Piezoelectrically mediated acoustic phonon tunneling

Although purely acoustic waves cannot exist in vacuum by definition, an acoustic phonon can infact "jump" or "tunnel" across a vacuum gap between two piezoelectric solids. The dissertation presents the author’s work to provide a generally applicable theoretical formulation and an...

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Main Author: Geng, Zhuoran
Other Authors: Faculty of Mathematics and Science, Matemaattis-luonnontieteellinen tiedekunta, University of Jyväskylä, Jyväskylän yliopisto
Format: Doctoral dissertation
Language:eng
Published: 2023
Online Access: https://jyx.jyu.fi/handle/123456789/86268
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author Geng, Zhuoran
author2 Faculty of Mathematics and Science Matemaattis-luonnontieteellinen tiedekunta University of Jyväskylä Jyväskylän yliopisto
author_facet Geng, Zhuoran Faculty of Mathematics and Science Matemaattis-luonnontieteellinen tiedekunta University of Jyväskylä Jyväskylän yliopisto Geng, Zhuoran Faculty of Mathematics and Science Matemaattis-luonnontieteellinen tiedekunta University of Jyväskylä Jyväskylän yliopisto
author_sort Geng, Zhuoran
datasource_str_mv jyx
description Although purely acoustic waves cannot exist in vacuum by definition, an acoustic phonon can infact "jump" or "tunnel" across a vacuum gap between two piezoelectric solids. The dissertation presents the author’s work to provide a generally applicable theoretical formulation and an experimental demonstration of acoustic phonon tunneling between arbitrarily an isotropic and oriented piezoelectric crystals. Within the continuum an isotropic linear elasticity theory and the quasistatic approximation, this work solves the acoustic wave tunneling problem with two different approaches for a plane-plane geometry, acquiring the solutions of reflection and transmission of all the partial waves for any incoming wave mode, taking fully into account mode conversions. Such formalism can be applied to a practical numerical or even ananalytical implementation, as a few chosen analytical and numerical examples demonstrate. A strikingly simple resonant tunneling condition was discovered in this work, which leads to the complete tunneling of an acoustic phonon, a unity transmission of the acoustic wave across vacuum without reflection. The detailed analytical proof and numerical demonstration of such complete phonon tunneling are presented. Furthermore, this formalism was applied to investigate the heat flux associated with the phonon tunneling mediated by piezoelectricity. A few numerical results are demonstrated and compared with other near-field heat transfer mechanisms. In particular, this work shows that such heat transfer is significant when a vacuum gap size is smaller than the phonon characteristic wavelength, and even becomes the dominant mechanism at temperatures lower than 50K. Lastly, an experimental demonstration of the heat transfer mediated by acoustic phonon tunneling is presented, using two suspended piezoelectric microscopic beams at sub-kelvin temperatures. The results of the measurements provide qualitative evidence of the heat transfer, with comparisons between different vacuum gap widths and with non-piezoelectric devices. However, the quantitatively determined transferred power is not in good agreement with the theoretical estimations, and possible causes of the discrepancy are discussed. Vaikka puhtaat akustiset aallot eivät voi esiintyä tyhjiössä määritelmänsä mukaan, akustinen fononi voi itse asiassa "hypätä" tai "tunneloitua" tyhjiöraon yli kahden pietsosähköisen materiaalin välillä. Tässä väitöskirjassa esitetään uusi yleisesti sovellettava teoria sekä kokeellinen demonstraatio akustisten fononien tunneloitumiselle kahden mielivaltaisesti anisotrooppisen ja suunnatun pietsosähköisen kiteen välillä. Käyttäen anisotrooppista jatkuvan aineen lineaarista elastisuusteoriaa ja kvasistaattista approksimaatiota, tässä työssä ratkaistaan akustisten aaltojen tunnelointiongelma käyttäen kahta eri lähestymistapaa taso-tasogeometriassa, saaden ratkaisut kaikkien osa-aaltojen heijastuksille ja läpäisyille, minkä tahansa sisääntulevan aaltomoodin tapauksessa, ottaen täysin huomioon moodikonversiot. Formalismia voidaan käyttää käytännön numeerisiin tai jopa analyyttisiin sovelluksiin, kuten muutamin esimerkein osoitetaan. Työssä löydettiin silmiinpistävän yksinkertainen resonanssitunnelointiehto, joka johtaa akustisen fononin täydelliseen tunnelointiin, eli akustisen aallon transmissioon tyhjiön yli ilman heijastuksia. Myös yksityiskohtainen analyyttinen todistus tälle täydelliselle fononitunneloinnille esitetään, kuten myös numeerinen todistus. Lisäksi formalismia käytettiin pietsosähköisen kytkennän mahdollistaman fononitunnelointi-lämpövuon tutkimiseen. Muutama numeerinen esimerkki esitetään, ja niitä verrataan muihin lähikentän lämmönsiirtomekanismeihin. Eiryisesti tämä työ osoitti, että tällainen lämmönsiirtomekanismi on merkittävä, kun tyhjiörako on pienempi kuin fononien karakteristinen aallonpituus, ja muodostuu dominoivaksi alle 50K lämpötiloissa. Lopuksi esitetään kokeellinen demonstraatio akustisten fononien tunneloinnin mahdollistamasta lämmönsiirrosta, käyttäen kahta itsekantavaa pietsosähköistä palkkia alle Kelvinin lämpötiloissa. Mittausten tulokset todistavat kvalitatiivisesti lämmönsiirron eriraon leveyksillä, seka verraten sitä ei-pietsosähköisiin näytteisiin. Mitattu lämpöteho ei kuitenkaan ole kvantitatiivisesti yhtenevät teoreettisten arvioiden kanssa. Tähän eroavuuteen johtavia mahdollisia syitä pohditaan lopuksi.
