Yong Zhang, Ming-Hui Gao, Guanzhang Liu, Lin Cao, Yang-Yang Lv, Senyang Pan, Jinglei Zhang, Li Pi, Shu-Hua Yao, Jian Zhou, Y. B. Chen, Yan-Feng Chen
{"title":"Fermiology and Zeeman splitting of the topological metalβ-ReO2probed by de Haas–van Alphen quantum oscillations under high magnetic fields","authors":"Yong Zhang, Ming-Hui Gao, Guanzhang Liu, Lin Cao, Yang-Yang Lv, Senyang Pan, Jinglei Zhang, Li Pi, Shu-Hua Yao, Jian Zhou, Y. B. Chen, Yan-Feng Chen","doi":"10.1103/physrevb.110.205109","DOIUrl":null,"url":null,"abstract":"Recently, <i>β-</i><mjx-container ctxtmenu_counter=\"59\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 4 (3 1 2))\"><mjx-mrow data-semantic-children=\"0,3\" data-semantic-content=\"4,0\" data-semantic- data-semantic-owns=\"0 4 3\" data-semantic-role=\"prefix function\" data-semantic-speech=\"re normal upper O 2\" data-semantic-type=\"appl\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">R</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>O</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> was theoretically proposed to be a candidate for Dirac nodal chain metal with hourglasslike energy-momentum dispersion and got considerable attention. Here, we have grown high-quality <i>β-</i><mjx-container ctxtmenu_counter=\"60\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 4 (3 1 2))\"><mjx-mrow data-semantic-children=\"0,3\" data-semantic-content=\"4,0\" data-semantic- data-semantic-owns=\"0 4 3\" data-semantic-role=\"prefix function\" data-semantic-speech=\"re normal upper O 2\" data-semantic-type=\"appl\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">R</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>O</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> single crystals with a residual-resistivity ratio as large as 428. The magnetoresistance (MR) can reach 7 × <mjx-container ctxtmenu_counter=\"61\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(4 (2 0 1) 3)\"><mjx-mrow data-semantic-children=\"2,3\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3\" data-semantic-role=\"endpunct\" data-semantic-speech=\"10 Superscript 4 Baseline percent sign\" data-semantic-type=\"punctuated\"><mjx-msup data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"superscript\"><mjx-mrow><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">1</mjx-c><mjx-c style=\"padding-top: 0.642em;\">0</mjx-c></mjx-mn></mjx-mrow><mjx-script style=\"vertical-align: 0.369em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>4</mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"4\" data-semantic-role=\"unknown\" data-semantic-type=\"punctuation\"><mjx-c>%</mjx-c></mjx-mo></mjx-mrow></mjx-math></mjx-container> measured under 9 T at 2 K. The fitting of MR and Hall data simultaneously by maximum entropy mobility spectrum reveals that there are two electron pockets and two hole pockets in <i>β-</i><mjx-container ctxtmenu_counter=\"62\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 4 (3 1 2))\"><mjx-mrow data-semantic-children=\"0,3\" data-semantic-content=\"4,0\" data-semantic- data-semantic-owns=\"0 4 3\" data-semantic-role=\"prefix function\" data-semantic-speech=\"re normal upper O 2\" data-semantic-type=\"appl\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">R</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>O</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> with comparable carrier concentrations, which leads to the large unsaturated MR in <i>β-</i><mjx-container ctxtmenu_counter=\"63\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 4 (3 1 2))\"><mjx-mrow data-semantic-children=\"0,3\" data-semantic-content=\"4,0\" data-semantic- data-semantic-owns=\"0 4 3\" data-semantic-role=\"prefix function\" data-semantic-speech=\"re normal upper O 2\" data-semantic-type=\"appl\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">R</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>O</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>. Furthermore, we characterize the fermiology parameters of <i>β-</i><mjx-container ctxtmenu_counter=\"64\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 4 (3 1 2))\"><mjx-mrow data-semantic-children=\"0,3\" data-semantic-content=\"4,0\" data-semantic- data-semantic-owns=\"0 4 3\" data-semantic-role=\"prefix function\" data-semantic-speech=\"re normal upper O 2\" data-semantic-type=\"appl\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">R</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>O</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> through de Haas–van