Illuminating "spin-polarized" Bloch wave-function projection from degenerate bands in decomposable centrosymmetric lattices

Abstract

The combination of space inversion and time reversal symmetries results in doubly-degenerate Bloch states with opposite spin. Many lattices with these symmetries can be constructed by combining a noncentrosymmetric potential (lacking this degeneracy) with its inverted copy. Using simple models, we unravel the evolution of local spin-splitting during this process of inversion symmetry restoration, in the presence of spin-orbit interaction and sublattice coupling. Importantly, through an analysis of quantum mechanical commutativity, we examine the difficulty of identifying states that are simultaneously spatially segregated and spin polarized. We also explain how surface-sensitive experimental probes (such as angle-resolved photoemission spectroscopy, or ARPES) of 'hidden spin polarization' in layered materials are susceptible to unrelated spin splitting intrinsically induced by broken inversion symmetry at the surface.

Uncovering and tailoring hidden Rashba spin–orbit splitting in centrosymmetric crystals

“…The significant magnitude illustrated above of the ensuing α R for “R-1 from R-2” relative to the “R-1 from trivial” scenario highlights the fact that the R-1 spin splitting is inherited from the R-2 effect in bulk Rashba systems, i.e., from the local asymmetric dipole fields of the individual sectors. This finding obviates the concern of Li and Appelbaum 20 who suggested that the Rashba surface spin splitting detected experimentally (e.g., via ARPES) might originate from the unavoidable inversion symmetry-broken surface, as this contribution is indistinguishable from bulk R-2 effect.…”

“…One expects, in general, that any linear combination of two degenerate states should still be an eigenstate and prevent us from obtaining a unique DWS for the energy-degenerate bands. 20 However, we demonstrated in Supplementary Note 3 that, in R-2 compounds, the symmetry of the wavevectors along direction prohibits the mixing of two degenerate states arising from two inversion-partner sectors ( S α and S β ), respectively, as a result of the glide reflection symmetry, and hence dissociates any linear combinations of the degenerate states for tracing back to the symmetry-enforced segregated states. Santos-Cottin et al 10 had shown the localization of wavefunction in BaNiS 2 to provide the basis to decouple two effective Rashba Hamiltonians associated with each sector.…”

“…This resolves another criticism raised by ref. 20 about potential difficulties in hidden spin polarization detection, namely the attribution of spin splitting to surface effects rather than to the bulk. This work sheds light on the view of the recent debate around the physical meaning and relevance of the “hidden spin polarization” concept and for the strong experimental and theoretical activity around it, motivated by the possibility to device materials with remarkable spin textures and technologically relevant properties.…”

Unveiling giant hidden Rashba effects in two-dimensional Si2Bi2

“…Even though a few experimental observations have shown clear evidences for the existence of the R-2 effects, the following important questions still remain unanswered: (1) Why do some R-2 materials exhibit parabolic band structure rather than the Rashbalike dispersion? (2) How can the R-2 SLL effect be distinguished from unavoidable substrate effects in the experiments 19 ? (3) Why does the degree of spin segregation depend on the band index of an R-2 material?…”

Direct observation of hidden spin polarization in 2H−MoTe2

“…Whereas in the centrosymmetric TMDC structures, a new type of spin effect, i.e., the hidden spin polarization [5], also known as layer-locked hidden spin texture in layered materials [3], has been observed [4,[25][26][27][28]. Although it is well established that the optical properties of inversion symmetric TMDC systems [29][30][31] are qualitatively affected by their hidden spin texture, a concern that the observed hidden spin texture [4,[25][26][27][28] might be mainly induced by the broken inversion symmetry in experiments was raised recently [32]. Therefore it is critical to perform combined experimental and theoretical studies on centrosymmetric TMDC materials such as 2H-MoTe 2 to explore the mechanism of the hidden spin polarization [5].…”