Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface

G.E. Volovik; Tero T. Heikkil\"a

Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface

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arxiv 1011.4185 v2 pith:DHLAUJP6 submitted 2010-11-18 cond-mat.str-el hep-ph

Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface

Tero T. Heikkil\"a , G.E. Volovik This is my paper

classification cond-mat.str-el hep-ph

keywords dimensionalbandflatsurfacesystemtopologicalchangescrossover

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We consider the dimensional crossover in the topological matter, which involves the transformation of different types of topologically protected zeroes in the fermionic spectrum. In the considered case, the multiple Dirac (Fermi) point in quasi 2-dimensional system evolves into the flat band on the surface of the 3-dimensional system when the number of atomic layers increases. This is accompanied by formation of the spiral nodal lines in the bulk. We also discuss the topological quantum phase transition at which the surface flat band shrinks and changes its chirality, while the nodal spiral changes its helicity.

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Topological charge of fermions and Landau theory of Fermi liquid
cond-mat.str-el 2026-04 conditional novelty 5.0

The particle charge of a fermion is equivalent to its topological charge, which underpins the stability of the Fermi surface, the applicability of Landau Fermi liquid theory, and the Luttinger theorem in insulators.