Quantum spin Hall phase in multilayer graphene

TL;DR

This paper investigates the persistence and induction of quantum spin Hall phases in multilayer graphene and heterostructures, revealing layer-dependent topological properties and the potential for proximity-induced topological states.

Contribution

It demonstrates that odd-layer multilayer graphene hosts gapless edge states, and heterostructures can acquire topological phases through interlayer coupling and proximity effects.

Findings

Odd-layer multilayers have gapless edge states.

Even-layer multilayers are topologically trivial.

Heterostructures can exhibit proximity-induced quantum spin Hall phases.

Abstract

The so called quantum spin Hall phase is a topologically non trivial insulating phase that is predicted to appear in graphene and graphene-like systems. In this work we address the question of whether this topological property persists in multilayered systems. We consider two situations: purely multilayer graphene and heterostructures where graphene is encapsulated by trivial insulators with a strong spin-orbit coupling. We use a four orbital tight-binding model that includes the full atomic spin-orbit coupling and we calculate the $Z_{2}$ topological invariant of the bulk states as well as the edge states of semi-infinite crystals with armchair termination. For homogeneous multilayers we find that even when the spin-orbit interaction opens a gap for all the possible stackings, only those with odd number of layers host gapless edge states while those with even number of layers are trivial insulators. For the heterostructures where graphene is encapsulated by trivial insulators, it turns out that the interlayer coupling is able to induce a topological gap whose size is controlled by the spin-orbit coupling of the encapsulating materials, indicating that the quantum spin Hall phase can be induced by proximity to trivial insulators.