{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/102400"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/102400","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Physics and applications of magnetic interactions in topological insulators","abstract":"Despite the theoretical development and experimental discovery of a variety of topological materials over the past decade, their use in next-generation technologies remains limited. To better characterize the utility of these unique materials for engineering applications, we critically study the physics and application of topological insulators (TIs), paying particular attention to how magnetic interactions can alter their high-frequency response. To model AC transport within these materials, we develop a novel simulation framework that self-consistently solves frequency-domain quantum transport equations with the full solution of Maxwell's equations in three-dimensions. By simulating the radiation pattern of a quantum-confined monopole antenna using this methodology, we show that the field profile deviates from classical expectations and demonstrate the utility of the simulation technique in modeling nanoscale devices where both quantum mechanics and electrodynamic coupling are relevant. Such a simulation tool allows for accurate performance benchmarking over a wide range of operating frequencies of device designs utilizing topological materials. Having developed a comprehensive quantum transport simulation framework, we turn our attention to the study of the magnetic proximity effect, whereby a ferromagnet placed in proximity to a 3D TI creates a mass gap in the Dirac surface states and generates a quantum anomalous Hall effect (QAHE). Although this platform has long been proposed for technological applications ranging from topological transistors to qubits for quantum computing, the microscopic details of the proximity effect have to date been neglected. By constructing a contact self-energy for the ferromagnet, we show that when metallic bands of the ferromagnet are present at the Dirac point, the effective Hamiltonian describing the heterostructure is non-Hermitian with broadening that can obscure the mass gap. We calculate the Hall conductivity of the non-Hermitian effective Hamiltonian and show that it is no longer quantized due to the finite lifetime of quasiparticle states. When the ferromagnet is insulating at the Dirac point, however, a finite spectral gap forms, enabling the observation of the QAHE. We then use this knowledge of the magnetic proximity effect to design a paradigmatically different inductor. By placing magnetic islands on the surface of the 3D TIs to locally create a QAHE, we show that current is directed into highly inductive loops. Using our high-frequency transport simulation technique, we show that this topological inductor provides inductance densities and operating frequencies that exceed those of competing technologies. Thus, we demonstrate that the physics of TIs can be successfully leveraged to design high-performance post-CMOS device architectures.","abstract_html":"Despite the theoretical development and experimental discovery of a variety of topological materials over the past decade, their use in next-generation technologies remains limited. To better characterize the utility of these unique materials for engineering applications, we critically study the physics and application of topological insulators (TIs), paying particular attention to how magnetic interactions can alter their high-frequency response. To model AC transport within these materials, we develop a novel simulation framework that self-consistently solves frequency-domain quantum transport equations with the full solution of Maxwell's equations in three-dimensions. By simulating the radiation pattern of a quantum-confined monopole antenna using this methodology, we show that the field profile deviates from classical expectations and demonstrate the utility of the simulation technique in modeling nanoscale devices where both quantum mechanics and electrodynamic coupling are relevant. Such a simulation tool allows for accurate performance benchmarking over a wide range of operating frequencies of device designs utilizing topological materials. Having developed a comprehensive quantum transport simulation framework, we turn our attention to the study of the magnetic proximity effect, whereby a ferromagnet placed in proximity to a 3D TI creates a mass gap in the Dirac surface states and generates a quantum anomalous Hall effect (QAHE). Although this platform has long been proposed for technological applications ranging from topological transistors to qubits for quantum computing, the microscopic details of the proximity effect have to date been neglected. By constructing a contact self-energy for the ferromagnet, we show that when metallic bands of the ferromagnet are present at the Dirac point, the effective Hamiltonian describing the heterostructure is non-Hermitian with broadening that can obscure the mass gap. We calculate the Hall conductivity of the non-Hermitian effective Hamiltonian and show that it is no longer quantized due to the finite lifetime of quasiparticle states. When the ferromagnet is insulating at the Dirac point, however, a finite spectral gap forms, enabling the observation of the QAHE. We then use this knowledge of the magnetic proximity effect to design a paradigmatically different inductor. By placing magnetic islands on the surface of the 3D TIs to locally create a QAHE, we show that current is directed into highly inductive loops. Using our high-frequency transport simulation technique, we show that this topological inductor provides inductance densities and operating frequencies that exceed those of competing technologies. Thus, we demonstrate that the physics of TIs can be successfully leveraged to design high-performance post-CMOS device architectures.","abstract_has_math":false,"creators":["Philip, Timothy M."