Observation of the exciton Mott transition in the photoluminescence of coupled quantum wells

Indirect excitons in coupled quantum wells have long radiative lifetimes and form a cold quasi-two-dimensional population suitable for studying collective quantum effects. Here we report the observation of the exciton Mott transition from an insulating (excitons) to a conducting (ionized electron-hole pairs) phase, which occurs gradually as a function of carrier density and temperature. The transition is inferred from spectral and time-resolved photoluminescence measurements around a carrier density of $2\times {10}^{10}{\mathrm{cm}}^{-2}$ and temperatures of 12–16 K. An externally applied electric field is employed to tune the dynamics of the transition via the quantum-confined Stark effect. Our results provide evidence of a gradual nature of the exciton Mott transition.

Figure 1

The Mott transition of indirect excitons. (a) An exciton gas (left) is ionized into an EH (electron-hole) plasma (right) as the exciton density or temperature is increased as sketched. The holes (electrons) are illustrated as light blue (black) spheres. (b) Band diagram and indirect transition of the CQWs, cf. Appendix pp2. (c) The experimental phase diagram: the exciton intensity relative to the total intensity as a function of the incident (inc.) pumping intensity and the temperature. (d) The data in panel (c) are modeled by a statistical distribution function, see the main text for details. Contours of the relative exciton intensity of 0.2, 0.5, and 0.8 are indicated by the black lines.

Figure 2

Investigation of the exciton Mott transition as a function of excitation intensity and temperature. (a) Spectra of the IX taken at different incident intensities for a constant temperature of 12.5 K. At low powers the PL stems mainly from excitons and is gradually overtaken by the EH plasma at larger carrier densities. (b) PL of the IX as a function of temperature for a constant excitation intensity of $1.5\mathrm{W}/{\mathrm{cm}}^2$. As the temperature is increased, the excitons are ionized into free carriers. (c), (d) Ratio between the PL stemming from the exciton resonance and the total PL extracted from panels (a) and (b).

Figure 3

(a) Density-temperature phase diagram of the exciton Mott transition. The critical exciton density $n_c$ is estimated for each temperature (data points). Two regions are distinguished where either the insulating excitons or the metallic plasma dominates. The black dashed line is a linear fit, $n_c=\beta T+\gamma$. (b) Binding energy of the IX across the Mott transition extracted from the data shown in Figs. 2 and 2. As the carrier density $n$ is increased, the binding energy of the IX is reduced due to screening of the Coulomb interaction (left panel). At a carrier density of $1\times {10}^{10}{\mathrm{cm}}^{-2}$ and at 12.5 K, the binding energy $E_b$ is 6.5 meV and becomes larger with increasing temperature (right panel). The error bars are calculated from the fitting errors of the centers of the exciton and EH-plasma distributions. Inset: PL spectrum fitted with a sum of two Voigt functions, where the distance between the peaks yields $E_b$.

Figure 4

Energy structure and the relevant optical transitions of the CQWs. (a) The band diagram at an external bias voltage of 19 kV/cm at which the Mott transition is observed. The first three electron ($\mathrm{e}1, \mathrm{e}2, \mathrm{e}3$) and hole (h1, h2, h3) energy levels and squared wave functions are shown. The indirect-exciton PL originates from the $\mathrm{e}1 \to$ h1 (red arrow) transition, while the direct excitons originate from $\mathrm{e}1 \to$ h3 and $\mathrm{e}2 \to$ h1 (black arrows). (b) Measured emission energy of DX2 (black circles) and the IX (red triangles) vs electric field at an excitation intensity of $545\mathrm{W}/{\mathrm{cm}}^2$, which agrees very well with the theoretical predictions (solid lines). Inset: the IX decay dynamics recorded at a pumping intensity of $319\mathrm{W}/{\mathrm{cm}}^2$ and an electric field of 19 kV/cm.

Figure 5

Time-resolved decay dynamics of excitons (red dots) and EH plasma (blue triangles) taken at a pumping intensity of $1\mathrm{W}/{\mathrm{cm}}^2$ under 19 kV/cm applied bias. The curves are fitted well by a single (excitons) or double (EH plasma) exponent (black solid lines). Inset: the corresponding spectrum of the indirect transition under pulsed excitation. The red dot and blue triangle denote the two spectral positions probed by the time-resolved measurement.

Figure 6

Photoluminescence spectra of CQWs (purple line) acquired at an electric field of 19 kV/cm shown on a linear and semilogarithmic scale for an excitation intensity of $0.7\mathrm{W}/{\mathrm{cm}}^2$ [(a), (c)] and $47\mathrm{W}/{\mathrm{cm}}^2$ [(b), (d)], respectively. The IX peak is fitted with a sum of two Voigt functions (green line), where the excitonic (EH-plasma) contribution is depicted in red (blue). The peak at high energies stems from the direct exciton.