{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:49:58Z","timestamp":1760230198196,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2022,7,14]],"date-time":"2022-07-14T00:00:00Z","timestamp":1657756800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nanomaterials"],"abstract":"<jats:p>We investigate the phase transitions and the properties of the topological insulator in InGaN\/GaN and InN\/InGaN double quantum wells grown along the [0001] direction. We apply a realistic model based on the nonlinear theory of elasticity and piezoelectricity and the eight-band k\u00b7p method with relativistic and nonrelativistic linear-wave-vector terms. In this approach, the effective spin\u2013orbit interaction in InN is negative, which represents the worst-case scenario for obtaining the topological insulator in InGaN-based structures. Despite this rigorous assumption, we demonstrate that the topological insulator can occur in InGaN\/GaN and InN\/InGaN double quantum wells when the widths of individual quantum wells are two and three monolayers (MLs), and three and three MLs. In these structures, when the interwell barrier is sufficiently thin, we can observe the topological phase transition from the normal insulator to the topological insulator via the Weyl semimetal, and the nontopological phase transition from the topological insulator to the nonlocal topological semimetal. We find that in InGaN\/GaN double quantum wells, the bulk energy gap in the topological insulator phase is much smaller for the structures with both quantum well widths of 3 MLs than in the case when the quantum well widths are two and three MLs, whereas in InN\/InGaN double quantum wells, the opposite is true. In InN\/InGaN structures with both quantum wells being three MLs and a two ML interwell barrier, the bulk energy gap for the topological insulator can reach about 1.2\u00a0meV. We also show that the topological insulator phase rapidly deteriorates with increasing width of the interwell barrier due to a decrease in the bulk energy gap and reduction in the window of In content between the normal insulator and the nonlocal topological semimetal. For InN\/InGaN double quantum wells with the width of the interwell barrier above five or six MLs, the topological insulator phase does not appear. In these structures, we find two novel phase transitions, namely the nontopological phase transition from the normal insulator to the nonlocal normal semimetal and the topological phase transition from the nonlocal normal semimetal to the nonlocal topological semimetal via the buried Weyl semimetal. These results can guide future investigations towards achieving a topological insulator in InGaN-based nanostructures.<\/jats:p>","DOI":"10.3390\/nano12142418","type":"journal-article","created":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T01:57:11Z","timestamp":1657850231000},"page":"2418","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Polarization-Induced Phase Transitions in Ultra-Thin InGaN-Based Double Quantum Wells"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7681-3292","authenticated-orcid":false,"given":"S\u0142awomir P.","family":"\u0141epkowski","sequence":"first","affiliation":[{"name":"Institute of High Pressure Physics\u2014Unipress, Polish Academy of Sciences, ul. Soko\u0142owska 29\/37, 01-142 Warszawa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdur Rehman","family":"Anwar","sequence":"additional","affiliation":[{"name":"Institute of High Pressure Physics\u2014Unipress, Polish Academy of Sciences, ul. Soko\u0142owska 29\/37, 01-142 Warszawa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3045","DOI":"10.1103\/RevModPhys.82.3045","article-title":"Colloquium: Topological insulators","volume":"82","author":"Hasan","year":"2010","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"021004","DOI":"10.1103\/RevModPhys.88.021004","article-title":"Colloquium: Topological band theory","volume":"88","author":"Bansil","year":"2016","journal-title":"Rev. Mod. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"176802","DOI":"10.1103\/PhysRevLett.110.176802","article-title":"Topologically protected quantum transport in locally exfoliated bismuth at room temperature","volume":"110","author":"Sabater","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1038\/nphys3048","article-title":"One-dimensional topological edge states of bismuth bilayers","volume":"10","author":"Drozdov","year":"2014","journal-title":"Nat. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1126\/science.aan6003","article-title":"Observation of the quantum spin Hal effect up to 100 kelvin in a monolayer crystal","volume":"359","author":"Wu","year":"2018","journal-title":"Science"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1757","DOI":"10.1126\/science.1133734","article-title":"Quantum spin Hall effect and topological phase transition in HgTe quantum wells","volume":"314","author":"Bernevig","year":"2006","journal-title":"Science"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1126\/science.1148047","article-title":"Quantum spin Hall effect in HgTe quantum wells","volume":"318","author":"Konig","year":"2007","journal-title":"Science"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"236601","DOI":"10.1103\/PhysRevLett.100.236601","article-title":"Quantum spin Hall effect in inverted type-II semiconductors","volume":"100","author":"Liu","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"136603","DOI":"10.1103\/PhysRevLett.107.136603","article-title":"Evidence for helical edge modes in inverted InAs\/GaSb quantum wells","volume":"107","author":"Knez","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"193304","DOI":"10.1103\/PhysRevB.83.193304","article-title":"Two-dimensional electron-hole system in HgTe-based quantum wells with surface orientation (112)","volume":"83","author":"Kvon","year":"2011","journal-title":"Phys. Rev. