[{"citation":{"chicago":"Phan, Duc T. “Resonant Microwave Spectroscopy of Al-InAs.” Institute of Science and Technology Austria, 2023. <a href=\"https://doi.org/10.15479/14547\">https://doi.org/10.15479/14547</a>.","ista":"Phan DT. 2023. Resonant microwave spectroscopy of Al-InAs. Institute of Science and Technology Austria.","apa":"Phan, D. T. (2023). <i>Resonant microwave spectroscopy of Al-InAs</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/14547\">https://doi.org/10.15479/14547</a>","mla":"Phan, Duc T. <i>Resonant Microwave Spectroscopy of Al-InAs</i>. Institute of Science and Technology Austria, 2023, doi:<a href=\"https://doi.org/10.15479/14547\">10.15479/14547</a>.","ama":"Phan DT. Resonant microwave spectroscopy of Al-InAs. 2023. doi:<a href=\"https://doi.org/10.15479/14547\">10.15479/14547</a>","ieee":"D. T. Phan, “Resonant microwave spectroscopy of Al-InAs,” Institute of Science and Technology Austria, 2023.","short":"D.T. Phan, Resonant Microwave Spectroscopy of Al-InAs, Institute of Science and Technology Austria, 2023."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"GradSch"},{"_id":"AnHi"}],"file":[{"file_name":"Phan_Thesis_pdfa.pdf","access_level":"open_access","content_type":"application/pdf","relation":"main_file","checksum":"db0c37d213bc002125bd59690e9db246","date_created":"2023-11-17T13:36:44Z","file_size":34828019,"date_updated":"2023-11-22T09:46:06Z","creator":"pduc","file_id":"14548"},{"checksum":"8d3bd6afa279a0078ffd13e06bb6d56d","relation":"source_file","content_type":"application/zip","access_level":"closed","file_name":"dissertation_src.zip","file_id":"14549","date_updated":"2023-11-17T13:47:54Z","creator":"pduc","file_size":279319709,"date_created":"2023-11-17T13:44:53Z"}],"supervisor":[{"full_name":"Higginbotham, Andrew P","id":"4AD6785A-F248-11E8-B48F-1D18A9856A87","last_name":"Higginbotham","first_name":"Andrew P","orcid":"0000-0003-2607-2363"}],"month":"11","file_date_updated":"2023-11-22T09:46:06Z","publication_identifier":{"issn":["2663 - 337X"]},"publication_status":"published","has_accepted_license":"1","acknowledged_ssus":[{"_id":"NanoFab"},{"_id":"Bio"}],"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","tmp":{"image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)"},"abstract":[{"text":"Superconductor-semiconductor heterostructures currently capture a significant amount of research interest and they serve as the physical platform in many proposals towards topological quantum computation.\r\nDespite being under extensive investigations, historically using transport techniques, the basic properties of the interface between the superconductor and the semiconductor remain to be understood.\r\n\r\nIn this thesis, two separate studies on the Al-InAs heterostructures are reported with the first focusing on the physics of the material motivated by the emergence of a new phase, the Bogoliubov-Fermi surface. \r\nThe second focuses on a technological application, a gate-tunable Josephson parametric amplifier.\r\n\r\nIn the first study, we investigate the hypothesized unconventional nature of the induced superconductivity at the interface between the Al thin film and the InAs quantum well.\r\nWe embed a two-dimensional Al-InAs hybrid system in a resonant microwave circuit allowing measurements of change in inductance.\r\nThe behaviour of the resonance in a range of temperature and in-plane magnetic field has been studied and compared with the theory of conventional s-wave superconductor and a two-component theory that includes both contribution of the $s$-wave pairing in Al and the intraband $p \\pm ip$ pairing in InAs.