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The dissertation presents the author\u2019s work to provide a generally applicable theoretical formulation and an experimental demonstration of acoustic phonon tunneling between arbitrarily an isotropic and oriented piezoelectric crystals.\nWithin the continuum an isotropic linear elasticity theory and the quasistatic approximation, this work solves the acoustic wave tunneling problem with two different approaches for a plane-plane geometry, acquiring the solutions of reflection and transmission of all the partial waves for any incoming wave mode, taking fully into account mode conversions. Such formalism can be applied to a practical numerical or even ananalytical implementation, as a few chosen analytical and numerical examples demonstrate.\nA strikingly simple resonant tunneling condition was discovered in this work, which leads to the complete tunneling of an acoustic phonon, a unity transmission of the acoustic wave across vacuum without reflection. The detailed analytical proof and numerical demonstration of such complete phonon tunneling are presented.\nFurthermore, this formalism was applied to investigate the heat flux associated with the phonon tunneling mediated by piezoelectricity. A few numerical\nresults are demonstrated and compared with other near-field heat transfer mechanisms. In particular, this work shows that such heat transfer is significant when a vacuum gap size is smaller than the phonon characteristic wavelength, and even becomes the dominant mechanism at temperatures lower than 50K.\nLastly, an experimental demonstration of the heat transfer mediated by acoustic phonon tunneling is presented, using two suspended piezoelectric microscopic beams at sub-kelvin temperatures. The results of the measurements provide qualitative evidence of the heat transfer, with comparisons between different vacuum gap widths and with non-piezoelectric devices. However, the quantitatively determined transferred power is not in good agreement with the theoretical estimations, and possible causes of the discrepancy are discussed.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Vaikka puhtaat akustiset aallot eiv\u00e4t voi esiinty\u00e4 tyhji\u00f6ss\u00e4 m\u00e4\u00e4ritelm\u00e4ns\u00e4 mukaan, akustinen fononi voi itse asiassa \"hyp\u00e4t\u00e4\" tai \"tunneloitua\" tyhji\u00f6raon\nyli kahden pietsos\u00e4hk\u00f6isen materiaalin v\u00e4lill\u00e4. T\u00e4ss\u00e4 v\u00e4it\u00f6skirjassa esitet\u00e4\u00e4n uusi yleisesti sovellettava teoria sek\u00e4 kokeellinen demonstraatio akustisten fononien tunneloitumiselle kahden mielivaltaisesti anisotrooppisen ja suunnatun pietsos\u00e4hk\u00f6isen kiteen v\u00e4lill\u00e4.\nK\u00e4ytt\u00e4en anisotrooppista jatkuvan aineen lineaarista elastisuusteoriaa ja kvasistaattista approksimaatiota, t\u00e4ss\u00e4 ty\u00f6ss\u00e4 ratkaistaan akustisten aaltojen tunnelointiongelma k\u00e4ytt\u00e4en kahta eri l\u00e4hestymistapaa taso-tasogeometriassa, saaden ratkaisut kaikkien osa-aaltojen heijastuksille ja l\u00e4p\u00e4isyille, mink\u00e4 tahansa sis\u00e4\u00e4ntulevan aaltomoodin tapauksessa, ottaen t\u00e4ysin huomioon moodikonversiot. Formalismia voidaan k\u00e4ytt\u00e4\u00e4 k\u00e4yt\u00e4nn\u00f6n numeerisiin tai jopa analyyttisiin sovelluksiin, kuten muutamin esimerkein osoitetaan.\nTy\u00f6ss\u00e4 l\u00f6ydettiin silmiinpist\u00e4v\u00e4n yksinkertainen resonanssitunnelointiehto, joka johtaa akustisen fononin t\u00e4ydelliseen tunnelointiin, eli akustisen aallon transmissioon tyhji\u00f6n yli ilman heijastuksia. My\u00f6s yksityiskohtainen analyyttinen todistus t\u00e4lle t\u00e4ydelliselle fononitunneloinnille esitet\u00e4\u00e4n, kuten my\u00f6s numeerinen todistus.\nLis\u00e4ksi formalismia k\u00e4ytettiin pietsos\u00e4hk\u00f6isen kytkenn\u00e4n mahdollistaman fononitunnelointi-l\u00e4mp\u00f6vuon tutkimiseen. Muutama numeerinen esimerkki esitet\u00e4\u00e4n, ja niit\u00e4 verrataan muihin l\u00e4hikent\u00e4n l\u00e4mm\u00f6nsiirtomekanismeihin. Eiryisesti t\u00e4m\u00e4 ty\u00f6 osoitti, ett\u00e4 t\u00e4llainen l\u00e4mm\u00f6nsiirtomekanismi on merkitt\u00e4v\u00e4, kun tyhji\u00f6rako on pienempi kuin fononien karakteristinen aallonpituus, ja muodostuu dominoivaksi alle 50K l\u00e4mp\u00f6tiloissa.