{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/110400"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/110400","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"An efficient computational framework for prediction of corrugation in twisted bilayer graphene","abstract":"\"The discovery of unconventional superconductivity at a specific \"\"magic\"\" angle in twisted bilayer graphene (TBG) has stirred a lot of interest in the scientific community. When two graphene layers are placed on top of each other with a twist, a moir\\'e pattern emerges. By controlling the period of the moir\\'e in twisted bilayer graphene, we can tune the properties of TBG. Specifically, long periods of moir\\'e in bilayer graphene have shown remarkable electronic properties. However, materials with large moir\\'e periods are often difficult to study because of the expensive computational framework of electronic structure. Therefore, we develop a simple computational framework that can predict the corrugated structure of TBG of large periods in a computationally tractable way. From our density functional theory (DFT) simulations, we find that the structure of TBG becomes corrugated upon relaxation due to the change of interlayer distances in different stacking regions. The corrugation increases with decreasing twist angle in the TBG. Moreover, we also find that the AA region in the TBG shrinks and the AB region becomes larger at low twist angles (less than 1.5$^{\\circ}$). Our framework is able to capture this phenomenon of shrinking of the AA region and map the corrugation for low twist angles with precision. With our framework, it would be possible to map the atomic coordinates of the corrugated structure of TBG which can help us to study different properties of low twist angle TBG more accurately. In this way, this framework may open the door to more tunable exotic properties in twisted bilayer graphene.\"","abstract_html":"&quot;The discovery of unconventional superconductivity at a specific &quot;&quot;magic&quot;&quot; angle in twisted bilayer graphene (TBG) has stirred a lot of interest in the scientific community. When two graphene layers are placed on top of each other with a twist, a moir\\&#x27;e pattern emerges. By controlling the period of the moir\\&#x27;e in twisted bilayer graphene, we can tune the properties of TBG. Specifically, long periods of moir\\&#x27;e in bilayer graphene have shown remarkable electronic properties. However, materials with large moir\\&#x27;e periods are often difficult to study because of the expensive computational framework of electronic structure. Therefore, we develop a simple computational framework that can predict the corrugated structure of TBG of large periods in a computationally tractable way. From our density functional theory (DFT) simulations, we find that the structure of TBG becomes corrugated upon relaxation due to the change of interlayer distances in different stacking regions. The corrugation increases with decreasing twist angle in the TBG. Moreover, we also find that the AA region in the TBG shrinks and the AB region becomes larger at low twist angles (less than 1.5<span class=\"etd-inline-math\"><sup>\\circ</sup></span>). Our framework is able to capture this phenomenon of shrinking of the AA region and map the corrugation for low twist angles with precision. With our framework, it would be possible to map the atomic coordinates of the corrugated structure of TBG which can help us to study different properties of low twist angle TBG more accurately. In this way, this framework may open the door to more tunable exotic properties in twisted bilayer graphene.&quot;","abstract_has_math":true,"creators":["Rakib, Tawfiqur"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Johnson, Harley T.","Ertekin, Elif T"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-09-17T01:10:26Z","date_published":"2021-09-17T01:10:26Z","updated_at":"2026-07-22T22:24:50Z","subjects":["Graphene","twist","corrugation","moir\\'e","superconductivity"],"languages":["en"],"rights":["© 2020 Tawfiqur Rakib"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/110400","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Johnson, Harley T.","Ertekin, Elif T"]},{"key":"dc:creator","label":"Author","values":["Rakib, Tawfiqur"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2021-09-17T01:10:26Z","2020-12-10","2021-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Graphene","twist","corrugation","moir\\'e","superconductivity"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["© 2020 Tawfiqur Rakib"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/110400"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"The discovery of unconventional superconductivity at a specific \"\"magic\"\" angle in twisted bilayer graphene (TBG) has stirred a lot of interest in the scientific community. When two graphene layers are placed on top of each other with a twist, a moir\\'e pattern emerges. By controlling the period of the moir\\'e in twisted bilayer graphene, we can tune the properties of TBG. Specifically, long