Inversion symmetry in bilayer graphene allows for layered opposite Rashba spin-orbit coupling (LO-RSOC) -- the situation when RSOC has same magnitude but sign two coupled spatially separated layers. We show that LO-RSOC results loss of spin chirality momentum space, contrast to common uniform RSOC. This makes it difficult experimentally establish whether (on scale 10 meV) exists, because band s...

Abstract Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that routinely generated. In applications constrained by memory intensity, excessively large datasets may hinder discovery, making reduction a critical component data-driven methods. Datasets growing two directions: number points their dimensionality. Whereas dimension typic...

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.