Proximity spin-orbit and exchange coupling in ABA and ABC trilayer graphene van der Waals heterostructures

TL;DR

This paper explores how proximity effects from adjacent materials influence spin-orbit and exchange interactions in trilayer graphene, revealing tunable properties crucial for spintronic applications.

Contribution

It provides first-principles calculations and model Hamiltonians for proximity-induced spin interactions in ABA and ABC trilayer graphene, including electric field tunability.

Findings

Proximity effects can be tuned by electric fields.

Model parameters for spin interactions are extracted.

Band structures and spin splittings are characterized.

Abstract

We investigate the proximity spin-orbit and exchange couplings in ABA and ABC trilayer graphene encapsulated within monolayers of semiconducting transition-metal dichalcogenides and the ferromagnetic semiconductor Cr$_2$Ge$_2$Te$_6$. Employing first-principles calculations we obtain the electronic structures of the multilayer stacks and extract the relevant proximity-induced orbital and spin interaction parameters by fitting the low-energy bands to model Hamiltonians. We also demonstrate the tunability of the proximity effects by a transverse electric field. Using the model Hamiltonians we also study mixed spin-orbit/exchange coupling encapsulation, which allows to tailor the spin interactions very efficiently by the applied field. We also summarize the spin-orbit physics of bare ABA, ABC, and ABB trilayers, and provide, along with the first-principles results of the electronic band structures, density of states, spin splittings, and electric-field tunabilities of the bands, qualitative understanding of the observed behavior and realistic model parameters as a resource for model simulations of transport and correlation physics in trilayer graphene.