Superradiant Charge Density Waves in a Driven Cavity-Matter Hybrid

Abstract

Optical cavities enable strong, long-range, light-matter interactions that can drive collective ordering phenomena, such as superradiant self-organization in ultracold atomic gases. Extending these ideas to solid-state electron systems could enable continuous-wave optical control of electronic order, but is impeded by the mismatch between optical wavelengths and electronic length scales. Here, we propose a platform for realizing superradiant charge density waves (sCDWs) in doped, driven transition-metal dichalcogenides coupled to an optical cavity. A nanoscale grating generates electric fields at large in-plane optical momenta, allowing cavity photons to couple efficiently to electronic density fluctuations through exciton-polaron processes. Using a linear-stability analysis, we determine the threshold for superradiant ordering and map out the driven phase diagram. We show that tuning the grating periodicity to match the enhanced electronic density fluctuations - such as those near Wigner crystallization - substantially lowers the required pump intensity. Our results establish a novel route toward cavity-controlled electronic order in quantum materials.

Figures (4)

• Figure 1: Proposed experimental setup. (a) Monolayer TMD on a grated substrate illuminated by a pump laser (orange) and interacting with an optical cavity mode (red). The sample is tilted for optimal coupling to the cavity and leads can be unobstructively attached to perform transport measurements. (b) Simulated electric field close to one repeat unit of the grating. $E_x$ is the electric field along $x$ and $E_0$ is the pump field far away from the grating. The thin horizontal line above the grating boundary (staggered line) shows the position of the encapsulated TMD sample. (c) Level diagram for the proposed light-matter coupling scheme. Pump and cavity fields can excite or annihilate excitons that combine with electrons $\ket{e}$ from opposite valleys to form attractive polarons $\ket{A}$. The pump frequency is closely detuned to the cavity mode and the attractive polaron branch. (d) Schematic phase diagram as a function of pump laser intensity and temperature: in the normal phase, the density of mobile electrons is uniform. Above a critical pump intensity, the cavity superradiates (the cavity mode acquires a coherent displacement) while the electrons order into stripes.
• Figure 2: Critical power near the Wigner crystal phase transition. Near a critical density $n_c$, the enhanced static structure factor (inset) significantly reduces the critical pump intensity $\mathrm{I}_c$ if the grating period $\lambda$ matches the wavevector of the yet-unformed crystal. We use QMC data at zero temperature to compute $\chi(\mathbf{Q})$ and superimpose our results with two experimentally relevant regimes (shaded regions). "Laser thinning" refers to the regime wherein the onset of sample damage is expected Hu2017MoS2LaserThinning. The green region marks the intensity band of current Raman experiments in 2D materials aslan_probing_2018byrley_photochemically_2019. The vertical line in the inset marks the ordering wavevector of the Wigner crystal. The dramatic decrease in threshold intensity highlights the importance of coupling to enhanced fluctuations.
• Figure 3: Finite-temperature phase boundary. (a) Critical temperature as a function of pump laser intensity for different ordering wavevectors $Q$, measured in units of the Fermi wavevector. Results were obtained through RPA calculations for $\varepsilon_F=7\rm~meV$. For $Q>2k_{\rm F}$, the phase boundaries imply re-entrant behavior upon cooling. (b) Critical pump intensity as a function of ordering momentum for a range of temperatures. To achieve the minimal laser power necessary for superradiance, it is optimal to tune the grating periodicity close to $2k_{\rm F}$.
• Figure S1: Scattering efficiency$\eta_{\mathbf{G}}$ defined as the ratio of the intensity due to the first-order spatial mode component to the intensity of the long-wavelength laser field.