| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
Prev
Next
|
|
|
Edge states enhanced by long-range hopping: An analytical study |
| Huiping Wang(王会平)1,†, Li Ren(任莉)1, Liguo Qin(秦立国)1, and Yueyin Qiu(邱岳寅)2 |
1 School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
2 School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China |
|
|
|
|
Abstract We analyze the behavior of edge states in long-range (LR) interacting systems. In terms of lattice model Hamiltonian with the LR coupling, we determine analytically the condition of existence of edge states within the transfer matrix method (TMM). The expressions we obtain are general and hold for any choice of the LR hopping. The reason why edge states can appear is the transfer matrix in the bulk different from that in the boundary layers. Our predictions are in good agreement with numerical results by exact diagonalization. Our result is helpful in solving novel edge states in one- and two-dimensional (2D) superconductors with LR hopping and pairing.
|
Received: 31 December 2020
Revised: 09 February 2021
Accepted manuscript online: 25 February 2021
|
|
PACS:
|
73.20.At
|
(Surface states, band structure, electron density of states)
|
| |
61.50.Ah
|
(Theory of crystal structure, crystal symmetry; calculations and modeling)
|
| |
73.22.Dj
|
(Single particle states)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11847061) and the Startup Program of Shanghai University of Engineering Science. |
Corresponding Authors:
Huiping Wang
E-mail: hp_wang@fudan.edu.cn
|
Cite this article:
Huiping Wang(王会平), Li Ren(任莉), Liguo Qin(秦立国), and Yueyin Qiu(邱岳寅) Edge states enhanced by long-range hopping: An analytical study 2021 Chin. Phys. B 30 107301
|
[1] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[2] Bernevig A B and Hughes T L 2013 Topological Insulators and Topological Superconductors (Princeton, NJ: Princeton University Press)
[3] Kitaev A Y 2003 Ann. Phys. 303 2
[4] Nayak C, Simon S H, Stern A, Freedman M and Das Sarma S 2008 Rev. Mod. Phys. 80 1083
[5] Stern A 2010 Nature 464 187
[6] Meier D, Seidel J, Cano A, Delaney K, Kumagai Y, Mostovoy M, Spaldin N A, Ramesh R and Fiebig M 2012 Nat. Mater. 11 284
[7] Miao M S, Yan Q, Van de Walle C G, Lou W K, Li L L and Chang K 2012 Phys. Rev. Lett. 109 186803
[8] Zhang D, Lou W, Miao M, Zhang S C and Chang K 2013 Phys. Rev. Lett. 111 156402
[9] Chang K and Lou W K 2011 Phys. Rev. Lett. 106 206802
[10] Viyuela O, Fu L and Martin-Delgado M A 2018 Phys. Rev. Lett. 120 017001
[11] Di Liberto M, Malpetti D, Japaridze G I and Morais Smith C 2014 Phys. Rev. A 90 023634
[12] DeGottardi W, Thakurathi M, Vishveshwara S and Sen D 2013 Phys. Rev. B 88 165111
[13] Hastings M B and Koma T 2006 Commun. Math. Phys. 265 781
[14] Santos L F, Borgonovi F and Celardo G L 2016 Phys. Rev. Lett. 116 250402
[15] Maghrebi M F, Gong Z X and Gorshkov A V 2017 Phys. Rev. Lett. 119 023001
[16] Vodola D, Lepori L, Ercolessi E, Gorshkov A V and Pupillo G 2014 Phys. Rev. Lett. 113 156402
[17] Hauke P and Tagliacozzo L 2013 Phys. Rev. Lett. 111 207202
[18] Lepori L, Giuliano D and Paganelli S 2018 Phys. Rev. B 97 041109
[19] Vodola D, Lepori L, Ercolessi E and Pupillo G 2016 New J. Phys. 18 015001
[20] Lepori L and DellAnna L 2017 New J. Phys. 19 103030
[21] Gong Z X, Maghrebi M F, Hu A, Foss-Feig M, Richerme P, Monroe C and Gorshkov A V 2016 Phys. Rev. B 93 205115
[22] Gong Z X, Maghrebi M F, Hu A, Wall M L, Foss-Feig M and Gorshkov A V 2016 Phys. Rev. B 93 041102
[23] Viyuela O, Vodola D, Pupillo G and Martin-Delgado M A 2016 Phys. Rev. B 94 125121
[24] Lepori L, Vodola D, Pupillo G, Gori G and Trombettoni A 2016 Ann. Phys. (NY) 374 35
[25] Alecce A and DellAnna L 2017 Phys. Rev. B 95 195160
[26] Gori G, Paganelli S, Sharma A, Sodano P and Trombettoni A 2015 Phys. Rev. B 91 245138
[27] Giuliano D, Paganelli S and Lepori L 2018 Phys. Rev. B 97 155113
[28] Lepori L, Giuliano D and Paganelli S 2018 Phys. Rev. B 97 041109
[29] Sabyasachi N and Arti G 2019 Phys. Rev. B 99 224203
[30] Beatriz P G, Miguel B, Alvaro G L and Gloria P 2019 Phys. Rev. B 99 035146
[31] Ahmadi N, Abouie J and Baeriswyl D 2020 Phys. Rev. B 101 195117
[32] Xu X W, Li Y Z, Liu Z F and Chen A X 2020 Phys. Rev. A 101 063839
[33] Wang H P and Tao R B 2015 Chin. Phys. B 24 117301
[34] Wang H P, Gao T and Tao R B 2015 Sci. Rep. 5 8679
[35] Dy K S and Brasher D James 1980 Phys. Rev. B 22 4868
[36] Ho W, Cunningham S L, Weinberg W H and Dobrzynski L 1975 Phys. Rev. B 12 3027
[37] Mostoller M and Rajagopal A K 1982 Phys. Rev. B 25 6168
[38] Wang H P, Ren L, Qin L G and Qiu Y 2020 J. Phys. Soc. Jpn. 89 074705
[39] Lee D H and Joannopoulos J D 1981 Phys. Rev. B 23 4988
[40] Zhao Y Y, Li W and Tao R B 2012 Physica B 407 724 |
| No Suggested Reading articles found! |
|
|
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
|
|
|