\r\nMeasuring the temperature dependence of resonant frequency, no discrepancy is found between data and the conventional theory.\r\nWe observe the breakdown of superconductivity due to an applied magnetic field which contradicts the conventional theory.\r\nIn contrast, the data can be captured quantitatively by fitting to a two-component model.\r\nWe find the evidence of the intraband $p \\pm ip$ pairing in the InAs and the emergence of the Bogoliubov-Fermi surfaces due to magnetic field with the characteristic value $B^* = 0.33~\\mathrm{T}$.\r\nFrom the fits, the sheet resistance of Al, the carrier density and mobility in InAs are determined.\r\nBy systematically studying the anisotropy of the circuit response, we find weak anisotropy for $B < B^*$ and increasingly strong anisotropy for $B > B^*$ resulting in a pronounced two-lobe structure in polar plot of frequency versus field angle.\r\nStrong resemblance between the field dependence of dissipation and superfluid density hints at a hidden signature of the Bogoliubov-Fermi surface that is burried in the dissipation data.\r\n\r\nIn the second study, we realize a parametric amplifier with a Josephson field effect transistor as the active element.\r\nThe device's modest construction consists of a gated SNS weak link embedded at the center of a coplanar waveguide resonator.\r\nBy applying a gate voltage, the resonant frequency is field-effect tunable over a range of 2 GHz.\r\nModelling the JoFET minimally as a parallel RL circuit, the dissipation introduced by the JoFET can be quantitatively related to the gate voltage.\r\nWe observed gate-tunable Kerr nonlinearity qualitatively in line with expectation.\r\nThe JoFET amplifier has 20 dB of gain, 4 MHz of instantaneous bandwidth, and a 1dB compression point of -125.5 dBm when operated at a fixed resonant frequency.\r\nIn general, the signal-to-noise ratio is improved by 5-7 dB when the JoFET amplifier is activated compared.\r\nThe noise of the measurement chain and insertion loss of relevant circuit elements are calibrated to determine the expected and the real noise performance of the JoFET amplifier.\r\nAs a quantification of the noise performance, the measured total input-referred noise of the JoFET amplifier is in good agreement with the estimated expectation which takes device loss into account.\r\nWe found that the noise performance of the device reported in this document approaches one photon of total input-referred added noise which is the quantum limit imposed in nondegenerate parametric amplifier.","lang":"eng"}],"date_created":"2023-11-17T13:45:26Z","day":"16","author":[{"id":"29C8C0B4-F248-11E8-B48F-1D18A9856A87","full_name":"Phan, Duc T","last_name":"Phan","first_name":"Duc T"}],"title":"Resonant microwave spectroscopy of Al-InAs","oa_version":"Published Version","date_published":"2023-11-16T00:00:00Z","degree_awarded":"PhD","status":"public","keyword":["superconductor-semiconductor","superconductivity","Al","InAs","p-wave","superconductivity","JPA","microwave"],"year":"2023","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"10851"},{"relation":"part_of_dissertation","status":"public","id":"13264"}]},"page":"80","ddc":["530"],"_id":"14547","date_updated":"2023-11-30T10:56:04Z","type":"dissertation","alternative_title":["ISTA Thesis"],"article_processing_charge":"No","doi":"10.15479/14547","publisher":"Institute of Science and Technology Austria"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"6","citation":{"ieee":"D. T. Phan <i>et al.