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Gilbert, Matthew J.","Lyding, Joseph","Mason, Nadya","Ravaioli, Umberto"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-02-06T19:32:41Z","date_published":"2019-02-06T19:32:41Z","updated_at":"2026-07-22T22:24:40Z","subjects":["topological insulator","magnetism, non-equilibrium Green function","quantum transport, high-frequency dynamics, non-Hermitian, open quantum systems, inductors"],"languages":["en"],"rights":["Copyright 2018 Timothy M. Philip"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/102400","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Gilbert, Matthew J.","Lyding, Joseph","Mason, Nadya","Ravaioli, Umberto"]},{"key":"dc:creator","label":"Author","values":["Philip, Timothy M."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-02-06T19:32:41Z","2018-09-17","2018-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"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":["topological insulator","magnetism, non-equilibrium Green function","quantum transport, high-frequency dynamics, non-Hermitian, open quantum systems, inductors"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Timothy M. 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By simulating the radiation pattern of a quantum-confined monopole antenna using this methodology, we show that the field profile deviates from classical expectations and demonstrate the utility of the simulation technique in modeling nanoscale devices where both quantum mechanics and electrodynamic coupling are relevant. Such a simulation tool allows for accurate performance benchmarking over a wide range of operating frequencies of device designs utilizing topological materials. Having developed a comprehensive quantum transport simulation framework, we turn our attention to the study of the magnetic proximity effect, whereby a ferromagnet placed in proximity to a 3D TI creates a mass gap in the Dirac surface states and generates a quantum anomalous Hall effect (QAHE). Although this platform has long been proposed for technological applications ranging from topological transistors to qubits for quantum computing, the microscopic details of the proximity effect have to date been neglected. By constructing a contact self-energy for the ferromagnet, we show that when metallic bands of the ferromagnet are present at the Dirac point, the effective Hamiltonian describing the heterostructure is non-Hermitian with broadening that can obscure the mass gap. We calculate the Hall conductivity of the non-Hermitian effective Hamiltonian and show that it is no longer quantized due to the finite lifetime of quasiparticle states. When the ferromagnet is insulating at the Dirac point, however, a finite spectral gap forms, enabling the observation of the QAHE. We then use this knowledge of the magnetic proximity effect to design a paradigmatically different inductor. By placing magnetic islands on the surface of the 3D TIs to locally create a QAHE, we show that current is directed into highly inductive loops. Using our high-frequency transport simulation technique, we show that this topological inductor provides inductance densities and operating frequencies that exceed those of competing technologies. Thus, we demonstrate that the physics of TIs can be successfully leveraged to design high-performance post-CMOS device architectures.","Submission original under an indefinite embargo labeled 'Open Access'. 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To better characterize the utility of these unique materials for engineering applications, we critically study the physics and application of topological insulators (TIs), paying particular attention to how magnetic interactions can alter their high-frequency response. To model AC transport within these materials, we develop a novel simulation framework that self-consistently solves frequency-domain quantum transport equations with the full solution of Maxwell's equations in three-dimensions. By simulating the radiation pattern of a quantum-confined monopole antenna using this methodology, we show that the field profile deviates from classical expectations and demonstrate the utility of the simulation technique in modeling nanoscale devices where both quantum mechanics and electrodynamic coupling are relevant. Such a simulation tool allows for accurate performance benchmarking over a wide range of operating frequencies of device designs utilizing topological materials. Having developed a comprehensive quantum transport simulation framework, we turn our attention to the study of the magnetic proximity effect, whereby a ferromagnet placed in proximity to a 3D TI creates a mass gap in the Dirac surface states and generates a quantum anomalous Hall effect (QAHE). Although this platform has long been proposed for technological applications ranging from topological transistors to qubits for quantum computing, the microscopic details of the proximity effect have to date been neglected. By constructing a contact self-energy for the ferromagnet, we show that when metallic bands of the ferromagnet are present at the Dirac point, the effective Hamiltonian describing the heterostructure is non-Hermitian with broadening that can obscure the mass gap. We calculate the Hall conductivity of the non-Hermitian effective Hamiltonian and show that it is no longer quantized due to the finite lifetime of quasiparticle states. When the ferromagnet is insulating at the Dirac point, however, a finite spectral gap forms, enabling the observation of the QAHE. We then use this knowledge of the magnetic proximity effect to design a paradigmatically different inductor. By placing magnetic islands on the surface of the 3D TIs to locally create a QAHE, we show that current is directed into highly inductive loops. Using our high-frequency transport simulation technique, we show that this topological inductor provides inductance densities and operating frequencies that exceed those of competing technologies. Thus, we demonstrate that the physics of TIs can be successfully leveraged to design high-performance post-CMOS device architectures.","Submission original under an indefinite embargo labeled 'Open Access'. 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