Topological phase diagrams and Majorana zero modes of the Kitaev ladder and tube

doi:10.1088/1674-1056/27/4/047401

中国物理B ›› 2018, Vol. 27 ›› Issue (4): 47401-047401.doi: 10.1088/1674-1056/27/4/047401

• CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES • 上一篇下一篇

Topological phase diagrams and Majorana zero modes of the Kitaev ladder and tube

Yiming Wang(王一鸣), Zhidan Li(李志聃), Qiang Han(韩强)

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

收稿日期:2017-12-26 修回日期:2018-01-26 出版日期:2018-04-05 发布日期:2018-04-05
通讯作者: Qiang Han E-mail:hanqiang@ruc.edu.cn
基金资助:
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).

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

Received:2017-12-26 Revised:2018-01-26 Online:2018-04-05 Published:2018-04-05
Contact: Qiang Han E-mail:hanqiang@ruc.edu.cn
Supported by:
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).

摘要/Abstract

摘要：

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.

关键词: topological phase transition, Majorana zero modes, Kitaev model

Abstract:

Key words: topological phase transition, Majorana zero modes, Kitaev model

中图分类号: (Theories and models of superconducting state)

74.20.-z

74.78.-w (Superconducting films and low-dimensional structures) 71.10.Pm (Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))

王一鸣, 李志聃, 韩强. Topological phase diagrams and Majorana zero modes of the Kitaev ladder and tube[J]. 中国物理B, 2018, 27(4): 47401-047401.

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[J]. Chin. Phys. B, 2018, 27(4): 47401-047401.

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Topological phase diagrams and Majorana zero modes of the Kitaev ladder and tube

Topological phase diagrams and Majorana zero modes of the Kitaev ladder and tube

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