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Chin. Phys. B, 2018, Vol. 27(4): 047401    DOI: 10.1088/1674-1056/27/4/047401
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.

Keywords:  topological phase transition      Majorana zero modes      Kitaev model  
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

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