\nLopuksi esitet\u00e4\u00e4n kokeellinen demonstraatio akustisten fononien tunneloinnin mahdollistamasta l\u00e4mm\u00f6nsiirrosta, k\u00e4ytt\u00e4en kahta itsekantavaa pietsos\u00e4hk\u00f6ist\u00e4 palkkia alle Kelvinin l\u00e4mp\u00f6tiloissa. Mittausten tulokset todistavat kvalitatiivisesti l\u00e4mm\u00f6nsiirron eriraon leveyksill\u00e4, seka verraten sit\u00e4 ei-pietsos\u00e4hk\u00f6isiin n\u00e4ytteisiin. Mitattu l\u00e4mp\u00f6teho ei kuitenkaan ole kvantitatiivisesti yhtenev\u00e4t teoreettisten arvioiden kanssa. T\u00e4h\u00e4n eroavuuteen johtavia mahdollisia syit\u00e4 pohditaan lopuksi.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2023-04-05T09:25:49Z\r\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2023-04-05T09:25:49Z (GMT). No. of bitstreams: 0\r\n Previous issue date: 2023", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.publisher", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": null, "element": "publisher", "qualifier": null, "schema": "dc"}, {"key": "dc.relation.ispartofseries", "value": "JYU Dissertations", "language": null, "element": "relation", "qualifier": "ispartofseries", "schema": "dc"}, {"key": "dc.relation.haspart", "value": "<b>Artikkeli I:</b> Geng, Z., & Maasilta, I. J. (2022). Acoustic wave tunneling across a vacuum gap between two piezoelectric crystals with arbitrary symmetry and orientation. <i>Physical Review Research, 4(3), Article 033073.</i> DOI: <a href=\"https://doi.org/10.1103/PhysRevResearch.4.033073\"target=\"_blank\"> 10.1103/PhysRevResearch.4.033073</a>", "language": null, "element": "relation", "qualifier": "haspart", "schema": "dc"}, {"key": "dc.relation.haspart", "value": "<b>Artikkeli II:</b> Z. Geng & I. J. Maasilta. Complete tunneling of acoustic waves between piezoelectric crystals. <i>Submitted manuscript.</i> <a href=\"https://arxiv.org/abs/2209.08287\"target=\"_blank\">Preprint</a>", "language": null, "element": "relation", "qualifier": "haspart", "schema": "dc"}, {"key": "dc.relation.haspart", "value": "<b>Artikkeli III:</b> Z. Geng & I. J. Maasilta. Heat transfer across a vacuum gap induced by piezoelectrically mediated acoustic phonon tunneling. <i>Manuscript.</i> <a href=\"https://arxiv.org/abs/2303.05084\"target=\"_blank\">Preprint</a>", "language": null, "element": "relation", "qualifier": "haspart", "schema": "dc"}, {"key": "dc.relation.haspart", "value": "<b>Artikkeli IV:</b> Z. Geng & I. J. Maasilta. Experimental demonstration of heat transfer mediated by acoustic phonon tunneling between vacuum separated piezoelectric solids. <i>Manuscript.</i>", "language": null, "element": "relation", "qualifier": "haspart", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": null, "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.title", "value": "Piezoelectrically mediated acoustic phonon tunneling", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "doctoral thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:ISBN:978-951-39-9532-4", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Mathematics and Science", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_db06", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.relation.issn", "value": "2489-9003", "language": null, "element": "relation", "qualifier": "issn", "schema": "dc"}, {"key": "dc.rights.copyright", "value": "\u00a9 The Author & University of Jyv\u00e4skyl\u00e4", "language": null, "element": "rights", "qualifier": "copyright", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "doctoralThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
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spellingShingle Geng, Zhuoran Piezoelectrically mediated acoustic phonon tunneling
title Piezoelectrically mediated acoustic phonon tunneling
title_full Piezoelectrically mediated acoustic phonon tunneling
title_fullStr Piezoelectrically mediated acoustic phonon tunneling Piezoelectrically mediated acoustic phonon tunneling
title_full_unstemmed Piezoelectrically mediated acoustic phonon tunneling Piezoelectrically mediated acoustic phonon tunneling
title_short Piezoelectrically mediated acoustic phonon tunneling
title_sort piezoelectrically mediated acoustic phonon tunneling
title_txtP Piezoelectrically mediated acoustic phonon tunneling
url https://jyx.jyu.fi/handle/123456789/86268 http://www.urn.fi/URN:ISBN:978-951-39-9532-4
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