透過您的圖書館登入
IP:3.144.139.201
  • 學位論文

Two-Dimensional Extended Su-Schrieffer-Heeger Model

Two-Dimensional Extended Su-Schrieffer-Heeger Model

指導教授 : 高賢忠

並列摘要


The edge state is known to be a characteristic of a topological material. In two-dimensional topological systems, one can use the emph{Chern number} to describe the topological property of the systems. However, the Chern number fails to discern the topology for two special cases of two-band systems: (a) when the parameter space is restricted to a plane, and (b) when the system is a semimetal. One should find another way instead to characterize the nontrivial topology. In this thesis, the SSH model is extended from one dimension to two dimensions by four different ways. None of them can be described by the Chern number. However, by applying the dimensional reduction, the systems are reduced to one dimension and are equivalent to the generalized SSH model, whose topological nontriviality is characterized by the emph{winding number}. Since the open boundary conditions are preserved under the dimensional reduction, the edge effect should be described by the reduced Hamiltonian. Therefore, we find the quasi-bulk-boundary correspondence to connect the edge states of the two-dimensional systems and the winding number of the reduced Hamiltonian. Moreover, if the edges of SSH chains are preserved under the extension in the thesis, the edge states are also preserved.

參考文獻


[1] W. P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in Polyacetylene”, Phys. Rev. Lett. 42, (1698)
[2] J. K. Asbóth, L. Oroszlány, A. P´ alyi, A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions, (Springer, Switzerland, 2016).
[3] M. Nakahara. Geometry, Topology and Physics, 2nd Edition, (CRC Press, 2003)
[4] D. J. Griffiths, Introduction to Quantum Mechanics, (Pearson Education Limited, Harlow, 2014)
[5] A. Kitaev, “Periodic table for topological insulators and superconduc tors”, AIP. Conf. Proc. 1134, 22 (2009).

延伸閱讀