|
|
Different topological phase transitions in the Su-Schrieffer-Heeger model under different disorder structures |
Yan Gu(古燕)1,† and Zhanpeng Lu(陆展鹏)2,‡ |
1 Shanxi Vocational University of Engineering Science and Technology, Jinzhong 030619, China; 2 Institute of Theoretical Physics and State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China |
|
|
Abstract We investigate the topological phase transition in the Su-Schrieffer-Heeger model with the long-range hopping and quasi-periodic modulation. By numerically calculating the real-space winding number, we obtain topological phase diagrams for different disordered structures. These diagrams suggest that topological phase transitions are different by selecting the specific disordered structure. When quasi-periodic modulation is applied to intracell hopping, the resulting disorder induces topological Anderson insulator (TAI) phase with high winding number ($W$=2), but the topological states are destroyed as the disorder increases. Conversely, when intercell hoppings are modulated quasi-periodically, both TAI phase and the process of destruction and restoration of topological zero modes can be induced by disorder. These topological states remain robust even under strong disorder conditions. Our work demonstrates that disorder effects do not always disrupt topological states; rather, with a judicious selection of disordered structures, topological properties can be preserved.
|
Received: 19 March 2024
Revised: 03 June 2024
Accepted manuscript online: 20 June 2024
|
PACS:
|
02.40.-k
|
(Geometry, differential geometry, and topology)
|
|
73.43.Nq
|
(Quantum phase transitions)
|
|
73.20.At
|
(Surface states, band structure, electron density of states)
|
|
72.80.Ng
|
(Disordered solids)
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12205176) and the High-level Talent Research Start-up Project (Grant No. RCK202231). |
Corresponding Authors:
Yan Gu, Zhanpeng Lu
E-mail: guyan@sxgkd.edu.cn;201712605002@email.sxu.edu.cn
|
Cite this article:
Yan Gu(古燕) and Zhanpeng Lu(陆展鹏) Different topological phase transitions in the Su-Schrieffer-Heeger model under different disorder structures 2024 Chin. Phys. B 33 090202
|
[1] Thouless D J, Kohmoto M, Nightingale M P and Nijs M D 1982 Phys. Rev. Lett. 49 405 [2] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045 [3] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057 [4] Bansil A, Lin H and Das T 2016 Rev. Mod. Phys. 88 021004 [5] Chiu C K, Teo J C Y, Schnyder A P and Ryu S 2016 Rev. Mod. Phys. 88 035005 [6] Armitage N P, Mele E J and Vishwanath A 2018 Rev. Mod. Phys. 90 015001 [7] Su W P, Schrieffer J R and Heeger A J 1979 Phys. Rev. Lett. 42 1698 [8] Jackiw R and Rebbi C 1976 Phys. Rev. D 13 3398 [9] Heeger A J, Kivelson S, Schrieffer J R and Su W P 1988 Rev. Mod. Phys. 60 781 [10] Ganeshan S, Sun K and Sarma S D 2013 Phys. Rev. Lett. 110 180403 [11] Song F, Yao S and Wang Z 2019 Phys. Rev. Lett. 123 246801 [12] Xu Z, Zhang R, Chen S, Fu L and Zhang Y 2020 Phys. Rev. A 101 013635 [13] Xiao T, Xie D, Dong Z, Chen T, Yi W and Yan B 2021 Sci. Bull. 66 2175 [14] Anderson P W 1958 Phys. Rev. 109 1492 [15] Lee P A and Ramakrishnan T V 1985 Rev. Mod. Phys. 57 287 [16] Billy J, Josse V, Zuo Z, Bernard A, Hambrecht B, Lugan P, Clément D, Sanchez-Palencia L, Bouyer P and Aspect A 2008 Nature 453 891 [17] Roati G, D’Errico C, Fallani L, Fattori M, Fort C, Zaccanti M, Modugno G, Modugno M and Inguscio M 2008 Nature 453 895 [18] Chabanov A A, Stoytchev M and Genack A Z 2000 Nature 404 850 [19] Pradhan P and Sridhar S 2000 Phys. Rev. Lett. 85 2360 [20] Goblot V, Štrkalj A, Pernet N, Lado J L, Dorow C, Lemaître A, Gratiet L L, Harouri A, Sagnes I, Ravets S, Amo A, Bloch J and Zilberberg O 2020 Nat. Phys. 16 832 [21] Zhai L J, Huang G Y and Yin S 2021 Phys. Rev. B 104 014202 [22] Wang Y, Zhang L, Sun W, Poon T F J and Liu X J 2022 Phys. Rev. B 106 L140203 [23] Ahmed A, Ramachandran A, Khaymovich I M and Sharma A 2022 Phys. Rev. B 106 205119 [24] Li J, Chu R L, Jain J K and Shen S Q 2009 Phys. Rev. Lett. 102 136806 [25] Groth C W, Wimmer M, Akhmerov A R, Tworzydlo J and Beenakker C W J 2009 Phys. Rev. Lett. 103 196805 [26] Guo H M, Rosenberg G, Refael G and Franz M 2010 Phys. Rev. Lett. 105 216601 [27] Zhang Y Y, Chu R L, Zhang F C and Shen S Q 2012 Phys. Rev. B 85 035107 [28] Song J, Liu H, Jiang H, Sun Q F and Xie X C 2012 Phys. Rev. B 85 195125 [29] Girschik A, Libisch F and Rotter S 2013 Phys. Rev. B 88 014201 [30] Mondragon-Shem I, Hughes T L, Song J and Prodan E 2014 Phys. Rev. Lett. 113 046802 [31] Zhang Z Q, Wu B L, Song J and Jiang H 2019 Phys. Rev. B 100 184202 [32] Zhang D W, Tang L Z, Lang L J, Yan H and Zhu S L 2020 Sci. China Phys. Mech. Astron. 