Strong manipulation of the valley splitting upon twisting and gating in MoSe2/CrI3 and WSe2/CrI3

Abstract

Van der Waals (vdW) heterostructures provide a rich playground to engineer electronic, spin, and optical properties of individual two-dimensional materials. We investigate the twist-angle and gate dependence of the proximity-induced exchange coupling in the monolayer transition-metal dichalcogenides (TMDCs) MoSe 2 and WSe 2 due to the vdW coupling to the ferromagnetic semiconductor CrI 3 , from first-principles calculations. A model Hamiltonian, which captures the relevant band edges at the K/K valleys of the proximitized TMDCs, is employed to quantify the proximity-induced exchange. Upon twisting from 0 • to 30 • , we find a transition of the TMDC valence band (VB) edge exchange splitting from about −2 to 2 meV, while the conduction band (CB) edge exchange splitting remains nearly unchanged at around −3 meV. For the VB of WSe 2 (MoSe 2 ) on CrI 3 , the exchange coupling changes sign at around 8 • (16 • ). We find that even at the angles with almost zero spin splittings of the VB, the real-space spin polarization profile of holes at the band edge is highly nonuniform, with alternating spin up-and spin-down orbitals. Furthermore, a giant tunability of the proximity-induced exchange coupling is provided by a transverse electric field of a few V/nm. Within our first-principles framework, we are limited to commensurate structures, and thus considered a maximum strain of 2.2% for the individual monolayers. By investigating different atomic stacking configurations of the strained supercells, we demonstrate that proximity exchange varies locally in space within experimentally realistic setups. We complement our ab initio results by calculating the excitonic valley splitting to provide experimentally verifiable optical signatures of the proximity exchange. Specifically, we predict that the valley splitting increases almost linearly as a function of the twist angle. Furthermore, the proximity exchange is highly tunable by gating, allowing to tailor the valley splitting in the range of 0 to 12 meV in WSe 2 /CrI 3 , which is equivalent to external magnetic fields of up to about 60 T. Our results highlight the important impact of the twist angle and gating when employing magnetic vdW heterostructures in experimental geometries.

Proximity-induced exchange interaction and prolonged valley lifetime in MoSe2/CrSBr van-der-Waals heterostructure with orthogonal spin-orbit fields

“…5d,e by the indicated color code. One can see that the out-ofplane spin directions of ML-MoSe 2 at the K valleys are largely conserved in the heterobilayer, which was previously found also for other systems [53][54][55]. We find the valence-band edges of MoSe 2 for the two valleys K and K' (in our case folded towards P 3 and -P 3 ) about 37.4 meV and 43.6 meV above the Fermi level, resulting in a splitting of ∼ 6 meV (see Fig.…”

Proximity-enhanced valley Zeeman splitting at the WS2/graphene interface

“…These unexpected proximity effects in the conduction bands of TMDs are also present in other van der Waals heterostructures. For instance, in TMDs coupled to ferromagnetic materials [95][96][97][98][99], the proximity-induced exchange splitting is also quite complex and can be stronger in the conduction band depending on the particular geometry and stacking of the heterostructure.…”

Signatures of Electric Field and Layer Separation Effects on the Spin-Valley Physics of MoSe2/WSe2 Heterobilayers: From Energy Bands to Dipolar Excitons

“…Furthermore, the van der Waals nature of TMDC materials facilitates the vertical stacking and integration of different layers, the key ingredient driving the burgeoning research field of van der Waals heterostructures [ 15 , 16 , 17 , 18 ]. These novel heterostructures offer a fantastic playground in which to investigate the emergent physical phenomena and effects of proximity interaction, which is certainly not limited to TMDCs [ 19 , 20 , 21 , 22 ], but also encompasses other attractive materials, such as graphene [ 13 , 23 , 24 , 25 , 26 , 27 ], boron nitride [ 28 , 29 , 30 ], ferromagnetic CrX (X = I,Br) [ 31 , 32 , 33 , 34 , 35 ], and many others.…”