Coherent momentum control of forbidden excitons

Abstract

A double-edged sword in two-dimensional material science and technology is optically forbidden dark exciton. On the one hand, it is fascinating for condensed matter physics, quantum information processing, and optoelectronics due to its long lifetime. On the other hand, it is notorious for being optically inaccessible from both excitation and detection standpoints. Here, we provide an efficient and low-loss solution to the dilemma by reintroducing photonics bound states in the continuum (BICs) to manipulate dark excitons in the momentum space. In a monolayer tungsten diselenide under normal incidence, we demonstrated a giant enhancement (~1400) for dark excitons enabled by transverse magnetic BICs with intrinsic out-of-plane electric fields. By further employing widely tunable Friedrich-Wintgen BICs, we demonstrated highly directional emission from the dark excitons with a divergence angle of merely 7°. We found that the directional emission is coherent at room temperature, unambiguously shown in polarization analyses and interference measurements. Therefore, the BICs reintroduced as a momentum-space photonic environment could be an intriguing platform to reshape and redefine light-matter interactions in nearby quantum materials, such as low-dimensional materials, otherwise challenging or even impossible to achieve.

Fig. 1. Dark exciton brightening and directional emission.

a Schematic of directional emission of dark excitons in the WSe₂ monolayer with normally incident pumping light. The dark excitons PL signal can then be directionally emitted through the Friedrich-Wintgen bound states in the continuum (BIC) supported by the same PhC slab. b Split-band configuration of bright and dark exciton states. The spin-forbidden optical transition of the dark exciton (X_D) is brightened by the converted ${\mathbf{E}}_{\mathit{\perp }}$ with enhancement on the top surface of the PhC slab. CB, conduction band; VB, valence band. c A scanning electron microscope (SEM) image of the PhC slab made of silicon nitride (Si₃N₄). d and e BIC, and cavity modes obtain optical confinement in momentum (k) and real (x) space, respectively. f A sketch of the optical band structure of the PhC slab with three types of the BICs: ① and ④ are the on-Γ symmetry-protected BICs, ② is the off-Γ accidental BIC, and ③ is the Friedrich-Wintgen BIC due to the destructive interference of resonances belonging to different bands (red and blue).

Fig. 2. Brightening of dark excitons with BICs.

a The band structure of a PhC slab that supports a symmetry-protected on-Γ BIC with a zero-degree incident angle. The blue bands are the transverse magnetic mode-like (TM-like) bands whereas the red bands are the transverse electric mode-like (TE-like) bands. Only four of the bands (solid lines) can be observed under p-polarized incident light. The PhC only supports the on-Γ BIC to illustrate the dark exciton brightening. b The simulated (left) and the measured (right) angle-resolved reflection spectra mapping of the PhC slab. It is clear to see the two on-Γ BICs at wavelengths 694 nm and 750 nm, respectively. c Electric-field profile ${\mathbf{E}}_{\mathbf{z}}/{\mathbf{E}}_{\mathbf{0}}$ of the on-Γ BICs, plotted on the top surface of the PhC slab (top) and the y = −r/2 slice (bottom). d The reflection spectrum with an oblique incident angle of 3° is shown by the black dashed line, while the maximum local electric field amplitude enhancement ratio on the top of the PhC slab is plotted in red. WSe₂ monolayer was considered. e The PL spectra of dark excitons and bright excitons. The blue spectrum was taken when the pump laser matched the on-Γ BICs at the wavelength of 694 nm (on-BIC) whereas the red spectrum was taken when the pump laser was at the wavelength of 647 nm (off-BIC). f A log plot of the power dependence of PL intensity of dark excitons. The black line is a fit of the dark exciton emissions exhibiting a linear power dependence. The fitted slop α is 0.9 indicating the PL stem from dark excitons rather than bi-excitons.

Fig. 3. Tunable Friedrich-Wintgen BICs.

a The dispersion spectra of the PhC that supports BICs. The Friedrich-Wintgen BIC due to the interference of two TM-like bands is highlighted by the white dashed box. b A close look of the Friedrich-Wintgen BIC at a wavelength of 770 nm and oblique incident angle of 47.85° (red line). The white dashed line indicates the origin of the two modes. c Spectra at a series of different incident angles. Avoided crossing and linewidth vanishing of the lower branch band at 47.85° are observed due to the interference between the two modes. d Quality factors (Q-factors) of two bands that form the Friedrich-Wintgen BIC as a function of the oblique incident angle. The blue circles and the red circles represent the Q-factors of the upper branch and the lower branch of the avoided crossing bands, respectively. Q-factors of the lower branch are rapidly increasing when the oblique incident angle approaches 47.85° where the Friedrich-Wintgen BIC occurred. e Friedrich-Wintgen BIC modes for X_D directional emission are tunable for different deflection angles. The thicker the PhC slab, the higher the deflection angle of the Friedrich-Wintgen BIC emission channel. f Quasi-linear relations (blue) between the deflection angle by Friedrich-Wintgen BICs and the PhC slab thickness. The Friedrich-Wintgen BIC can be tuned in the momentum space from 31.4° to 59.5° and maintain the wavelength close to ~770 nm (red).

Fig. 4. Directionality control of dark excitons.

a PL emission momentum distribution mapping with ${\mathbf{k}}_{\mathbf{x}}$ and ${\mathbf{k}}_{\mathbf{y}}$ axis. Four shining emission spots, located at the Γ-X line and ${\mathbf{k}}_{\mathbf{x}}$ or ${\mathbf{k}}_{\mathbf{y}}$= 0.74 with C₄ symmetry, are clearly visible. b Polarization analysis of the PL emission momentum distribution in a. The four shining emission spots show radial polarization indicating they are from dark excitons. c Angle-resolved PL emission spectra mapping extracted from y-polarized PL emission momentum distribution mapping in b. It is clear to see the dark exciton directional emissions have small divergence angles at wavelengths of around 772 nm and towards oblique emission angles of around 48°. d The measured (red solid line) and FDTD simulated (dark green dashed line) PL intensity as a function of the in-plane momentum (${\mathbf{k}}_{\mathbf{y}}/\mathbf{k}$) along the y-direction. The full-width-half-maximum (FWHM) of the measured X_D emission lobes is 7° indicating the ultra-low divergence angle of the directional emission. e Spectra extracted from oblique angles of 48° and 23° for the dark exciton emission and the bright exciton emission, respectively. f The simulated PL emission momentum distribution by the Lumerical FDTD. Four shining emission spots show high correspondence to the measured PL emission pattern in a.

Fig. 5. Room-temperature coherence of the directional emission.

Momentum distribution and spatial interference enabled by a cylindrical lens for the directional emission of dark excitons supports an interference pattern b. The destructive interference in the middle of b is due to a π-phase shift between the left and right parts of the light field in a, showing that the directional emission is strongly coherent at room temperature. Momentum distribution and spatial interference for a coherent laser beam. The center of d is brighter than that of c, which is caused by constructive interference. Momentum distribution and spatial interference for incoherent bright exciton emission of monolayer WSe₂ on SiO₂/Si substrate. The intensity profile of f is similar to that of e because the bright exciton lots its valley coherence at room temperature.