CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
Prev
Next
|
|
|
Topological phase diagrams and Majorana zero modes of the Kitaev ladder and tube |
Yiming Wang(王一鸣)1, Zhidan Li(李志聃)1, Qiang Han(韩强)1,2 |
1. Department of Physics, Renmin University of China, Beijing 100872, China;
2. Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, China |
|
|
Abstract In this paper, we study two quasi-one-dimensional (1D) Kitaev models with ladder-like and tube-like spatial structures, respectively. Our results provide the phase diagrams and explicit expressions of the Majorana zero modes. The topological phase diagrams are obtained by decomposing the topological invariants and the topological conditions for topologically nontrivial phases are given precisely. For systems which belongs to topological class BDI, we obtain the regions in the phase diagrams where the topological numbers show even-odd effect. For the Kitaev tube model a phase factor induced by the magnetic flux in the axial direction of the tube is introduced to alter the classification of the tube Hamiltonian from class BDI to D. The Kitaev tube of class D is characterized by the Z2 index when the number of chains is odd while 0, 1, 2 when the number of chains is even. The phase diagrams show periodic behaviors with respect to the magnetic flux. The bulk-boundary correspondence is demonstrated by the observations that the topological conditions for the bulk topological invariant to take nontrivial values are precisely those for the existence of the Majorana zero modes.
|
Received: 26 December 2017
Revised: 26 January 2018
Accepted manuscript online:
|
PACS:
|
74.20.-z
|
(Theories and models of superconducting state)
|
|
74.78.-w
|
(Superconducting films and low-dimensional structures)
|
|
71.10.Pm
|
(Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11274379), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (Grant No. 14XNLQ07). |
Corresponding Authors:
Qiang Han
E-mail: hanqiang@ruc.edu.cn
|
Cite this article:
Yiming Wang(王一鸣), Zhidan Li(李志聃), Qiang Han(韩强) Topological phase diagrams and Majorana zero modes of the Kitaev ladder and tube 2018 Chin. Phys. B 27 047401
|
[1] |
Kitaev A Y 2001 Phys.-Usp. 44 131
|
[2] |
Majorana E 1937 Nuovo Cimento 14 171
|
[3] |
Kitaev A Y 2009 AIP Conf. Proc. 1134 22
|
[4] |
Alicea J 2012 Rep. Prog. Phys. 75 076501
|
[5] |
Fendley P 2012 J. Stat. Mech. 2012 11020
|
[6] |
Niu Y, Chung S B, Hsu C H, Mandal I, Raghu S and Chakravarty S2012 Phys. Rev. B 85 035110
|
[7] |
DeGottardi W, Thakurathi M, Vishveshwara S and Sen D 2013 Phys. Rev. B 88 165111
|
[8] |
Greiter M, Schnells V and Thomale R 2014 Ann. Phys. 351 1026
|
[9] |
Hegde S S, Shivamoggi V, Vishveshwara S and Sen D 2015 New J. Phys. 17 053036
|
[10] |
Hegde S S and Vishveshwara S 2016 Phys. Rev. B 94 115166
|
[11] |
Sau J D, Clarke D J and Tewari S 2011 Phys. Rev. B 84 094505
|
[12] |
Alicea J, Oreg Y, Refael G, von Oppen F and Fisher M P A 2011 Nat. Phys. 7 412
|
[13] |
Leijnse M and Flensberg K 2012 Semicond. Sci. Technol. 27 124003
|
[14] |
van Heck B, Akhmerov A R, Hassler F, Burrello M and Beenakker CW J 2012 New J. Phys. 14 035019
|
[15] |
Hyart T, van Heck B, Fulga I C, Burrello M, Akhmerov A R andBeenakker C W J 2013 Phys. Rev. B 88 035121
|
[16] |
Burnell F J 2014 Phys. Rev. B 89 224510
|
[17] |
Fu L and Kane C L 2008 Phys. Rev. Lett. 100 096407
|
[18] |
Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002
|
[19] |
Lutchyn R M, Sau J D and Das Sarma S 2010 Phys. Rev. Lett. 105 077001
|
[20] |
Stanescu T D, Lutchyn R M and Das Sarma S 2011 Phys. Rev. B 84 144522
|
[21] |
Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M andKouwenhoven L P 2012 Science 336 1003
|
[22] |
Das A, Ronen Y, Most Y, Oreg Y, Heiblum M and Shtrikman H 2012 Nat. Phys. 8 887
|
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
|
|
|