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Phys Rev Lett. 2002 Aug 12;89(7):077002. Epub 2002 Jul 26.

Topological origin of zero-energy edge states in particle-hole symmetric systems.

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Department of Applied Physics, University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Japan.


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 variance of the Peierls instability caused by the presence of edges is also discussed.

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