Papers

Peer-reviewed
May 16, 2018

Non-commutative Chern numbers for generic aperiodic discrete systems

Journal of Physics A: Mathematical and Theoretical
  • Chris Bourne
  • ,
  • Emil Prodan

Volume
51
Number
23
First page
235202
Last page
Language
English
Publishing type
Research paper (scientific journal)
DOI
10.1088/1751-8121/aac093
Publisher
Institute of Physics Publishing

The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a unifying theoretical framework for topological electronic, photonic, phononic etc (aperiodic) systems. We then discuss, in physical terms, the philosophy behind an operator theoretic analysis used to systematize such systems. A model calculation of the Hall conductance of a 2-dimensional amorphous lattice is given, where we present numerical evidence of its quantization in the mobility gap regime. Motivated by such facts, we then present the main result of our work, which is the extension of the Chern number formulas to Hamiltonians associated to lattices without a canonical labeling of the sites, together with index theorems that assure the quantization and stability of these Chern numbers in the mobility gap regime. Our results cover a broad range of applications, in particular, those involving quasi-crystalline, amorphous as well as synthetic (i.e. algorithmically generated) lattices.

Link information
DOI
https://doi.org/10.1088/1751-8121/aac093
URL
http://orcid.org/0000-0001-8234-0081
ID information
  • DOI : 10.1088/1751-8121/aac093
  • ISSN : 1751-8121
  • ISSN : 1751-8113
  • ORCID - Put Code : 44826036
  • SCOPUS ID : 85047749204

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