63 267062 [33] Tang L Z, Zhang L F, Zhang G Q and Zhang D W 2020 Phys. Rev. A 101 063612 [34] Zhang G Q, Tang L Z, Zhang L F, Zhang D W and Zhu S L 2021 Phys. Rev. B 104 L161118 [35] Liu S N, Zhang G Q, Tang L Z and Zhang D W 2022 Phys. Lett. A 431 128004 [36] Wu Y P, Tang L Z, Zhang G Q and Zhang D W 2022 Phys. Rev. A 106 L051301 [37] Zhang W J, Wu Y P, Tang L Z and Zhang G Q 2022 Commun. Theor. Phys. 74 075702 [38] Tang L Z, Liu S N, Zhang G Q and Zhang D W 2022 Phys. Rev. A 105 063327 [39] Meier E J, An F A, Dauphin A, Maffei M, Massignan P, Hughes T L and Gadway B 2018 Science 362 929 [40] Stützer S, Plotnik Y, Lumer Y, Titum P, Lindner N H, Segev M, Rechts-man M C and Szameit A 2018 Nature 560 461 [41] Hsu H C and Chen T W 2020 Phys. Rev. B 102 205425 [42] Song J and Prodan E 2014 Phys. Rev. B 89 224203 [43] Song F, Yao S and Wang Z 2019 Phys. Rev. Lett. 123 246801 [44] Kitaev A 2006 Ann. Phys. 321 2 [45] Malakar R K and Ghosh A K 2023 J. Phys.: Condens. Matter 35 335401 |
[1] |
ZHAN LI (詹黎), TU JIN-HONG (屠锦洪), GUO JIA-RONG (郭嘉荣). ANALYSIS OF THE GENERAL EFFECTS IN DOUBLE-GRATING DIFFRACTION-INTERFERENCE SYSTEM[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(1): 27
-44
. |
[2] |
LIANG ZHONG-CHENG (梁忠诚). INTERFACE STRESS, TENSION AND FREE ENERGY DENSITY OF CONDENSED MATTER[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(2): 104
-112
. |
[3] |
ZHENG JIAN-GUO (郑建国), LI QI (李齐), FENG DUAN (冯端). DISLOCATION DISSOCIATION ON CLIMB PLANE IN TEXTURED YBa2Cu3O7-$\delta$ SUPERCONDUCTOR[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(1): 35
-41
. |
[4] |
HU CHENG-ZHENG (胡承正), DING DI-HUA (丁棣华), YANG WEN-GE (杨文革). EXPRESSION OF THE ELASTIC ENERGY IN TWO-DIMENSIONAL QUASICRYSTALS[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(1): 42
-47
. |
[5] |
JIN JI-RONG (金继荣), JIN XIN (金新), JI HE-LIN (吉和林), ZHANG YI-TONG (张贻瞳), XU XIAO-NONG (徐小农), SHI ZHI-XIANG (施智祥), ZHANG ZHI-PING (张治平), YAO XI-XIAN (姚希贤), ZHUANG RUI-FANG (庄瑞芳), XIE HUI (谢晖). INVESTIGATION OF THE EFFECT OF SLOW NEUTRON IRRADIATION ON HALOGEN-DOPED HIGH-Tc SUPERCONDUCTORS AND ITS MECHANISM[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(1): 56
-64
. |
[6] |
CHEN XIAO-BO (陈晓波), ZHANG GUANG-YIN (张光寅), WANG HONG (王虹), LIU YAN-BIN (刘言滨), CHEN JIN-KAI (陈金铠), SHANG MEI-RU (商美茹), LI JIANG-WEI(李江卫). BLUE-GREEN UP-CONVERSION LUMINESCENCE OF NONCHYSTALLINE HoP5O14 INDUCED BY PULSE DCM DYE LASER[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(10): 771
-775
. |
[7] |
LIN YONG-YAO (林永耀), MO DANG (莫党), GONG KE-CHENG (龚克成), ZHANG GUI-PING (张贵萍). ELLIPSOMETRIC SPECTRA OF CONDUCTING POLYANILINE[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(11): 816
-824
. |
[8] |
WU CHENG-PEI (吴承佩), LIU WAN-YU (刘皖育), LI XU-HUI (厉旭辉), XU KUI (徐葵), YU WEN-HAI (俞文海). STUDY ON PREPARATION OF UV CROSS-LINKING FILMS OF POLYURETHANE-LiClO4 COMPLEXES AND THEIR IONIC CONDUCTIVITY[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(11): 841
-849
. |
[9] |
XU ZHU-AN (许祝安), CAI MENG (蔡盟), ZHANG XIAO-JUN (张小俊), ZHANG QI-RUI (张其瑞), ZHOU XIAN-YI (周先意). POSITRON LIFETIME STUDIES OF Y1-xCaxBa2Cu3O7-$\delta$ AND Y1-xCaxBa2Cu3-xFexO7-$\delta$[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(11): 850
-856
. |
[10] |
TANG GUI-DE (唐贵德), NIE XIANG-FU (聂向富), SUN HUI-YUAN (孙会元), MENG GUANG-QING (孟广庆), HAN BAO-SHAN (韩宝善). ANNIHILATION OF VERTICAL-BLOCH-LINE CHAINS IN THE WALLS OF THE SECOND KIND OF DUMBBELL DOMAINS SUBJECTED TO AN IN-PLANE FIELD[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(11): 863
-869
. |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|