{"id":3773,"date":"2023-09-08T15:58:51","date_gmt":"2023-09-08T13:58:51","guid":{"rendered":"https:\/\/www.uni.lu\/fstm-en\/blog\/research-groups\/theory-of-mesoscopic-quantum-systems\/research\/"},"modified":"2025-05-02T16:09:11","modified_gmt":"2025-05-02T14:09:11","slug":"research","status":"publish","type":"research-groups","link":"https:\/\/www.uni.lu\/fstm-en\/research-groups\/theory-of-mesoscopic-quantum-systems\/research\/","title":{"rendered":"Research"},"content":{"rendered":"<div class=\"section py-0 static\">\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\"><!-- SecondaryNavigationMirror --><div class=\"js-secondary-nav--sticky wp-block-unilux-blocks-secondary-navigation\" id=\"0a012db4-f286-4610-942c-f0f52f80ba3c\">\n    <nav id=\"secondary-navigation\" role=\"navigation\" aria-label=\"Secondary menu\" class=\"secondary-nav\">\n        <button class=\"secondary-nav__button btn btn-solid--primary w-full\" aria-expanded=\"false\" aria-controls=\"secondary-navigation__list\" title=\"The selected page is Overview\" type=\"button\">\n            <span class=\"btn__name mr-auto\">Overview<\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\" \/>\n            <\/svg>\n        <\/button>\n\n        <ul id=\"secondary-navigation__list\" class=\"secondary-nav__list\">\n            <li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/theory-of-mesoscopic-quantum-systems\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Overview<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/theory-of-mesoscopic-quantum-systems\/research\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link isactived\" aria-current=\"page\">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Research<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/theory-of-mesoscopic-quantum-systems\/people\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">People<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/theory-of-mesoscopic-quantum-systems\/join-us\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Join us<\/span>\n    <\/a>\n<\/li>\n        <\/ul>\n    <\/nav>\n<\/div>\n<!-- end SecondaryNavigationMirror --><\/div><\/section>\n\n\n\n<section class=\"wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<h1 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"research-in-our-group\"\n    >\nResearch in our group<\/h1>\n\n\n\n<p>In recent years, we have worked very actively on&nbsp;<strong>topological materials<\/strong>, whose band structures are characterized mathematically by topological invariants. These materials display interesting surface phenomena and can host emergent quantum particles like Majorana fermions. In particular, we have worked on the effect of electronic correlations and spin-orbit coupling on such materials.<\/p>\n\n\n\n<p>A recurring theme have been&nbsp;<strong>quantum transport phenomena<\/strong>&nbsp;in various mesoscopic settings. In this domain, our group has experience with the description of charge or heat transport in systems such as nanowires, topological insulators, quantum dots, and graphene. Recently, we have explored how transport is affected by electronic correlations in nanowires and graphene.<\/p>\n\n\n\n<p>In quantum mechanics, the description of many-particle systems in the presence of interactions is a hard problem which calls for highly specialized techniques. Our group performs mainly analytical calculations on simplified model systems using methods from quantum field theory. In addition to this, we often test these model predictions against numerical simulations.<\/p>\n<\/div><\/section>\n\n\n\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\"><div class=\"content-card content-card--right content-card__overlay--hidden wp-block-unilux-blocks-content-card\">\n    \n<h2 class=\"content-card__heading has-text-align-left wp-block-unilux-blocks-heading\"    >\nTopological superconductivity<\/h2>\n<div class=\"content-card__visual wp-block-unilux-blocks-content-card-visual-area\">\n    \n<section class=\"wp-block-unilux-blocks-image-video-wrapper\">\n    <figure class=\"wp-block-dev4-reusable-blocks-image  object-fit--cover\">\n    \n<img decoding=\"async\" class=\"wp-block-image unilux-custom-image-block\"\n                alt=\"\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/ChristmasParafermions.png\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/ChristmasParafermions-225x300.png 225w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/ChristmasParafermions-768x1024.png 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/ChristmasParafermions-1152x1536.png 1152w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/ChristmasParafermions.png 1500w\"\n                style=\"object-position: 62.00% 89.00%; font-family: &quot;object-fit: cover; object-position: 62.00% 