periods of moir\\'e in bilayer graphene have shown remarkable electronic properties. However, materials with large moir\\'e periods are often difficult to study because of the expensive computational framework of electronic structure. Therefore, we develop a simple computational framework that can predict the corrugated structure of TBG of large periods in a computationally tractable way. From our density functional theory (DFT) simulations, we find that the structure of TBG becomes corrugated upon relaxation due to the change of interlayer distances in different stacking regions. The corrugation increases with decreasing twist angle in the TBG. Moreover, we also find that the AA region in the TBG shrinks and the AB region becomes larger at low twist angles (less than 1.5$^{\\circ}$). Our framework is able to capture this phenomenon of shrinking of the AA region and map the corrugation for low twist angles with precision. With our framework, it would be possible to map the atomic coordinates of the corrugated structure of TBG which can help us to study different properties of low twist angle TBG more accurately. In this way, this framework may open the door to more tunable exotic properties in twisted bilayer graphene.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-09-16 without embargo terms","The student, Tawfiqur Rakib, accepted the attached license on 2020-12-09 at 10:34.","The student, Tawfiqur Rakib, submitted this Thesis for approval on 2020-12-09 at 10:48.","This Thesis was approved for publication on 2020-12-10 at 15:52.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16104 on 2021-09-16 at 16:39:00","Made available in DSpace on 2021-09-17T01:10:26Z (GMT). No. of bitstreams: 3 RAKIB-THESIS-2021.pdf: 4647221 bytes, checksum: 3997ff619cf1b4e750ce7979e635471d (MD5) RAKIB_thesis-2021.zip: 5423395 bytes, checksum: 3ebc48af9993cfa04264f10ab111ed8d (MD5) LICENSE.txt: 4211 bytes, checksum: fa7e9e4106dbe2b719f3bd94a10aa9bb (MD5) Previous issue date: 2020-12-10"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["An efficient computational framework for prediction of corrugation in twisted bilayer graphene"]}]}],"canonical_facts":{"dc:contributor":["Johnson, Harley T.","Ertekin, Elif T"],"dc:creator":["Rakib, Tawfiqur"],"dc:date":["2021-09-17T01:10:26Z","2020-12-10","2021-05"],"dc:description":["\"The discovery of unconventional superconductivity at a specific \"\"magic\"\" angle in twisted bilayer graphene (TBG) has stirred a lot of interest in the scientific community. When two graphene layers are placed on top of each other with a twist, a moir\\'e pattern emerges. By controlling the period of the moir\\'e in twisted bilayer graphene, we can tune the properties of TBG. Specifically, long periods of moir\\'e in bilayer graphene have shown remarkable electronic properties. However, materials with large moir\\'e periods are often difficult to study because of the expensive computational framework of electronic structure. Therefore, we develop a simple computational framework that can predict the corrugated structure of TBG of large periods in a computationally tractable way. From our density functional theory (DFT) simulations, we find that the structure of TBG becomes corrugated upon relaxation due to the change of interlayer distances in different stacking regions. The corrugation increases with decreasing twist angle in the TBG. Moreover, we also find that the AA region in the TBG shrinks and the AB region becomes larger at low twist angles (less than 1.5$^{\\circ}$). Our framework is able to capture this phenomenon of shrinking of the AA region and map the corrugation for low twist angles with precision. With our framework, it would be possible to map the atomic coordinates of the corrugated structure of TBG which can help us to study different properties of low twist angle TBG more accurately. In this way, this framework may open the door to more tunable exotic properties in twisted bilayer graphene.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-09-16 without embargo terms","The student, Tawfiqur Rakib, accepted the attached license on 2020-12-09 at 10:34.","The student, Tawfiqur Rakib, submitted this Thesis for approval on 2020-12-09 at 10:48.","This Thesis was approved for publication on 2020-12-10 at 15:52.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16104 on 2021-09-16 at 16:39:00","Made available in DSpace on 2021-09-17T01:10:26Z (GMT). No. of bitstreams: 3 RAKIB-THESIS-2021.pdf: 4647221 bytes, checksum: 3997ff619cf1b4e750ce7979e635471d (MD5) RAKIB_thesis-2021.zip: 5423395 bytes, checksum: 3ebc48af9993cfa04264f10ab111ed8d (MD5) LICENSE.txt: 4211 bytes, checksum: fa7e9e4106dbe2b719f3bd94a10aa9bb (MD5) Previous issue date: 2020-12-10"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/110400"],"dc:language":["en"],"dc:rights":["© 2020 Tawfiqur Rakib"],"dc:subject":["Graphene","twist","corrugation","moir\\'e","superconductivity"],"dc:title":["An efficient computational framework for prediction of corrugation in twisted bilayer graphene"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:50Z"}