{"id":1791,"date":"2015-05-01T20:00:54","date_gmt":"2015-05-01T20:00:54","guid":{"rendered":"http:\/\/casgroups.case.edu\/physics-senior-projects\/?p=1791"},"modified":"2016-06-17T15:13:36","modified_gmt":"2016-06-17T15:13:36","slug":"dirac-theory-of-topological-insulator-boundaries","status":"publish","type":"post","link":"https:\/\/casgroups.case.edu\/physics-senior-projects\/dirac-theory-of-topological-insulator-boundaries\/","title":{"rendered":"Dirac theory of topological insulator boundaries"},"content":{"rendered":"<h3 class=\"style21\" align=\"center\"><span class=\"style22\">Joseph Flannery with Harsh Mathur<\/span><\/h3>\n<h3 align=\"center\"><span class=\"style21\"><span class=\"style20\"><em>Dirac theory of topological insulator boundaries<\/em><\/span><\/span><\/h3>\n<p align=\"left\">A topological insulator is a material that behaves as an insulator\u00a0in its interior but whose surface contains bound conducting states.\u00a0The bulk of a topological insulator may be described by a massive\u00a0Dirac model while the gapless surface states follow the massless\u00a0Dirac equation. Currently lattice models are needed to give a unified\u00a0description of the bulk and surface states [1]. In this project we will\u00a0construct a unified description of the bulk and surface states working\u00a0with a continuum Dirac description by imposing appropriate boundary\u00a0conditions on the massive Dirac\u00a0equation at the insulator surface.\u00a0These boundary conditions must be consistent with the requirement \u00a0that the Dirac Hamiltonian operator be hermitian and symmetries such\u00a0as time-reversal and charge conjugation. The continuum description\u00a0of topological insulators will be used to analyze insulators with\u00a0nontrivial topologies and\u00a0geometries. Electrons on the surface of\u00a0cylindrical topological insulators have been shown to behave as though the cylinder is threaded by an Aharonov-Bohm flux [2]. In this project\u00a0we will\u00a0explore\u00a0analogous effects on spheres and tori.<\/p>\n<p align=\"left\">[1] M.Z. Hasan and C.L. Kane, Reviews of Modern Physics\u00a0<strong>82,<\/strong>\u00a03045 (2010)<\/p>\n<p align=\"left\">[2] Yi Zhang and Ashvin Vishwanath, Physical Review Letters\u00a0<strong>105<\/strong>, 206601 (2010)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Joseph Flannery with Harsh Mathur<em>Dirac theory of topological insulator boundaries<\/em><\/p>\n<p align=\"left\">A topological insulator is a material that behaves as an insulator\u00a0in its interior but whose surface contains bound conducting states.\u00a0The bulk of a topological insulator may be described by a massive\u00a0Dirac model while the gapless surface states follow the massless\u00a0Dirac equation. Currently lattice models are needed to give a unified\u00a0description of the bulk and surface states [1]. In this project we will\u00a0construct a unified description of the bulk and surface states working\u00a0with a continuum Dirac description by imposing appropriate boundary\u00a0conditions on the massive Dirac\u00a0equation at the insulator surface.\u00a0<\/p>\n<p><a href=\"https:\/\/casgroups.case.edu\/physics-senior-projects\/dirac-theory-of-topological-insulator-boundaries\/\" class=\"more-link\">Continue reading&#8230; <span class=\"screen-reader-text\">Dirac theory of topological insulator boundaries<\/span><\/a><\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[43,1,40,5,11,19],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/posts\/1791"}],"collection":[{"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/comments?post=1791"}],"version-history":[{"count":1,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/posts\/1791\/revisions"}],"predecessor-version":[{"id":1792,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/posts\/1791\/revisions\/1792"}],"wp:attachment":[{"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/media?parent=1791"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/categories?post=1791"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/casgroups.case.edu\/physics-senior-projects\/wp-json\/wp\/v2\/tags?post=1791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}