</i>, “Gate-tunable superconductor-semiconductor parametric amplifier,” <i>Physical Review Applied</i>, vol. 19, no. 6. American Physical Society, 2023.","short":"D.T. Phan, P. Falthansl-Scheinecker, U. Mishra, W.M. Strickland, D. Langone, J. Shabani, A.P. Higginbotham, Physical Review Applied 19 (2023).","ama":"Phan DT, Falthansl-Scheinecker P, Mishra U, et al. Gate-tunable superconductor-semiconductor parametric amplifier. <i>Physical Review Applied</i>. 2023;19(6). doi:<a href=\"https://doi.org/10.1103/PhysRevApplied.19.064032\">10.1103/PhysRevApplied.19.064032</a>","apa":"Phan, D. T., Falthansl-Scheinecker, P., Mishra, U., Strickland, W. M., Langone, D., Shabani, J., &#38; Higginbotham, A. P. (2023). Gate-tunable superconductor-semiconductor parametric amplifier. <i>Physical Review Applied</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevApplied.19.064032\">https://doi.org/10.1103/PhysRevApplied.19.064032</a>","mla":"Phan, Duc T., et al. “Gate-Tunable Superconductor-Semiconductor Parametric Amplifier.” <i>Physical Review Applied</i>, vol. 19, no. 6, 064032, American Physical Society, 2023, doi:<a href=\"https://doi.org/10.1103/PhysRevApplied.19.064032\">10.1103/PhysRevApplied.19.064032</a>.","chicago":"Phan, Duc T, Paul Falthansl-Scheinecker, Umang Mishra, W. M. Strickland, D. Langone, J. Shabani, and Andrew P Higginbotham. “Gate-Tunable Superconductor-Semiconductor Parametric Amplifier.” <i>Physical Review Applied</i>. American Physical Society, 2023. <a href=\"https://doi.org/10.1103/PhysRevApplied.19.064032\">https://doi.org/10.1103/PhysRevApplied.19.064032</a>.","ista":"Phan DT, Falthansl-Scheinecker P, Mishra U, Strickland WM, Langone D, Shabani J, Higginbotham AP. 2023. Gate-tunable superconductor-semiconductor parametric amplifier. Physical Review Applied. 19(6), 064032."},"language":[{"iso":"eng"}],"oa":1,"article_number":"064032","department":[{"_id":"AnHi"},{"_id":"OnHo"}],"month":"06","arxiv":1,"publication_status":"published","publication_identifier":{"eissn":["2331-7019"]},"intvolume":"        19","abstract":[{"text":"We build a parametric amplifier with a Josephson field-effect transistor (JoFET) as the active element. The resonant frequency of the device is field-effect tunable over a range of 2 GHz. The JoFET amplifier has 20 dB of gain, 4 MHz of instantaneous bandwidth, and a 1-dB compression point of -125.5 dBm when operated at a fixed resonance frequency.\r\n\r\n","lang":"eng"}],"acknowledged_ssus":[{"_id":"NanoFab"},{"_id":"M-Shop"}],"article_type":"original","date_created":"2023-07-23T22:01:12Z","volume":19,"title":"Gate-tunable superconductor-semiconductor parametric amplifier","oa_version":"Preprint","author":[{"first_name":"Duc T","full_name":"Phan, Duc T","id":"29C8C0B4-F248-11E8-B48F-1D18A9856A87","last_name":"Phan"},{"last_name":"Falthansl-Scheinecker","id":"85b43b21-15b2-11ec-abd3-e2c252cc2285","full_name":"Falthansl-Scheinecker, Paul","first_name":"Paul"},{"id":"4328fa4c-f128-11eb-9611-c107b0fe4d51","full_name":"Mishra, Umang","last_name":"Mishra","first_name":"Umang"},{"first_name":"W. M.","last_name":"Strickland","full_name":"Strickland, W. M."},{"first_name":"D.","full_name":"Langone, D.","last_name":"Langone"},{"first_name":"J.","full_name":"Shabani, J.","last_name":"Shabani"},{"first_name":"Andrew P","orcid":"0000-0003-2607-2363","full_name":"Higginbotham, Andrew P","id":"4AD6785A-F248-11E8-B48F-1D18A9856A87","last_name":"Higginbotham"}],"day":"09","scopus_import":"1","date_published":"2023-06-09T00:00:00Z","acknowledgement":"We thank Shyam Shankar for helpful feedback on the manuscript. We gratefully acknowledge the support of the ISTA nanofabrication facility, the Miba Machine Shop, and the eMachine Shop. The NYU team acknowledges support from Army Research