Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems

2001/12/31 by Shinsei Ryu, Yasuhiro Hatsugai · 1 voice · 1 citation
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.supr-con

paper · pdf · doi:10.1103/physrevlett.89.077002

published as Phys. Rev. Lett. 89, 077002 (2002) · Completely rewritten. Discussions on coexistence of is- or id_{xy}-wave order parameter near edges in d_{x^{2}-y^{2}}-wave superconductors are added; 4 pages, 3 figures

arxiv created 2002/08/06 · arxiv updated 2009/11/30

Abstract

A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological properties, combined with the chiral symmetry, play an essential role. It provides a unified framework to discuss zero-energy edge modes for several systems such as fully gapped superconductors, two-dimensional d-wave superconductors, and graphite ribbons. A variants of the Peierls instability caused by the presence of edges is also discussed.

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• Exact analytical edge states in the extended Su-Schrieffer-Heeger model

Discussions

• I was studying this paper recently, and I do not quite understand its main proof. In the paper, the inter-site hoppings of the Hamiltonian are described by some $h_k$ loop. On the second page, it stat [stackexchange, 1 points]