89.00%;&quot;; aspect-ratio: 3\/2; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure><\/section>\n<div class=\"wp-block-unilux-blocks-wrapper content-card__overlay\">\n<a class=\"wp-block-unilux-blocks-button-highlight-rounded bottom-left\" \n    href=\"#\"\n    target=\"_self\"\n>\n    \n<span class=\"btn-highlight-rounded__name wp-block-unilux-blocks-plain-text\"><\/span>    <span class=\"icon-rounded\">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg>    <\/span>\n<\/a><\/div>\n<\/div><div class=\"content-card__body  wp-block-unilux-blocks-content-card-free-area\">\n    \n<div class=\"wp-block-columns is-layout-flex wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Majorana fermions have been theoretically predicted more than 70 years ago, but whether they exist as fundamental particles remains an open question to this day. The prediction and subsequent experimental indications of Majorana bound states as quasiparticles in certain solid-state systems have therefore sparked a flurry of research activity, driven also by their usefulness in topological quantum computing.<br><br><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Parafermionic bound states are generalizations of MBS which occur in strongly correlated systems, such as fractional quantum Hall states. They are more suitable for topological quantum computation than MBS because their braiding allows additional protected operations. We explore ways to experimentally realize such parafermionic states and how to use them for quantum computation. An essential prerequisite is to better understand the interplay between two important \u201cmacroscopic\u201d quantum effects: superconductivity and quantum Hall physics.<\/p>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<p><strong>References: <\/strong><\/p>\n\n\n\n<ol class=\"ulux-list\">\n<li class=\"ulux-list-item\">Michelsen, Andreas Bock and Recher, Patrik and Braunecker, Bernd and Schmidt, Thomas L.,&nbsp;<em>Supercurrent-Enabled Andreev Reflection in a Chiral Quantum Hall Edge State<\/em>, Physical Review Research&nbsp;<strong>5<\/strong>, 013066 (2023)<\/li>\n\n\n\n<li class=\"ulux-list-item\">Teixeira, Raphael L. R. C. and Haller, Andreas and Singh, Roshni and Mathew, Amal and Idrisov, Edvin G. and Dias da Silva, Luis G. G. V. and Schmidt, Thomas L.,&nbsp;<em>Overlap of Parafermionic Zero Modes at a Finite Distance<\/em>, Physical Review Research&nbsp;<strong>4<\/strong>, 043094 (2022)<\/li>\n\n\n\n<li class=\"ulux-list-item\">Michelsen, Andreas B. and Schmidt, Thomas L. and Idrisov, Edvin G.,&nbsp;<em>Current Correlations of Cooper-Pair Tunneling into a Quantum Hall System<\/em>, Phys. Rev. B&nbsp;<strong>102<\/strong>, 125402 (2020)<\/li>\n\n\n\n<li class=\"ulux-list-item\">Schmidt, Thomas L.,&nbsp;<em>Bosonization for Fermions and Parafermions<\/em>, Eur. Phys. J. Special Topics&nbsp;<strong>229<\/strong>, 621 (2020)<\/li>\n\n\n\n<li class=\"ulux-list-item\">Groenendijk, Solofo and Calzona, Alessio and Tschirhart, Hugo and Idrisov, Edvin G. and Schmidt, Thomas L.,&nbsp;<em>Parafermion braiding in fractional quantum Hall edge states with a finite chemical potential<\/em>, Phys. Rev. B&nbsp;<strong>100<\/strong>, 205424 (2019)<\/li>\n\n\n\n<li class=\"ulux-list-item\">Alessio Calzona and Tobias Meng and Maura Sassetti and Thomas L. Schmidt,&nbsp;<em>Z4 parafermions in one-dimensional fermionic lattices<\/em>, Phys. Rev. B&nbsp;<strong>98<\/strong>, 201110(R) (2018)<\/li>\n\n\n\n<li class=\"ulux-list-item\">Christopher J. Pedder and Tobias Meng and Rakesh Tiwari and Thomas L. Schmidt,&nbsp;<em>Missing Shapiro steps and the $8\u03c0$-periodic Josephson effect in interacting helical electron systems<\/em>, Phys. Rev. B&nbsp;<strong>96<\/strong>, 165429 (2017)<\/li>\n<\/ol>\n<\/div><\/section>\n<\/div><\/section>\n\n\n\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\"><div class=\"content-card content-card--right content-card__overlay--hidden wp-block-unilux-blocks-content-card\">\n    \n<h2 class=\"content-card__heading has-text-align-left wp-block-unilux-blocks-heading\"        id=\"quantum-magnetism\"\n    >\nQuantum magnetism <\/h2>\n<div class=\"content-card__visual wp-block-unilux-blocks-content-card-visual-area\">\n    \n<section class=\"wp-block-unilux-blocks-image-video-wrapper\">\n    <figure class=\"wp-block-dev4-reusable-blocks-image  object-fit--cover\">\n    \n<img decoding=\"async\" class=\"wp-block-image unilux-custom-image-block\"\n                alt=\"\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/skyrmion.jpg\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/skyrmion-300x188.jpg 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/skyrmion-1024x640.jpg 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/skyrmion-768x480.jpg 