Experimental Study of the Exciton Gas-Liquid Transition in Coupled Quantum Wells

Subhradeep Misra, Michael Stern, Arjun Joshua, Vladimir Umansky, and Israel Bar-Joseph

Phys. Rev. Lett. 120, 047402 – Published 26 January 2018

Abstract

We study the exciton gas-liquid transition in $GaAs / AlGaAs$ coupled quantum wells. Below a critical temperature, $T_{C} = 4.8 K$ , and above a threshold laser power density the system undergoes a phase transition into a liquid state. We determine the density-temperature phase diagram over the temperature range 0.1–4.8 K. We find that the latent heat increases linearly with temperature at $T ≲ 1.1 K$ , similarly to a Bose-Einstein condensate transition, and becomes constant at $1.1 ≲ T < 4.8 K$ . Resonant Rayleigh scattering measurements reveal that the disorder in the sample is strongly suppressed and the diffusion coefficient sharply increases with decreasing temperature at $T < T_{C}$ , allowing the liquid to spread over large distances away from the excitation region. We suggest that our findings are manifestations of a quantum liquid behavior.

Received 27 August 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.047402

Physics Subject Headings (PhySH)

Excitons Phase diagrams Quantum phase transitions

III-V semiconductors Quantum wells

Photoluminescence Rayleigh scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Subhradeep Misra¹, Michael Stern², Arjun Joshua¹, Vladimir Umansky¹, and Israel Bar-Joseph^1,*

¹Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
²Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 5290002, Israel

^*Corresponding author. ibj@weizmann.ac.il

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Issue

Vol. 120, Iss. 4 — 26 January 2018

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Images

Figure 1
The upper and lower panels show the PL spectra and PL images, respectively, at different pump powers at a fixed $V_{g} = - 3.0 V$ and $T = 0.3 K$ . The mesa is $100 μ m \times 100 μ m$ and is marked by dashed lines. (a) At low power, $P = 10 μ W$ , the WW direct exciton peak, $X_{WW}$ , is observed and the image is a smooth Gaussian (the low energy shoulder is due to a trion peak). (b) At power above threshold, $P = 40 μ W$ , a new broad spectral line $Z$ is observed in the spectrum and correspondingly, a dark ring appears in the PL image around the center of the illumination spot. (c) As the power is further increased, $P = 60 μ W$ , the $X_{WW}$ line disappears and the emission spectrum is dominated by the $Z$ line. Also, the dark boundary disappears in the PL image.
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Figure 2
The phase diagram of the system obtained by measuring the threshold power $P_{C}$ as a function of temperature at $V = - 2.6 V$ . The inset shows the latent heat $L$ as a function of temperature using the C-C equation. The solid lines in the main figure are fit to the integrated C-C equation using the values of $L$ from the inset.
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Figure 3
RRS measurements with overlapping pump ( $50 μ W$ ) and probe ( $5 μ W$ ) beams at $V = - 3.4 V$ . (a) The measured RRS spectrum at $T = 0.6 K$ (blue circles) and a Lorentzian fit (solid red line). The dashed line shows the RRS spectrum at preliquid voltage, $V = - 1 V$ . (b) Image of the mesa emission ( $RRS + PL$ ) when the probe energy is set at the NW exciton peak and $T = 0.6 K$ . The spotty RRS pattern is clearly observed. (c) The RRS spectra at several temperatures below $T_{C}$ . (d) The RRS integrated intensity as a function of temperature. It is seen that it is constant at $T < 1.1 K$ , then changes by less than 20% at $1.1 < T < 4 K$ , and rapidly diminishes towards $T_{C}$ .
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Figure 4
Images of the mesa emission ( $RRS + PL$ ) for probe excitation in resonance with the NW exciton at $- 3.0 V$ and $T = 0.6 K$ . (a) Overlapping pump and probe at intermediate pump power ( $40 μ W$ ), where phase separation occurs. (b) Nonoverlapping pump (at the top) and probe (at the bottom) at high pump power ( $60 μ W$ ). The orange dashed square marks the mesa.
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Figure 5
Two-beam PL measurements at $P = 50 μ W$ , $V = - 3.0 V$ , $T = 0.6 K$ . (a) A typical setting of the pump (top) and probe (bottom) experiment. The small rectangle marks the area from which PL is collected. (b) The PL spectrum from the WW and NW without (blue) and with (red) the pump beam. The indirect exciton appears as a weak peak at 1.500 eV, outside the range of this figure [16]. (c) The integrated PL intensity from the marked area as a function of probe power when the pump is switched on.
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