• Overview of Chinese core journals
  • Chinese Science Citation Database(CSCD)
  • Chinese Scientific and Technological Paper and Citation Database (CSTPCD)
  • China National Knowledge Infrastructure(CNKI)
  • Chinese Science Abstracts Database(CSAD)
  • JST China
  • SCOPUS
Advanced Search
SUN Ye-Yang, LI Jun-Kai, YANG Zhao-Ju. Looking for the nontrivial states of matter from fractals[J]. PHYSICS, 2023, 52(4): 232-238. DOI: 10.7693/wl20230402
Citation: SUN Ye-Yang, LI Jun-Kai, YANG Zhao-Ju. Looking for the nontrivial states of matter from fractals[J]. PHYSICS, 2023, 52(4): 232-238. DOI: 10.7693/wl20230402
shu

Looking for the nontrivial states of matter from fractals

  • School of Physics, Zhejiang University, Hangzhou 310027, China

More Information
  • Received Date: March 26, 2023
  • Available Online: April 11, 2023
    Graphical Abstract
    • Abstract
  • Fractals are ubiquitous in nature, characterized by the properties of selfsimilarity and fractional dimensions. Recent theoretical and experimental studies on fractal lattices have demonstrated the existence of topological insulators without the concept of “bulk” in the fractional dimension. Topological states in fractals exhibit novel properties, such as the squeezed topological phases and topological boundary states distributed in various generations of fractal geometry. These unique differences from conventional topological insulators provide a new perspective for examining the interaction between the spatial dimensions and topological phase transitions. This article briefly reviews the history of topological states in fractal systems and focuses on the topological fractal insulators in artificial microstructures.
    • FullText(HTML)
    • References (44)
  • [1]
    Mandelbrot B B. The Fractal Geometry of Nature. Times Book, 1982
    [2]
    Shechtman D,Blech I,Gratias D et al. Phys. Rev. Lett.,1984,53:1951
    [3]
    Hasan M Z,Kane C L. Rev. Mod. Phys.,2010,82:3045
    [4]
    Qi X L,Zhang S C. Rev. Mod. Phys.,2011,83:1057
    [5]
    Ozawa T,Price H M,Amo A et al. Rev. Mod. Phys.,2019,91:015006
    [6]
    Ma G,Xiao M,Chan C T. Nat. Rev. Phys.,2019,1:281
    [7]
    Zhang X J,Xiao M,Cheng Y et al. Commun. Phys.,2018,1:97
    [8]
    Xue H R,Yang Y H,Zhang B L. Nat. Rev. Mater.,2022,7:974
    [9]
    Brzezińska M,Cook A M,Neupert T. Phys. Rev. B,2018,98:205116
    [10]
    Pai S,Prem A. Phys. Rev. B,2019,100:155135
    [11]
    Kempkes S N,Slot M R,Freeney S E et al. Nat. Phys.,2019,15:127
    [12]
    Yang Z J,Lustig E,Lumer Y et al. Light Sci. Appl.,2020,9:128
    [13]
    Iliasov A A,Katsnelson M I,Yuan S. Phys. Rev. B,2020,101:045413
    [14]
    Fremling M,van Hooft M,Smith C M et al. Phys. Rev. Research,2020,2:013044
    [15]
    Liu C,Zhou Y N,Wang G Y et al. Phys. Rev. Lett.,2021,126:176102
    [16]
    Ivaki M N,Sahlberg I,Pöyhönen K et al. Commun. Phys.,2022,5:327
    [17]
    Manna S,Nandy S,Roy B. Phys. Rev. B,2022,105:L201301
    [18]
    Zheng S,Man X,Kong Z L et al. Sci. Bull.,2022,67:2069
    [19]
    Li J,Mo Q,Jiang J H et al. Sci. Bull.,2022,67:2040
    [20]
    Biesenthal T,Maczewsky L J,Yang Z et al. Science,2022,376:1114
    [21]
    Li J K,Sun Y Y,Mo Q Y et al. Observation of Squeezed Chern Insulator in an Acoustic Fractal Lattice. 2022,arXiv:2205.05297
    [22]
    Alexander S. Phys. Rev. B,1984,29:5504
    [23]
    Banavar J R,Kadanoff L,Pruisken A M M. Phys. Rev. B,1985, 31:1388
    [24]
    Song Z G,Zhang Y Y,Li S S. Appl. Phys. Lett.,2014,104:233106
    [25]
    He J,Liang Y,Kou S P. Europhys. Lett.,2015,112:17010
    [26]
    Haldane F D M. Phys. Rev. Lett.,1988,61:2015
    [27]
    Titum P,Lindner N H,Rechtsman M C et al. Phys. Rev. Lett., 2015,114:056801
    [28]
    Wang X S,Brataas A,Troncoso R E. Phys. Rev. Lett.,2020,125:217202
    [29]
    Thouless D J,Kohmoto M,Nightingale M P et al. Phys. Rev. Lett.,1982,49:405
    [30]
    Benalcazar W A, Bernevig B A, Hughes T L. Science,2017,357:61
    [31]
    Langbehn J,Peng Y,Trifunovic L et al. Phys. Rev. Lett.,2017, 119:246401
    [32]
    Song Z,Fang Z,Fang C. Phys. Rev. Lett.,2017,119:246402
    [33]
    Schindler F,Cook A M,Vergniory M G et al. Sci. Adv.,2018,4:eaat0346
    [34]
    Ezawa M. Phys. Rev. Lett.,2018,120:026801
    [35]
    Trifunovic L,Brouwer P W. Phys. Rev. X,2019,9:011012
    [36]
    Xie B,Wang H X,Zhang X et al. Nat. Rev. Phys.,2021,3:520
    [37]
    Noh J,Benalcazar W A,Huang S et al. Nat. Photonics,2018,12:408
    [38]
    Ni X,Weiner M,Alù A et al. Nat. Mater.,2019,18:113
    [39]
    Zhang X,Wang H,Lin Z et al. Nat. Phys.,2019,15:582
    [40]
    Xue H,Yang Y,Gao F et al. Nat. Mater.,2019,18:108
    [41]
    Zhang W et al. Light Sci. Appl.,2020,9:109
    [42]
    Pai S,Prem A. Phys. Rev. B,2019,100:155135
    [43]
    Wheeler W A,Wagner L K,Hughes T L. Phys. Rev. B,2019, 100:245135
    [44]
    Manna S,Duncan C W,Weidner C A. Anyon Braiding on A Fractal Lattice With A Local Hamiltonian. 2022,arXiv:2106.13816
    • Related Articles