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/skyrmion-1536x960.jpg 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/skyrmion-2048x1280.jpg 2048w\"\n                style=\"object-position: 35.00% 29.00%; font-family: &quot;object-fit: cover; object-position: 35.00% 29.00%;&quot;; aspect-ratio: 3\/2; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure><\/section>\n<div class=\"wp-block-unilux-blocks-wrapper content-card__overlay\">\n<a class=\"wp-block-unilux-blocks-button-highlight-rounded bottom-left\" \n    href=\"#\"\n    target=\"_self\"\n>\n    \n<span class=\"btn-highlight-rounded__name wp-block-unilux-blocks-plain-text\"><\/span>    <span class=\"icon-rounded\">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg>    <\/span>\n<\/a><\/div>\n<\/div><div class=\"content-card__body  wp-block-unilux-blocks-content-card-free-area\">\n    \n<div class=\"wp-block-columns is-layout-flex wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Skyrmions are topological magnetization patterns, which have been studied intensively over the past decade because of their suitability of information storage in magnetic memory chips. They have been mostly described by classical magnetism, but nanoscale skyrmions discovered in recent years raise the question about their quantum mechanical properties. An important cause of skyrmion formation is the Dzyaloshinskii-Moriya interaction, which exists is crytals with broken inversion symmetry.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>We investigate Heisenberg-like quantum systems with Dzyaloshinskii-Moriya interactions in one- and two-dimensional quantum magnets, described by Heisenberg-like Hamiltonians. We use a combination of analytical techniques (bosonization, spin-wave theory, mean-field theory) and numerical techniques (exact diagonalization, density-matrix renormalization group).<\/p>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<p><strong>References: <\/strong><\/p>\n\n\n\n<ol class=\"ulux-list\">\n<li class=\"ulux-list-item\">Haller, Andreas and Groenendijk, Solofo and Habibi, Alireza and Michels, Andreas and Schmidt, Thomas L.,&nbsp;<em>Quantum Skyrmion Lattices in Heisenberg Ferromagnets<\/em>, Physical Review Research&nbsp;<strong>4<\/strong>, 043113 (2022)<\/li>\n\n\n\n<li class=\"ulux-list-item\">Tschirhart, Hugo and Ong, Ernest T. S. and Sengupta, Pinaki and Schmidt, Thomas L.,&nbsp;<em>Phase diagram of spin-1 chains with Dzyaloshinskii-Moriya interaction<\/em>, Phys. Rev. B&nbsp;<strong>100<\/strong>, 195111 (2019)<\/li>\n<\/ol>\n\n\n\n<p><strong>Funding: <\/strong><\/p>\n\n\n\n<ol class=\"ulux-list\">\n<li class=\"ulux-list-item\">FNR CORE \u201cDetecting Quantum Skyrmions\u201d (DeQuSky).<\/li>\n\n\n\n<li class=\"ulux-list-item\">FNR AFR \u201cSpin-orbit coupling in low-dimensional correlated materials\u201d (SOCMAT).<\/li>\n<\/ol>\n<\/div><\/section>\n<\/div><\/section>\n\n\n\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\"><div class=\"content-card content-card--right content-card__overlay--hidden wp-block-unilux-blocks-content-card\">\n    \n<h2 class=\"content-card__heading has-text-align-left wp-block-unilux-blocks-heading\"        id=\"topological-materials\"\n    >\nTopological materials  <\/h2>\n<div class=\"content-card__visual wp-block-unilux-blocks-content-card-visual-area\">\n    \n<section class=\"wp-block-unilux-blocks-image-video-wrapper\">\n    <figure class=\"wp-block-dev4-reusable-blocks-image  object-fit--cover\">\n    \n<img decoding=\"async\" class=\"wp-block-image unilux-custom-image-block\"\n                alt=\"\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/TJunction.png\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/TJunction-300x169.png 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/TJunction-1024x576.png 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/TJunction-768x432.png 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/TJunction-1536x864.png 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/TJunction.png 1920w\"\n                style=\"object-position: 35.00% 29.00%; font-family: &quot;object-fit: cover; object-position: 35.00% 29.00%;&quot;; aspect-ratio: 3\/2; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure><\/section>\n<div class=\"wp-block-unilux-blocks-wrapper content-card__overlay\">\n<a class=\"wp-block-unilux-blocks-button-highlight-rounded bottom-left\" \n    href=\"#\"\n    target=\"_self\"\n>\n    \n<span class=\"btn-highlight-rounded__name wp-block-unilux-blocks-plain-text\"><\/span>    <span class=\"icon-rounded\">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg>    <\/span>\n<\/a><\/div>\n<\/div><div class=\"content-card__body  wp-block-unilux-blocks-content-card-free-area\">\n    \n<div class=\"wp-block-columns is-layout-flex wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Topological materials have electronic band structures which can be characterized by a topological, quantized winding number. A prominent example are topological insulators, which behave like band insulators in the bulk but have gapless, metallic states on their surfaces. Most topological materials have spin-orbit coupling, so the orbital motion of electrons is strongly correlated with their spin. This gives rise to interesting spin and charge transport properties in these materials.