of chiral and tunable optical modes upon the application of an external magnetic field. Moreover, we show the electrical tunability of the confined mode. Our work demonstrates a mechanism for confining light with high-quality excitonic materials, opening perspectives for spin-photon interfaces, and chiral cavity electrodynamics.

Figures (15)

• Figure 1: Design and fabrication of a cavity based on atomically thin mirrors. a) Mechanism for the realization of a nano-cavity based on atomically thin mirrors. Upper panel: Due to the high optical quality of the exciton in the material, the monolayer (ML) effectively acts as a mirror at the resonant wavelength. Lower panel: stacking two mirrors separated by dielectric material can lead to the formation of optical modes in the structure. b) Schematic representation of the TMD nano-cavity device: two atomically thin MoSe$_2$ mirrors embedded in hBN confine the electromagnetic mode. c-d) Individual reflectance spectra of the component monolayers before stacking the final device (red). The black lines show TMM fittings calculated by using a Lorentz oscillator model with the decay rates indicated in each panel. e) Simulation of the device reflectance calculated via TMM simulations. The inset shows a zoom-in of the reflectance and the corresponding Mode Effective Length calculated via FDTD, in a reduced range of wavelengths. f) Electric field intensity distribution from FDTD simulation. The minimum in both the reflectance spectrum and effective mode length (e), and enhancement of the electric field intensity profile at resonance (f) indicate the formation of a standing optical mode. g) TMM simulation of the device's spectrum upon variable exciton energy of the top monolayer $\rm{X}_{\rm top}$. $\rm{X}_{\rm bottom}$ denotes the excitonic resonance of the bottom monolayer and $\Delta\!=\!\rm{X}_{\rm top}-\rm{X}_{\rm bottom}$. The formation of a cavity mode manifests as a minimum in the reflectance for the range of parameters indicated by the dashed white ellipse, and its energy can be manipulated by detuning the resonances of the component MoSe$_2$ mirrors.
• Figure 2: Experimental characterization of the cavity sample. a) Microscope picture of the nano-cavity device with hBN layers and MoSe$_2$ bottom and top layers indicated in black, red, and blue, respectively. b) Experimental reflectance spectrum of the device. As theoretically predicted, the confined optical mode manifests as a narrow minimum in the reflectance spectrum (indicated by the arrow). c) PL spectrum of the device. The central emission (X$_{0}$) coincides with the device's resonant wavelength. A secondary peak from charged excitonic states is observed at longer wavelengths (X$^{\pm}$). d) Nanocavity dispersion calculated via TMM simulation. The confinement mechanism makes the cavity mode flat within our NA. e) Experimental dispersion of the device measured via far-field imaging. As theoretically predicted, the optical mode is flat in momentum.
• Figure 3: Chiral behavior induced by an external magnetic field $B$. a) Device's reflectance spectra for the orthogonal circular polarization states $\sigma^+$ (blue) and $\sigma^-$ (red) at three different values of $B$: 0 T (bottom), 5 T (middle), and 10 T (top). The insets show a depiction of the mechanism by which the chirality is established: the modes are degenerate in the absence of a magnetic field (black scheme), but the mode split in the presence of a magnetic field and exhibits a chiral light-matter response (blue and red scheme). The data is collected at a different spot than figure \ref{['device']}. b) Reflective circular dichroism of the nano-cavity device for increasing $B$. c) Energy difference between the $\sigma^+$ and $\sigma^-$ cavity modes as a function of $B$. A linear regression indicates a value of the magnetic factor g$=\!-4.46\pm0.45$; in good agreement with reported values and theoretical predictions.
• Figure 4: Tuning mechanisms of the optical mode. a) Independent electrical contacts on each MoSe$_2$ mirror (as shown in the inset) give control over the charge density, and hence over the excitonic resonance energy and oscillator strength. As a result, the cavity mode can be turned off (Blue line) or it can be tuned over a range of $\sim0.5$ nm, as shown in panel b. c) Pump intensity-dependent reflectance spectrum. The pump intensity axis (horizontal) does not follow a linear trend, because the power was not modified linearly. As the pump power increases, the optical mode red-shifts and broadens due to thermal fluctuations and saturation of the TMDs. After a critical intensity $I_p\!\approx\!7\!\times\!10^{-3}$ W$/\mu$m$^2$, the mode completely vanishes. d) Temperature dependence of the optical mode collected with a $10^{-4}$ W/$\mu$m$^2$ white pump. The data shows a tunability of $\approx\!10$ nm in the range of 4 K to 100 K. At $T\!=\!200$ K the mode is not identifiable anymore. In panels a) and d), the arrows serve as a guide for the eye to track the modification of the optical mode.
• Figure S1: Reflectance of the cavity as a function of cavity thickness and non-radiative decay rate. (A) Reflectance of the cavity formed by two TMD monolayers ($\lambda_0=756.2$ nm, $\Gamma_{\text{r}}=4.38$ meV, $\Gamma_{\text{nr}}=0.2$ meV) in air for different cavity thickness. The mode is not visible in the reflectance spectrum when the thickness of the cavity is exactly $\lambda_0/2$, as marked by the white dashed line. (B) Reflectance of the cavity for varying $\Gamma_{\text{nr}}$ and a cavity thickness of 350 nm ($\sim 0.46 \lambda_0$).