  • Related Articles

    [1]QIN Ya-Yuan, SHEN Yao, CHEN Gang, ZHAO Jun. Magnetic frustration and quantum fluctuation in rare-earth triangular-lattice magnets[J]. PHYSICS, 2021, 50(7): 454-462. DOI: 10.7693/wl20210703
    [2]LIU Zheng-Xin, WANG Xiao-Qun, ZHANG Qing-Ming. Spring in the desert of magnets——quantum spin liquids[J]. PHYSICS, 2021, 50(7): 429-442. DOI: 10.7693/wl20210701
    [3]SUN Pei-Jie, ZHAO Heng-Can. Quantum phase transitions in geometrically frustrated heavy-fermion compounds[J]. PHYSICS, 2020, 49(9): 579-585. DOI: 10.7693/wl20200902
    [4]CHEN Shuang, WU Jia-Min, SHI Yu-Sheng. General introduction of 3D printing materials and their applications[J]. PHYSICS, 2018, 47(11): 715-724. DOI: 10.7693/wl20181104
    [5]WANG Tian-Yu, SONG Qi, HAN Wei. Spin-orbit torque[J]. PHYSICS, 2017, 46(5): 288-298. DOI: 10.7693/wl20170503
    [6]CT invariant quantum spin Hall effect in ferromagnetic graphene[J]. PHYSICS, 2010, 39(06): 416-418.
    [7]The spin-orbit interaction and spin current[J]. PHYSICS, 2008, 37(08): 594-599.
    [8]Experimental observation of relativistic effects on the electronic wavefunction in molecules[J]. PHYSICS, 2008, 37(08): 576-578.
    [9]Kitaev model and topological quantum phase transitions[J]. PHYSICS, 2007, 36(07): 511-515.

  • Cited by

    Periodical cited type(2)

    1. 王艳红，符鹏，卢红成. 一维量子反铁磁性材料研究简介. 铸造技术. 2023(01): 15-22 .
    2. 徐豪，承舒凡，鲍嵩，温锦生. 强关联材料霍尔热导率实验测量综述（英文）. 物理学进展. 2022(05): 159-183 .

    Other cited types(9)

Catalog

    Get Citation
    PDF
    XML
    Article views (565) PDF downloads (1475) Cited by(11)
    Turn off MathJax
    Article Contents
    Abstract
    References
    Related Articles

    Copyright © China Research Institute of Radiowave Propagation 豫ICP备16036117号

    Address： Tel：010-82649029，82649277 Fax：0373-3052232 E-mail: physics@iphy.ac.cn

    Supported by: Beijing Renhe Information Technology Co., Ltd.  Baidu Analytics

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return