<\/p>\n\n\n\n<p><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>We investigate electronic and optical properties of topological materials. In recent year, we have studied in particular, open topological quantum systems which are coupled to an environment, as well as the realization of general-relativistic effects in topological systems. Currently, we are also studying magnetic topological insulators and their interplay with superconductors.<\/p>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<p><strong>References: <\/strong><\/p>\n\n\n\n<ol class=\"ulux-list\">\n<li class=\"ulux-list-item\">Habibi, Alireza and Musthofa, Ahmad Z. and Adibi, Elaheh and Ekstr\u00f6m, Johan and Schmidt, Thomas L. and Hasdeo, Eddwi H.,&nbsp;<em>Kerr and Faraday Rotations in Topological Flat and Dispersive Band Structures<\/em>, New Journal of Physics&nbsp;<strong>24<\/strong>, 063003 (2022)<\/li>\n\n\n\n<li class=\"ulux-list-item\">De Beule, Christophe and Groenendijk, Solofo and Meng, Tobias and Schmidt, Thomas L.,&nbsp;<em>Artificial Event Horizons in Weyl Semimetal Heterostructures and Their Non-Equilibrium Signatures<\/em>, SciPost Phys.&nbsp;<strong>11<\/strong>, 095 (2021)<\/li>\n\n\n\n<li class=\"ulux-list-item\">Farias, M. Bel\u00e9n and Groenendijk, Solofo and Schmidt, Thomas L.,&nbsp;<em>Generalized Chern Numbers Based on Open System Green\u2019s Functions<\/em>, New Journal of Physics&nbsp;<strong>23<\/strong>, 073009 (2021)<\/li>\n\n\n\n<li class=\"ulux-list-item\">K\u00f6lzer, Jonas and Moors, Kristof and Jalil, Abdur Rehman and Zimmermann, Erik and Rosenbach, Daniel and Kibkalo, Lidia and Sch\u00fcffelgen, Peter and Mussler, Gregor and Gr\u00fctzmacher, Detlev and Schmidt, Thomas L. and L\u00fcth, Hans and Sch\u00e4pers, Thomas,&nbsp;<em>In-Plane Magnetic Field-Driven Symmetry Breaking in Topological Insulator-Based Three-Terminal Junctions<\/em>, Commun. Mater.&nbsp;<strong>2<\/strong>, 116 (2021)<\/li>\n<\/ol>\n\n\n\n<p><strong>Funding: <\/strong><\/p>\n\n\n\n<ol class=\"ulux-list\">\n<li class=\"ulux-list-item\">QuantERA \u201cMagnetic topological insulators for robust Majorana bound states\u201d (MAGMA)<\/li>\n\n\n\n<li class=\"ulux-list-item\">FNR CORE \u201cDetecting Quantum Skyrmions\u201d (DeQuSky).<\/li>\n<\/ol>\n<\/div><\/section>\n<\/div><\/section>\n<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":105,"featured_media":3771,"parent":3772,"menu_order":0,"template":"","meta":{"featured_image_focal_point":[],"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"Theory of mesoscopic quantum systems","uluxPrePostTitle":"Research Group","_trash_the_other_posts":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false},"field-of-interest":[],"organisation":[],"authorship":[105,103,200,201,101],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.3 (Yoast SEO v22.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Research Theory of mesoscopic quantum systems - FSTM research group I 糖心Vlog<\/title>\n<meta name=\"description\" content=\"In recent years, we have worked very actively on&nbsp;topological materials, whose band structures are characterized mathematically by topological\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/theory-of-mesoscopic-quantum-systems\/research\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Research\" \/>\n<meta property=\"og:description\" content=\"In recent years, we have worked very actively on&nbsp;topological materials, whose band structures are characterized mathematically by topological\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/theory-of-mesoscopic-quantum-systems\/research\/\" \/>\n<meta property=\"og:site_name\" content=\"FSTM EN\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/fstm.uni.lu\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-05-02T14:09:11+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/09\/TMQS_group_SchmidtEOSumd.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"700\" \/>\n\t<meta property=\"og:image:height\" content=\"467\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/theory-of-mesoscopic-quantum-systems\/research\/\",\"url\":\"https:\/\/www.uni.lu\/fstm-en\/research-groups\/theory-of-mesoscopic-quantum-systems\/research\/\",\"name\":\"Research Theory of mesoscopic quantum systems - 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