Roton-maxon spectrum and instability for weakly interacting dipolar excitons in a semiconductor layer

The formation of the roton-maxon excitation spectrum and the roton instability effect for a weakly correlated Bose gas of dipolar excitons in a semiconductor layer are predicted. The stability diagram is calculated. According to our numerical estimations, the threshold of the roton instability for Bose-Einstein condensed exciton gas with roton-maxon spectrum is achievable experimentally, e.g., in GaAs semiconductor layers.

Figure 1

Spatially separated $e$ and $h$ in declined semiconductor layer (VB is the valence band and CB is the conduction band).

Figure 2

Qualitative illustration of appearance of the roton instability for dipolar system in the layer: The smooth crossover from 3D (unstable) branch to the 2D (stable) branch [quantitative examples are presented in Fig. 3]. In (a) and (b) the square of the Bogoliubov spectrum (1) of dipolar excitons in 3D (solid), 2D (dot-dashed), and the layer geometry (dashed). In (c) the width of the SL $L_1<L_2<\cdots <L_6$. In (d) momentum ${\mathbf{p}}_{\mathrm{r}}$ of the unstable mode.

Figure 3

(a) Calculation of the lowest branches of ${\varepsilon }_p^2$ at $g_s=0.2g_d$ and $\gamma =10$ (solid), $\gamma =17.5$ (dashed), $\gamma =22.5$ (dot-dashed), $\gamma =27.8$ (dot-dot-dashed), and $\gamma =32.5$ (dotted). (b) Stability diagram in $g_d/g_s$–$\gamma$. The stable phase without the roton minimum (1), with the roton minimum (2), and the unstable phase (3) are shown. (c) Critical value of momentum for threshold of instability $p_{\mathrm{r}}$ and roton wavelength $\lambda =2\pi /p_{\mathrm{r}}$. Units $\hslash =m=L=1$ are used in (a)–(c).