Office Grant No. W911NF2110303.","status":"public","publication":"Physical Review Applied","external_id":{"arxiv":["2206.05746"],"isi":["001012022600004"]},"related_material":{"record":[{"id":"14547","status":"public","relation":"dissertation_contains"}]},"year":"2023","isi":1,"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/2206.05746","open_access":"1"}],"type":"journal_article","date_updated":"2023-11-30T10:56:03Z","_id":"13264","publisher":"American Physical Society","doi":"10.1103/PhysRevApplied.19.064032","article_processing_charge":"No"},{"volume":128,"date_created":"2022-03-17T11:37:47Z","article_type":"original","day":"11","scopus_import":"1","author":[{"first_name":"Duc T","full_name":"Phan, Duc T","id":"29C8C0B4-F248-11E8-B48F-1D18A9856A87","last_name":"Phan"},{"id":"5479D234-2D30-11EA-89CC-40953DDC885E","full_name":"Senior, Jorden L","last_name":"Senior","orcid":"0000-0002-0672-9295","first_name":"Jorden L"},{"orcid":"0000-0001-9666-3543","first_name":"Areg","last_name":"Ghazaryan","id":"4AF46FD6-F248-11E8-B48F-1D18A9856A87","full_name":"Ghazaryan, Areg"},{"full_name":"Hatefipour, M.","last_name":"Hatefipour","first_name":"M."},{"first_name":"W. M.","full_name":"Strickland, W. M.","last_name":"Strickland"},{"first_name":"J.","full_name":"Shabani, J.","last_name":"Shabani"},{"first_name":"Maksym","orcid":"0000-0002-2399-5827","last_name":"Serbyn","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","full_name":"Serbyn, Maksym"},{"first_name":"Andrew P","orcid":"0000-0003-2607-2363","id":"4AD6785A-F248-11E8-B48F-1D18A9856A87","full_name":"Higginbotham, Andrew P","last_name":"Higginbotham"}],"title":"Detecting induced p±ip pairing at the Al-InAs interface with a quantum microwave circuit","oa_version":"Preprint","publication_status":"published","publication_identifier":{"issn":["0031-9007"],"eissn":["1079-7114"]},"acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"intvolume":"       128","abstract":[{"text":"Superconductor-semiconductor hybrid devices are at the heart of several proposed approaches to quantum information processing, but their basic properties remain to be understood. We embed a twodimensional Al-InAs hybrid system in a resonant microwave circuit, probing the breakdown of superconductivity due to an applied magnetic field. We find a fingerprint from the two-component nature of the hybrid system, and quantitatively compare with a theory that includes the contribution of intraband p±ip pairing in the InAs, as well as the emergence of Bogoliubov-Fermi surfaces due to magnetic field. Separately resolving the Al and InAs contributions allows us to determine the carrier density and mobility in the InAs.","lang":"eng"}],"department":[{"_id":"MaSe"},{"_id":"AnHi"}],"article_number":"107701","arxiv":1,"month":"03","citation":{"short":"D.T. Phan, J.L. Senior, A. Ghazaryan, M. Hatefipour, W.M. Strickland, J. Shabani, M. Serbyn, A.P. Higginbotham, Physical Review Letters 128 (2022).","ieee":"D. T. Phan <i>et al.</i>, “Detecting induced p±ip pairing at the Al-InAs interface with a quantum microwave circuit,” <i>Physical Review Letters</i>, vol. 128, no. 10. American Physical Society, 2022.","ama":"Phan DT, Senior JL, Ghazaryan A, et al. Detecting induced p±ip pairing at the Al-InAs interface with a quantum microwave circuit. <i>Physical Review Letters</i>. 