Observation of algebraic time order for two-dimensional dipolar excitons

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Observation of algebraic time order for two-dimensional dipolar excitons

Suzanne Dang, Marta Zamorano, Stephan Suffit, Kenneth West, Kirk Baldwin, Loren Pfeiffer, Markus Holzmann, and François Dubin

Phys. Rev. Research 2, 032013(R) – Published 13 July 2020

Abstract

We study dipolar excitons confined in a flat trap of a GaAs bilayer heterostructure. By quantifying density and density fluctuations at sub-Kelvin temperatures, we unveil the excitons' universal equation of state. This allows us to infer thermodynamically the critical phase-space density for the transition expected between normal and superfluid regimes. The region of this crossover is directly confirmed by a net change in the excitons' temporal coherence, from an exponential to an algebraic decay with an exponent compatible with the Berezinskii-Kosterlitz-Thouless theory.

Received 30 January 2020
Revised 10 June 2020
Accepted 18 June 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.032013

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

BKT transition Excitons Luminescence Superfluidity

III-V semiconductors Quantum wells

Optical absorption spectroscopy Photoluminescence

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Suzanne Dang¹, Marta Zamorano¹, Stephan Suffit ², Kenneth West³, Kirk Baldwin³, Loren Pfeiffer³, Markus Holzmann⁴, and François Dubin¹

¹Institut des Nanosciences de Paris, CNRS and Sorbonne Université, 4 place Jussieu, 75005 Paris, France
²Laboratoire de Materiaux et Phenomenes Quantiques, Université Paris Diderot, 75013 Paris, France
³PRISM, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08540, USA
⁴Université Grenoble Alpes, CNRS, LPMMC, 3800 Grenoble, France

Article Text

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Issue

Vol. 2, Iss. 3 — July - September 2020

Subject Areas

Semiconductor Physics

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Images

Figure 1
(a) Phase-space density $D = n λ_{T}^{2}$ measured at $T = 340$ mK (blue) and 750 mK (red), together with the results of Monte Carlo calculations for $\tilde{g} = 4$ and 6, respectively (solid lines). $D$ is obtained by analyzing the profile of the photoluminescence energy across the trap from a statistical ensemble of 20 repetitions for every experimental condition. Experimentally, the density in the trap is varied by scanning the delay to the loading phase. It is (c) about $2 \times 10^{10} {cm}^{- 2}$ at the center when the delay is set to 150 ns and (b) around $10^{9} {cm}^{- 2}$ when it is set to 370 ns. In the latter case the photoluminescence energy reproduces the profile of the trapping potential fitted by the solid red line. Error bars display the statistical deviations of our measurements.
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Figure 2
(a) Rescaled density fluctuations $σ^{2} λ_{T}^{2}$ per $μ m^{2}$ measured at 340 mK (red), 550 mK (brown), 950 mK (green), and 1.2 K (black). Data points are obtained by evaluating the variance for a set of 20 repetitions for every experimental setting, and $σ^{2} λ_{T}^{2}$ is then computed in intervals $β μ \sim 1$ to reach higher precision. (b) Temperature scaling of $\tilde{g}$ extracted by averaging the data shown in (a) for each bath temperature (blue). The red shaded area marks the logarithmic scaling of $\tilde{g}$ with temperature expected for thermal two-body collisions with the effective dipolar exciton-exciton interaction (see Supplemental Material of Ref. [11]).
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Figure 3
(a) Equations of state ( $D - D_{c}$ ) in rescaled units $β (μ - μ_{c}) / \tilde{g}$ , for experiments realized at 340 mK, 550 mK, 750 mK, 950 mK, 1.2 K, and 1.5 K (black, blue, green, red, cyan, and magenta, respectively). The solid red line displays the scaling predicted by Monte Carlo calculations. The resulting values of the critical chemical potential $β μ_{c}$ and of the critical phase-space density $D_{c}$ are shown in (b) and (c), respectively.
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Figure 4
(a) Amplitude of the first-order temporal coherence $| g^{(1)} |$ as a function of the time delay for a phase-space density below threshold ( $D = 3$ in black), at threshold ( $D \sim 7$ in blue), and above threshold ( $D = 11$ in red), in log-log scale. The inset displays the same data in linear scale. The black curve shows an exponential decay with a time constant equal to 3.8 ps while the blue and red lines show an algebraic decay $τ^{- η}$ with $η = 0.4$ and 0.2, blue and red, respectively, for comparison. The blue shaded area marks the minimum contrast possibly detected for the signal-to-noise ratio of our experiments. (b) Interference pattern measured for $D = 11$ and for a time delay set to 5 ps. (c) displays the interference signal across the center of the trap [dashed line in (b)], together with a sinusoidal fit to the data leading to a contrast of $35 %$ . (d) Spatially resolved photoluminescence emitted at 340 mK for a phase-space density $D \sim 3$ . The spectrum taken at the center of the trap, between the dashed lines, is shown in (e) where the solid red line displays a Lorentzian profile with 320 $μ eV$ full width at half maximum.
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