Topological map of the Hofstadter butterfly: Fine structure of Chern numbers and Van Hove singularities
Por:
Naumis, Gerardo G.
Publicada:
29 abr 2016
Categoría:
Physics and Astronomy (miscellaneous)
Resumen:
The Hofstadter butterfly is a quantum fractal with a highly complex nested set of gaps, where each gap represents a quantum Hall state whose quantized conductivity is characterized by topological invariants known as the Chern numbers. Here we obtain simple rules to determine the Chern numbers at all scales in the butterfly fractal and lay out a very detailed topological map of the butterfly by using a method used to describe quasicrystals: the cut and projection method. Our study reveals the existence of a set of critical points that separates orderly patterns of both positive and negative Cherns that appear as a fine structure in the butterfly. This fine structure can be understood as a small tilting of the projection subspace in the cut and projection method and by using a Chern meeting formula. Finally, we prove that the critical points are identified with the Van Hove singularities that exist at every band center in the butterfly landscape. © 2016 Elsevier B.V. All rights reserved.
Filiaciones:
Naumis, Gerardo G.:
Univ Nacl Autonoma Mexico, Inst Fis, Dept Quim Fis, Apartado Postal 20-364, Mexico City 01000, DF, Mexico
George Mason Univ, Dept Phys & Astron, Fairfax, VA 22030 USA
Inst Politecn Nacl, ESIA Zacatenco, Escuela Super Fis & Matemat, Mexico City, DF, Mexico
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