Non-Hermitian dispersion sign reversal of radiative resonances in two dimensions

In a recent publication [Wurdack et al., Nat. Commun. 14, 1026 (2023)], it was shown that in microcavities containing atomically thin semiconductors, non-Hermitian quantum mechanics can lead to negative exciton polariton masses. Here, we study the mass-sign reversal in two-dimensional systems and show that it is not contingent on the cavity. We show that it can occur generally in radiative resonances in two dimensions and derive conditions for it (critical dephasing threshold, etc.). In monolayer transition-metal dichalcogenides, this phenomenon is not invalidated by the strong electron-hole exchange interaction, which is known to make the exciton massless.

Figure 1

Sketch of 2D-layer exciton polariton with exciton (yellow dot) propagating with wave vector $\mathbf{q}$ in the plane of the layer, and emitted $p$-polarized ($s$-polarized) radiation field ${\mathbf{E}}_L$ (${\mathbf{E}}_T$) with wave vector ${\mathbf{q}}_{em}$. Inset: radiative cone.

Figure 2

Real (a) and imaginary (b) part of the dispersion relation of longitudinal (blue) and transverse (red) 2D-layer polaritons. The dephasing is ${\gamma }_D=4\mathrm{meV}$. The edge of the radiative cone is approximately at 8.23 $\mu {\mathrm{m}}^{-1}$. The real (imaginary) part of $\hslash {\omega }_L$ is discontinuous (continuous) at the edge of the radiative cone; the real and imaginary part of $\hslash {\omega }_T$ are discontinuous.

Figure 3

(a) Same as Fig. 2 for longitudinal mode, but only showing inside the radiative cone. (b) Same as (a) for blue curve, plus dispersion for ${\gamma }_D=0$ (red curve), 0.1 meV (green), and 1 meV (magenta). The red dashed curve shows the exciton dispersion.

Figure 4

Radiative mass in units of exciton mass vs dephasing. The inset shows the inverse radiative mass in the region of the extremum.

Figure 5

(a) Blue curve same as blue curve in Fig. 2. The redline shows ${\varepsilon }_{q_x,L}^{1s,\mathrm{static}}$. (b) Group velocity corresponding to blue curve in (a).