Large-scale characterization of ${\mathrm{Cu}}_{2}\mathrm{O}$ monocrystals via Rydberg excitons

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Large-scale characterization of ${Cu}_{2} O$ monocrystals via Rydberg excitons

Kerwan Morin, Delphine Lagarde, Angélique Gillet, Xavier Marie, and Thomas Boulier

Phys. Rev. Materials 8, 026202 – Published 27 February 2024

Abstract

Rydberg states of excitons can reach microns in size and require extremely pure crystals. We introduce an experimental method for the rapid and spatially resolved characterization of Rydberg excitons in copper oxide ( ${Cu}_{2} O$ ) with submicron resolution over large zones. Our approach involves illuminating and imaging the entire sample on a camera to realize a spatially resolved version of resonant absorption spectroscopy, without any mobile part. This yields spatial maps of Rydberg exciton properties, including their energy, linewidth, and peak absorption, providing a comprehensive quality assessment of the entire sample in a single shot. Furthermore, by imaging the sample photoluminescence over the same zone, we establish a strong relationship between the spectral quality map and the photoluminescence map of charged oxygen vacancies. This results in an independent, luminescence-based quality map that closely matches the results obtained through resonant spectroscopy. Our findings reveal that Rydberg excitons in natural ${Cu}_{2} O$ crystals are predominantly influenced by optically active charged oxygen vacancies, which can be easily mapped. Together, these two complementary methods provide valuable insights into ${Cu}_{2} O$ crystal properties.

Received 24 October 2023
Accepted 2 February 2024

DOI:https://doi.org/10.1103/PhysRevMaterials.8.026202

Physics Subject Headings (PhySH)

Excitons

Oxides Semiconductors

Imaging & optical processing Optical absorption spectroscopy Two-dimensional coherent spectroscopy

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Kerwan Morin, Delphine Lagarde, Angélique Gillet, Xavier Marie , and Thomas Boulier ^*

Université de Toulouse, INSA-CNRS-UPS, LPCNO, 135 Av. Rangueil, 31077 Toulouse, France

^*boulier@insa-toulouse.fr

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Vol. 8, Iss. 2 — February 2024

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Figure 1
Schematic of the experiment: a tunable CW laser, intensity and frequency locked, covers the whole sample. This sample, cooled below $3 K$ , is imaged onto a camera for WFTS. The transmitted laser light can also be measured on a photodiode to get more precise transmission spectra, but at the cost of spatial resolution. The laser can be tuned to above-gap energies and the PL can be imaged as well, in which case bandpass filters select the relevant emission energies.
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Figure 2
Graphical representation of the protocol: (a) Imaging the sample transmission at each laser energy results in a data stack containing the Rydberg spectra for all sample positions. (b) For a given sample position, the data is carefully smoothed before each Rydberg absorption peak is detected. Their properties (FWHM $Γ_{n}$ , peak height $H_{n}$ , and peak energy $E_{n}$ ) are extracted and the process is repeated for each pixel coordinate ( $x, y$ ).
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Figure 3
Exemplar maps and spectra. (a) Energy, linewidth, and height WFTS maps for $n$ = 8. The pictures diagonal spans $1 m m$ . The $n$ = 8 quality map is constructed from the latter two maps: quality = height/width. (b) Relative spatial variation of the energy (top) and linewidth (bottom, dashed lines are guides for the eye) for several principal quantum numbers $n$ , along a cut in the gradient direction (red dashed lines in (a), top panels). The broadening $Δ Γ / Γ$ has a strong ( $n^{3}$ ) variation with n, while the energy shifts are $n$ independent. (c), (d) Examples of spectra obtained at two sample positions, identified through the quality map as higher quality (c) and lower quality (d). Crucially, $n_{\max}$ correlates well with the quality of the lower Rydberg peaks: here, from the $n$ = 8 quality map alone we can immediately find a sample region with $n_{\max} = 17$ , while most other sample spots only show $n_{\max} = 11 \sim 14$ .
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Figure 4
Photoluminescence spectra and imaging. (a) Examples of PL spectra emitted from two sample regions of different quality. In both, a clear emission from the 1S exciton and associated phonon replica are present around $2 e V$ , along with a large emission in the $1.5 - 1.7 e V$ region originating from oxygen vacancies (VO). The spectra are normalized to have the same 1S peak height. The lower quality region emits relatively more oxygen vacancy PL, indicating a higher density of charged defects. (b) Zoom on the 1S exciton PL. (c) Photoluminescence pictures across the sample for two spectral regions: the oxygen vacancies (left) and the 1S exciton plus phonon replica (right). The two types of emission reveal different features, such as the fault line on the right and the bright spot on the bottom (red dashed circles) that only appear in the vacancies photoluminescence.
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Figure 5
PL vs WFTS vs $n_{\max}$ . (a) Comparison between the quality maps from direct WFTS and from PL imaging for two different samples. Most features, such as the quality gradient in sample 1 (top), are recognizable in both. Sample 2 (bottom) shows nontrivial crystallographic features visible with both methods (zoomed-in panels). (b) Evolution of the quality estimated from PL (red) and of the $n = 8$ linewidth with $n_{\max}$ (green). (c) Visual comparison between the two quality estimates (red) where the dashed line is the unit slope, and between the quality from WFTS and the linewidth of the $n = 8$ peak (green).
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Figure 6
Quality map of the same sample (sample 1) before (top) and after (bottom) the annealing process. The quality gradient, which we attribute to a density gradient of oxygen vacancies, disappeared and the average quality is thereby increased on large scales. Local variations remain, and we only observe a marginal improvement on $n_{\max}$ .
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Physical Review Materials

Large-scale characterization of Cu2O monocrystals via Rydberg excitons

Kerwan Morin, Delphine Lagarde, Angélique Gillet, Xavier Marie, and Thomas Boulier

Phys. Rev. Materials 8, 026202 – Published 27 February 2024

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Large-scale characterization of ${Cu}_{2} O$ monocrystals via Rydberg excitons