2022;128(10). doi:<a href=\"https://doi.org/10.1103/physrevlett.128.107701\">10.1103/physrevlett.128.107701</a>","mla":"Phan, Duc T., et al. “Detecting Induced P±ip Pairing at the Al-InAs Interface with a Quantum Microwave Circuit.” <i>Physical Review Letters</i>, vol. 128, no. 10, 107701, American Physical Society, 2022, doi:<a href=\"https://doi.org/10.1103/physrevlett.128.107701\">10.1103/physrevlett.128.107701</a>.","apa":"Phan, D. T., Senior, J. L., Ghazaryan, A., Hatefipour, M., Strickland, W. M., Shabani, J., … Higginbotham, A. P. (2022). Detecting induced p±ip pairing at the Al-InAs interface with a quantum microwave circuit. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevlett.128.107701\">https://doi.org/10.1103/physrevlett.128.107701</a>","ista":"Phan DT, Senior JL, Ghazaryan A, Hatefipour M, Strickland WM, Shabani J, Serbyn M, Higginbotham AP. 2022. Detecting induced p±ip pairing at the Al-InAs interface with a quantum microwave circuit. Physical Review Letters. 128(10), 107701.","chicago":"Phan, Duc T, Jorden L Senior, Areg Ghazaryan, M. Hatefipour, W. M. Strickland, J. Shabani, Maksym Serbyn, and Andrew P Higginbotham. “Detecting Induced P±ip Pairing at the Al-InAs Interface with a Quantum Microwave Circuit.” <i>Physical Review Letters</i>. American Physical Society, 2022. <a href=\"https://doi.org/10.1103/physrevlett.128.107701\">https://doi.org/10.1103/physrevlett.128.107701</a>."},"issue":"10","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa":1,"language":[{"iso":"eng"}],"_id":"10851","date_updated":"2023-11-30T10:56:03Z","type":"journal_article","article_processing_charge":"No","doi":"10.1103/physrevlett.128.107701","publisher":"American Physical Society","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2107.03695"}],"quality_controlled":"1","keyword":["General Physics and Astronomy"],"isi":1,"year":"2022","related_material":{"link":[{"relation":"press_release","description":"News on ISTA Website","url":"https://ista.ac.at/en/news/characterizing-super-semi-sandwiches-for-quantum-computing/"}],"record":[{"relation":"earlier_version","status":"public","id":"10029"},{"id":"14547","status":"public","relation":"dissertation_contains"}]},"external_id":{"pmid":[" 35333085"],"arxiv":["2107.03695"],"isi":["000771391100002"]},"ec_funded":1,"pmid":1,"date_published":"2022-03-11T00:00:00Z","acknowledgement":"M. S. acknowledges useful discussions with A. Levchenko and P. A. Lee, and E. Berg. This research was supported by the Scientific Service Units of IST Austria through resources provided by the MIBA Machine Shop and the nanofabrication facility. J. S. and A. G. acknowledge funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 754411.W. M. Hatefipour, W. M. Strickland and J. Shabani acknowledge funding from Office of Naval Research Award No. N00014-21-1-2450.","status":"public","publication":"Physical Review Letters","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}]},{"department":[{"_id":"MaSe"},{"_id":"AnHi"},{"_id":"MiLe"}],"article_number":"2107.03695","year":"2021","related_material":{"record":[{"relation":"later_version","status":"public","id":"10851"},{"id":"9636","status":"public","relation":"research_data"}]},"month":"07","arxiv":1,"external_id":{"arxiv":["2107.03695"]},"citation":{"apa":"Phan, D. T., Senior, J. L., Ghazaryan, A., Hatefipour, M., Strickland, W. M., Shabani, J., … Higginbotham, A. P. (n.d.). Breakdown of induced p±ip pairing in a superconductor-semiconductor hybrid. <i>arXiv</i>.","mla":"Phan, Duc T., et al. “Breakdown of Induced P±ip Pairing in a Superconductor-Semiconductor Hybrid.” <i>ArXiv</i>, 2107.03695.","ista":"Phan DT, Senior JL, Ghazaryan A, Hatefipour M, Strickland WM, Shabani J, Serbyn M, Higginbotham AP. Breakdown of induced p±ip pairing in a superconductor-semiconductor hybrid. arXiv, 2107.03695.","chicago":"Phan, Duc T, Jorden L Senior, Areg Ghazaryan, M. Hatefipour, W. M. Strickland, J. Shabani, Maksym Serbyn, and Andrew P Higginbotham. “Breakdown of Induced P±ip Pairing in a Superconductor-Semiconductor Hybrid.” <i>ArXiv</i>, n.d.","ieee":"D. T. Phan <i>et al.