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"155437","DOI":"10.1103\/PhysRevB.98.155437","article-title":"Two-dimensional semimetal in HgTe quantum well under hydrostatic pressure","volume":"98","author":"Prudkoglyad","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"186803","DOI":"10.1103\/PhysRevLett.109.186803","article-title":"Polarization-driven topological insulator transition in a GaN\/InN\/GaN quantum well","volume":"109","author":"Miao","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"15403","DOI":"10.1038\/s41598-018-33461-4","article-title":"Topological insulator with negative spin-orbit coupling and transition between Weyl and Dirac semimetals in inGaN-based quantum wells","volume":"8","author":"Bardyszewski","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"086403","DOI":"10.1103\/PhysRevLett.117.086403","article-title":"Strain engineering of the band gap of HgTe quantum wells using superlattice virtual substrates","volume":"117","author":"Leubner","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"056803","DOI":"10.1103\/PhysRevLett.119.056803","article-title":"R tuning edge states in strained-layer inAs\/GaInSb quantum spin Hall insulators","volume":"119","author":"Du","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"245419","DOI":"10.1103\/PhysRevB.97.245419","article-title":"Temperature-dependent terahertz spectroscopy of inverted-band three-layer InAs\/GaSb\/InAs quantum wells","volume":"97","author":"Krishtopenko","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"126802","DOI":"10.1103\/PhysRevLett.114.126802","article-title":"Persistence of a two-dimensional topological insulator state in wide HgTe quantum wells","volume":"114","author":"Olshanetsky","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"27001","DOI":"10.1209\/0295-5075\/118\/27001","article-title":"Magnetoconductance in InN\/GaN quantum wells in topological insulator phase","volume":"118","author":"Bardyszewski","year":"2017","journal-title":"EPL"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1154","DOI":"10.12693\/APhysPolA.126.1154","article-title":"Polarization-induced band inversion in In-rich InGaN\/GaN quantum wells","volume":"126","author":"Bardyszewski","year":"2014","journal-title":"Acta Phys. Pol. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"055702","DOI":"10.1088\/1361-648X\/29\/5\/055702","article-title":"Topological phase transition and evolution of edge states in In-rich InGaN\/GaN quantum wells under hydrostatic pressure","volume":"29","author":"Bardyszewski","year":"2017","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"152107","DOI":"10.1063\/1.4946860","article-title":"Growth kinetics and structural perfection of (InN)1\/(GaN)1-20 short-period superlattices on +c-GaN template in dynamic atomic layer epitaxy","volume":"108","author":"Kusakabe","year":"2016","journal-title":"Appl. Phys. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"024304","DOI":"10.1063\/1.5009060","article-title":"Compositional and strain analysis of In(Ga)N\/GaN short period superlattices","volume":"123","author":"Dimitrakopulos","year":"2018","journal-title":"J. Appl. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"20606","DOI":"10.1038\/s41598-021-99989-0","article-title":"Substitutional synthesis of sub-nanometer InGaN\/GaN quantum wells with high indium content","volume":"11","author":"Vasileiadis","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"195702","DOI":"10.1088\/1361-648X\/aa6860","article-title":"Anomalous Rashba spin-orbit interaction in electrically controlled topological insulator based on InN\/GaN quantum wells","volume":"29","author":"Bardyszewski","year":"2017","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1021\/acsnano.7b07996","article-title":"Piezotronic transistor based on topological insulators","volume":"12","author":"Hu","year":"2017","journal-title":"ACS Nano"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1016\/j.nanoen.2018.06.007","article-title":"High performance piezotronic logic nanodevices based on GaN\/InN\/GaN topological insulator","volume":"50","author":"Dan","year":"2018","journal-title":"Nano Energy"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"245304","DOI":"10.1103\/PhysRevB.104.245304","article-title":"Quantum anomalous Hall state with Chern number C = 2 in wurtzite quantum wells","volume":"104","author":"Litvinov","year":"2021","journal-title":"Phys. Rev. B"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"125309","DOI":"10.1103\/PhysRevB.85.125309","article-title":"Tunable quantum spin Hall effect in double quantum wells","volume":"85","author":"Michetti","year":"2012","journal-title":"Phys. Rev. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"30755","DOI":"10.1038\/srep30755","article-title":"Phase transitions in two tunnel-coupled HgTe quantum wells: Bilayer graphene analogy and beyond","volume":"6","author":"Krishtopenko","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"241302","DOI":"10.1103\/PhysRevB.101.241302","article-title":"Two-dimensional topological insulator state in double HgTe quantum well","volume":"101","author":"Gusev","year":"2020","journal-title":"Phys. Rev. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"195147","DOI":"10.1103\/PhysRevB.85.195147","article-title":"Valence band effective-mass Hamiltonians for the group-III nitrides from quasiparticle self-consistent GW band structures","volume":"85","author":"Punya","year":"2012","journal-title":"Phys. Rev. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"355402","DOI":"10.1088\/1361-648X\/ac0b22","article-title":"Third-order elastic constants and biaxial relaxation coefficient in wurtzite group-III nitrides by hybrid-density functional theory calculations","volume":"33","author":"Anwar","year":"2021","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3675","DOI":"10.1063\/1.1600519","article-title":"Band parameters for nitrogen-containing semiconductors","volume":"94","author":"Vurgaftman","year":"2003","journal-title":"J. Appl. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"075202","DOI":"10.1103\/PhysRevB.80.075202","article-title":"Influence of indium clustering on the band structure of semiconducting ternary and quaternary nitride alloys","volume":"80","author":"Gorczyca","year":"2009","journal-title":"Phys. Rev. B"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"130","DOI":"10.12693\/APhysPolA.141.130","article-title":"Biaxial relaxation coefficient in group-III nitride quantum wells and thin films","volume":"141","author":"Anwar","year":"2022","journal-title":"Acta Phys. Pol. A"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"105703","DOI":"10.1063\/1.4914416","article-title":"Inapplicability of Martin transformation to elastic constants of zinc-blende and wurtzite group-III nitride alloys","volume":"117","year":"2015","journal-title":"J. Appl. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1002\/(SICI)1521-3951(199911)216:1<391::AID-PSSB391>3.0.CO;2-K","article-title":"Spontaneous versus piezoelectric polarization in III-V nitrides: Conceptual aspects and practical consequences","volume":"216","author":"Bernardini","year":"1999","journal-title":"Phys. Stat. Sol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"121304","DOI":"10.1103\/PhysRevB.88.121304","article-title":"Nonlinear piezoelectricity in wurtzite semiconductors","volume":"88","author":"Prodhomme","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2491","DOI":"10.1103\/PhysRevB.54.2491","article-title":"k\u2219p method for strained wurtzite semiconductors","volume":"54","author":"Chuang","year":"1996","journal-title":"Phys. Rev. B"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"081202","DOI":"10.1103\/PhysRevB.88.081202","article-title":"Deformation potentials in AlGaN and InGaN alloys and their impact on optical polarization properties of nitride quantum wells","volume":"88","author":"Gorczyca","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_41","unstructured":"Huebner, K.H., and Thornton, E.A. (1982). The Finite Element Method for Engineers, Wiley."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.jcrysgro.2015.02.014","article-title":"Low-temperature growth of InGaN films over the entire composition range by MBE","volume":"425","author":"Fabien","year":"2015","journal-title":"J. Cryst. Growth"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"111111","DOI":"10.1063\/1.4895067","article-title":"Long wavelength emitting GaInN quantum wells on metamorphic GaInN buffer layers with enlarged in-plane lattice parameter","volume":"105","author":"Daubler","year":"2014","journal-title":"Appl. Phys. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"262103","DOI":"10.1063\/1.4989998","article-title":"Enhanced In incorporation in full InGaN heterostructure grown on relaxed InGaN pseudo-substrate","volume":"110","author":"Even","year":"2017","journal-title":"Appl. Phys. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2100427","DOI":"10.1002\/lpor.202100427","article-title":"Recent progress in micro-LED based display technologies","volume":"16","author":"Anwar","year":"2022","journal-title":"Laser Photonics Rev."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"245402","DOI":"10.1103\/PhysRevB.94.245402","article-title":"Pressure- and temperature-driven phase transitions in HgTe quantum wells","volume":"94","author":"Krishtopenko","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"156402","DOI":"10.1103\/PhysRevLett.111.156402","article-title":"Interface-induced topological insulator transition in GaAs\/Ge\/GaAs quantum wells","volume":"111","author":"Zhang","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"3259","DOI":"10.1002\/adfm.201505357","article-title":"Transforming common III-V and II-VI semiconductor compounds into topological heterostructures: The case of CdTe\/InSb superlattices","volume":"26","author":"Liu","year":"2016","journal-title":"Adv. Funct. Mater."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"105154","DOI":"10.1016\/j.nanoen.2020.105154","article-title":"Quantum piezotronic devices based on ZnO\/CdO quantum well topological insulator","volume":"77","author":"Hu","year":"2020","journal-title":"Nano Energy"}],"container-title":["Nanomaterials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-4991\/12\/14\/2418\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:50:40Z","timestamp":1760140240000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-4991\/12\/14\/2418"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,14]]},"references-count":49,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["nano12142418"],"URL":"https:\/\/doi.org\/10.3390\/nano12142418","relation":{},"ISSN":["2079-4991"],"issn-type":[{"type":"electronic","value":"2079-4991"}],"subject":[],"published":{"date-parts":[[2022,7,14]]}}}