Two-dimensional square buckled Rashba lead chalcogenides

Abstract

We propose the lead sulphide (PbS) monolayer as a 2D semiconductor with a large Rashba-like spin-orbit effect controlled by the out-of-plane buckling. The buckled PbS conduction band is found to possess Rashba-like dispersion and spin texture at the M and Γ points, with large effective Rashba parameters of λ ∼ 5 eVÅ and λ ∼ 1 eVÅ, respectively. Using a tight-binding formalism, we show that the Rashba effect originates from the very large spin-orbit interaction and the hopping term that mixes the in-plane and out-of-plane p orbitals of Pb and S atoms. The latter, which depends on the buckling angle, can be controlled by applying strain to vary the spin texture as well as the Rashba parameter at Γ and M . Our density functional theory results together with tight-binding formalism provide a unifying framework for designing Rashba monolayers and for manipulating their spin properties.Introduction-Over the past two decades there has been a growing interest in materials with strong spin-orbit interaction (SOI), as they are of a profound importance for fundamental understanding of quantum phenomena at the atomic level and applications to spintronics. This relativistic interaction is linked to important effects such as Rashba, Zeeman, spin-Hall effect, and topological insulator (TI) states [1][2][3][4].

Strain-induced gauge and Rashba fields in ferroelectric Rashba lead chalcogenide PbX monolayers ( X=S , Se, Te)

“…The dimension of the total Hilbert space is 16 × 16 with new basis of |µ → |m |m orb |s , where m = {|A , |B } is the sublattice degree of freedom, m orb = {|0, 0 , |1, 1 , |1, −1 , |1, 0 } is the orbital angular momentum degree of freedom, and s = {(|+ , |− } is the spin degree of freedom. We found a Rashba-like dispersion near the Γ and M points when the two sublattices are not equivalent 8,17 . In this paper, we develop a continuum strain model de-scribing changes in the Rashba dispersion near the M point, and thus the Hamiltonian is expanded around the M point k = (π/a, π/a).…”

“…Our firstprinciples calculations show that the buckled phase of the PbX monolayer is more stable than the centrosymmetric planar phase 8 , consistent with other DFT studies 16,48 . Detailed discussions on the bistable nature, ferroelectric properties and orbital-spin texture properties of lead chalcogenides can be found in our previous paper 8 . In the current work, the deformations (atomic distortions) are applied to the optimized buckled structure.…”

“…The bands near the symmetry points can be described within the TB framework including first nearest neighbors and SOI. The full derivation of the TB model can be found in our previous works 8,17 , and thus we will only outline the important parts; a more detailed derivation can be found in Appendix C.…”

“…In this paper, we develop a continuum strain model de-scribing changes in the Rashba dispersion near the M point, and thus the Hamiltonian is expanded around the M point k = (π/a, π/a). Exactly at M [q = 0], the Hamiltonian decomposes into several uncoupled blocks and the wave function of the conduction band is given by |Ψ ± mn = c 0 |m ⊗ |1, ±1 ⊗ |∓ + c 1 |m ⊗ |1, 0 ⊗ |± ± ic 2 |n ⊗ |1, ∓1 ⊗ |∓ , with c 0 , c 1 , and c 2 being real numbers 8,17 . The Hamiltonian for the valance band can be obtained by interchanging m and n.…”

“…However, the spin-splitting is not large. In our previous work based on density functional theory (DFT) calculations, we found that lead chalcogenide monolayers PbX (X=S, Se, Te) have large Rashba coupling λ ∼ 1 eVÅ in their noncentrosymmetric buckled phase 8 . In addition, the spin texture can be switched in a non-volatile way by applying an electric field or mechanical strain, which puts these materials into the family of ferroelectric Rashba semiconductors (FERSCs) 9,10 .…”