Three-dimensional topological phases in a layered honeycomb spin-orbital model

TL;DR

This paper introduces an exactly solvable 3D spin-orbital model exhibiting topological phases, phase transitions, and surface Majorana fermions, advancing understanding of topological matter in complex quantum systems.

Contribution

It presents a novel solvable model demonstrating topological phases, phase transitions, and surface states in a layered honeycomb spin-orbital system.

Findings

Critical phase with topologically protected Fermi points

Phase transition to a trivial gapped phase under magnetic field

Presence of gapless Majorana surface fermions

Abstract

We present an exactly solvable spin-orbital model based on the Gamma-matrix generalization of a Kitaev-type Hamiltonian. In the presence of small magnetic fields, the model exhibits a critical phase with a spectrum characterized by topologically protected Fermi points. Upon increasing the magnetic field, Fermi points carrying opposite topological charges move toward each other and annihilate at a critical field, signaling a phase transition into a gapped phase with trivial topology in three dimensions. On the other hand, by subjecting the system to a staggered magnetic field, an effective time-reversal symmetry essential to the existence of three-dimensional topological insulators is restored in the auxiliary free fermion problem. The nontrivial topology of the gapped ground state is characterized by an integer winding number and manifests itself through the appearance of gapless Majorana fermions confined to the two-dimensional surface of a finite system.