</i>, “Breakdown of induced p±ip pairing in a superconductor-semiconductor hybrid,” <i>arXiv</i>. .","short":"D.T. Phan, J.L. Senior, A. Ghazaryan, M. Hatefipour, W.M. Strickland, J. Shabani, M. Serbyn, A.P. Higginbotham, ArXiv (n.d.).","ama":"Phan DT, Senior JL, Ghazaryan A, et al. Breakdown of induced p±ip pairing in a superconductor-semiconductor hybrid. <i>arXiv</i>."},"ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2021-07-08T00:00:00Z","acknowledgement":"This research was supported by the Scientific Service Units of IST Austria through resources provided by the MIBA Machine Shop and the nanofabrication facility. JS and AG were supported by funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No.754411.","oa":1,"status":"public","publication":"arXiv","language":[{"iso":"eng"}],"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020"}],"_id":"10029","date_updated":"2024-02-21T12:36:52Z","date_created":"2021-09-21T08:41:02Z","type":"preprint","article_processing_charge":"No","day":"08","author":[{"first_name":"Duc T","last_name":"Phan","id":"29C8C0B4-F248-11E8-B48F-1D18A9856A87","full_name":"Phan, Duc T"},{"orcid":"0000-0002-0672-9295","first_name":"Jorden L","last_name":"Senior","full_name":"Senior, Jorden L","id":"5479D234-2D30-11EA-89CC-40953DDC885E"},{"last_name":"Ghazaryan","full_name":"Ghazaryan, Areg","id":"4AF46FD6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9666-3543","first_name":"Areg"},{"full_name":"Hatefipour, M.","last_name":"Hatefipour","first_name":"M."},{"first_name":"W. M.","full_name":"Strickland, W. M.","last_name":"Strickland"},{"last_name":"Shabani","full_name":"Shabani, J.","first_name":"J."},{"first_name":"Maksym","orcid":"0000-0002-2399-5827","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","full_name":"Serbyn, Maksym","last_name":"Serbyn"},{"full_name":"Higginbotham, Andrew P","id":"4AD6785A-F248-11E8-B48F-1D18A9856A87","last_name":"Higginbotham","first_name":"Andrew P","orcid":"0000-0003-2607-2363"}],"oa_version":"Preprint","title":"Breakdown of induced p±ip pairing in a superconductor-semiconductor hybrid","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2107.03695"}],"publication_status":"submitted","acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"abstract":[{"lang":"eng","text":"Superconductor-semiconductor hybrids are platforms for realizing effective p-wave superconductivity. Spin-orbit coupling, combined with the proximity effect, causes the two-dimensional semiconductor to inherit p±ip intraband pairing, and application of magnetic field can then result in transitions to the normal state, partial Bogoliubov Fermi surfaces, or topological phases with Majorana modes. Experimentally probing the hybrid superconductor-semiconductor interface is challenging due to the shunting effect of the conventional superconductor. Consequently, the nature of induced pairing remains an open question. Here, we use the circuit quantum electrodynamics architecture to probe induced superconductivity in a two dimensional Al-InAs hybrid system. We observe a strong suppression of superfluid density and enhanced dissipation driven by magnetic field, which cannot be accounted for by the depairing theory of an s-wave superconductor. These observations are explained by a picture of independent intraband p±ip superconductors giving way to partial Bogoliubov Fermi surfaces, and allow for the first characterization of key properties of the hybrid superconducting system."}]}]