Cysne et al. Reply:

Abstract

The outline presented by Du in the Comment [1] on our Letter [2] partially agrees with the pictorial view we have used to explain the orbital-Hall effect (OHE) in transition metal dichalcogenide (TMD) bilayers. In fact, most of the phenomenological description of the OHE effect in the TMD bilayer that he brought up in the Comment [1] is discussed in the third section-Low energy calculations-of our Letter [2]. Notwithstanding, according to Du [1], the OHE that we have shown to occur in 2H-TMD bilayers should be termed the "hidden valley-Hall effect," and the Berry curvatures of the two valence bands as "hidden Berry curvatures." We do not believe that such terminology brings new insights to our Letter.

Orbital Hall effect in bilayer transition metal dichalcogenides: From the intra-atomic approximation to the Bloch states orbital magnetic moment approach

“…For any infinitesimally small but finite interlayer hopping t ⊥ , the states of individual layers combine to form the bonding and antibonding superpositions , as seen in Eq. ( 9) [75]. These states have no intrinsic magnetic moment, a consequence of the inversion symmetry of bilayer 2H-TMD [see Fig.…”

“…In addition, as anticipated in Ref. [75], the transport of magnetic moment in unbiased bilayer 2H-TMD cannot be understood in terms of the individual layers [74], being necessary to employ the scheme based on OHE introduced in Ref. [55] together with the non-Abelian structure of the magnetic moment matrix [Eqs.…”

Orbitronics: Orbital currents in solids

“…For this reason, Bhowal and Vignale proposed that the VHE is better described by the OHE [26]. However, for disentangling the OHE and the VHE, Cysne et al proposed to use TMD bilayers where the inversion symmetry is present, which eliminates the valley-dependent Berry curvature and eventually the VHE while keeping the OHE finite [21].…”

Enhanced spin–orbit torque and field-free switching in Au/TMDs/Ni hybrid structures

“…19,20 On the other hand, based on some theoretical studies, the enhancement of SOT efficiency may also result from an orbital current, which is from the interface between Au and TMDs. [21][22][23] The orbital current is injected into the TMD layer and converted into spin current by the strong SOC, and then the converted spin current decays across the TMD layer which results in unconventional torques on Ni and enhances the SOT efficiency. 24 This work might provide strong experimental evidence that the interface between TMDs and HM can generate orbital currents.…”

“…The combination of Au with large conductivity and 2D materials with large SOC strength makes the Au/2D material an ideal research object for SOT, because of the potential SOC proximity effect 19,20 and the orbital current. [21][22][23][24] Recent studies demonstrated that the PMA and SOT in FM/HM structures can be greatly enhanced by introducing a 2D transition metal dichalcogenide (TMD) underlayer. [25][26][27][28] More importantly, it is proved that the spin current transmission at the interface of a magnetic structure can be enhanced by inserting a 2D TMD spacer.…”