Alphen (dHvA) effect studies at the high field up to 45.2 T. Aided by the Fermi surface (FS) calculated by first-principles, experimental dHvA analysis also substantiates the coexistence of two electron pockets and two hole pockets at the FS, which is in line with mobility spectrum analysis. Remarkably, the Landau fan diagram analysis for one of the electron pockets verifies the nontrivial Berry phase (≈0.87<i>π</i>) in <i>β-</i><mjx-container ctxtmenu_counter=\"65\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 4 (3 1 2))\"><mjx-mrow data-semantic-children=\"0,3\" data-semantic-content=\"4,0\" data-semantic- data-semantic-owns=\"0 4 3\" data-semantic-role=\"prefix function\" data-semantic-speech=\"re normal upper O 2\" data-semantic-type=\"appl\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">R</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>O</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>, suggesting that <i>β-</i><mjx-container ctxtmenu_counter=\"66\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 4 (3 1 2))\"><mjx-mrow data-semantic-children=\"0,3\" data-semantic-content=\"4,0\" data-semantic- data-semantic-owns=\"0 4 3\" data-semantic-role=\"prefix function\" data-semantic-speech=\"re normal upper O 2\" data-semantic-type=\"appl\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">R</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>O</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> may be a topological material. In addition, in the high field (>20 T), we also probed signatures of Zeeman splitting, from which the Landé <mjx-container ctxtmenu_counter=\"67\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"g\" data-semantic-type=\"identifier\"><mjx-c>𝑔</mjx-c></mjx-mi></mjx-math></mjx-container> factors are extracted as ∼0.33–0.43. The detailed fermiology of <i>β-</i><mjx-container ctxtmenu_counter=\"68\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 4 (3 1 2))\"><mjx-mrow data-semantic-children=\"0,3\" data-semantic-content=\"4,0\" data-semantic- data-semantic-owns=\"0 4 3\" data-semantic-role=\"prefix function\" data-semantic-speech=\"re normal upper O 2\" data-semantic-type=\"appl\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">R</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"5\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>O</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> provides valuable insights into the physical properties of other topological metals with similar characteristics.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.205109","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
Recently, β-ReO2 was theoretically proposed to be a candidate for Dirac nodal chain metal with hourglasslike energy-momentum dispersion and got considerable attention. Here, we have grown high-quality β-ReO2 single crystals with a residual-resistivity ratio as large as 428. The magnetoresistance (MR) can reach 7 × 104% measured under 9 T at 2 K. The fitting of MR and Hall data simultaneously by maximum entropy mobility spectrum reveals that there are two electron pockets and two hole pockets in β-ReO2 with comparable carrier concentrations, which leads to the large unsaturated MR in β-ReO2. Furthermore, we characterize the fermiology parameters of β-ReO2 through de Haas–van Alphen (dHvA) effect studies at the high field up to 45.2 T. Aided by the Fermi surface (FS) calculated by first-principles, experimental dHvA analysis also substantiates the coexistence of two electron pockets and two hole pockets at the FS, which is in line with mobility spectrum analysis. Remarkably, the Landau fan diagram analysis for one of the electron pockets verifies the nontrivial Berry phase (≈0.87π) in β-ReO2, suggesting that β-ReO2 may be a topological material. In addition, in the high field (>20 T), we also probed signatures of Zeeman splitting, from which the Landé 𝑔 factors are extracted as ∼0.33–0.43. The detailed fermiology of β-ReO2 provides valuable insights into the physical properties of other topological metals with similar characteristics.
期刊介绍:
Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide.
PRB covers the full range of condensed matter, materials physics, and related subfields, including:
-Structure and phase transitions
-Ferroelectrics and multiferroics
-Disordered systems and alloys
-Magnetism
-Superconductivity
-Electronic structure, photonics, and metamaterials
-Semiconductors and mesoscopic systems
-Surfaces, nanoscience, and two-dimensional materials
-Topological states of matter