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Mathematical Physics

Title: Topological invariants and corner states for Hamiltonians on a three-dimensional lattice

Authors: Shin Hayashi
Abstract: Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two topological invariants are defined. One is defined for the gapped bulk and edge Hamiltonians, and the non-triviality of the other means that the corner Hamiltonian is gapless. A correspondence between these two invariants is proved. Such gapped Hamiltonians can be constructed from Hamiltonians of 2-D type A and 1-D type AIII topological insulators, and its corner topological invariant is the product of topological invariants of these two phases.
Comments: v3: section 4 added, references and typos corrected. 15 pages, 1 figure
Subjects: Mathematical Physics (math-ph); K-Theory and Homology (math.KT)
MSC classes: 19K56 (Primary), 47B35, 81V99 (Secondary)
Cite as: arXiv:1611.09680 [math-ph]
  (or arXiv:1611.09680v3 [math-ph] for this version)

Submission history

From: Shin Hayashi [view email]
[v1] Tue, 29 Nov 2016 15:26:52 GMT (128kb)
[v2] Sun, 15 Jan 2017 02:23:51 GMT (128kb)
[v3] Mon, 19 Mar 2018 06:19:11 GMT (132kb)