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

TL;DR

This paper explores how increasing layers in topological materials causes a transition from multiple Dirac points to flat surface bands, involving complex bulk and surface topological changes.

Contribution

It introduces the concept of dimensional crossover in topological matter, detailing the evolution of Dirac points into flat bands and associated topological phase transitions.

Findings

Multiple Dirac points evolve into flat surface bands with increasing layers.

Formation of spiral nodal lines in the bulk during the crossover.

Topological quantum phase transition involves flat band shrinking and chirality change.

Abstract

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.