Unveiling a crystalline topological insulator in a Weyl semimetal with time-reversal symmetry

TL;DR

This paper explores a lattice model with time-reversal symmetry that transitions from a Weyl semimetal to a topological crystalline insulator, revealing new phases and spectral structures through analytical phase diagram analysis.

Contribution

It introduces a generalized lattice model supporting Weyl and topological crystalline insulating phases, providing analytical insights into their phase diagram and spectral node structure.

Findings

Weyl semimetal phase exists when next-nearest-neighbor hoppings vanish.

Topological crystalline insulators emerge within the Weyl phase when hoppings are considered.

Analytical phase diagram and node structure are derived from an effective Weyl Hamiltonian.

Abstract

We consider a natural generalization of the lattice model for a periodic array of two layers, A and B, of spinless electrons proposed by Fu [Phys. Rev. Lett. 106, 106802 (2011)] as a prototype for a crystalline insulator. This model has time-reversal symmetry and broken inversion symmetry. We show that when the intralayer next-nearest-neighbor hoppings ta2, a = A, B vanish, this model supports a Weyl semimetal phase for a wide range of the remaining model parameters. When the effect of ta2 is considered, topological crystalline insulating phases take place within the Weyl semimetal one. By mapping to an effective Weyl Hamiltonian we derive some analytical results for the phase diagram as well as for the structure of the nodes in the spectrum of the Weyl semimetal.